From: tedu Date: Tue, 6 May 2014 03:56:27 +0000 (+0000) Subject: knf approximation X-Git-Url: http://artulab.com/gitweb/?a=commitdiff_plain;h=f67ac449e381bbe1cf66329c53bf11a08d401fab;p=openbsd knf approximation --- diff --git a/lib/libcrypto/ec/ec2_mult.c b/lib/libcrypto/ec/ec2_mult.c index 1c575dc47ad..040d7bb2782 100644 --- a/lib/libcrypto/ec/ec2_mult.c +++ b/lib/libcrypto/ec/ec2_mult.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -74,178 +74,215 @@ #ifndef OPENSSL_NO_EC2M -/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective +/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective * coordinates. - * Uses algorithm Mdouble in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Uses algorithm Mdouble in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * modified to not require precomputation of c=b^{2^{m-1}}. */ -static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) - { +static int +gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) +{ BIGNUM *t1; int ret = 0; - + /* Since Mdouble is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t1 = BN_CTX_get(ctx); - if (t1 == NULL) goto err; + if (t1 == NULL) + goto err; - if (!group->meth->field_sqr(group, x, x, ctx)) goto err; - if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; - if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; - if (!group->meth->field_sqr(group, x, x, ctx)) goto err; - if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; - if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; - if (!BN_GF2m_add(x, x, t1)) goto err; + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, z, ctx)) + goto err; + if (!group->meth->field_mul(group, z, x, t1, ctx)) + goto err; + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, t1, ctx)) + goto err; + if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) + goto err; + if (!BN_GF2m_add(x, x, t1)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} -/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery +/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery * projective coordinates. - * Uses algorithm Madd in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Uses algorithm Madd in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). */ -static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, - const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) - { +static int +gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, + const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) +{ BIGNUM *t1, *t2; int ret = 0; - + /* Since Madd is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t1 = BN_CTX_get(ctx); t2 = BN_CTX_get(ctx); - if (t2 == NULL) goto err; + if (t2 == NULL) + goto err; - if (!BN_copy(t1, x)) goto err; - if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; - if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; - if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; - if (!BN_GF2m_add(z1, z1, x1)) goto err; - if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; - if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; - if (!BN_GF2m_add(x1, x1, t2)) goto err; + if (!BN_copy(t1, x)) + goto err; + if (!group->meth->field_mul(group, x1, x1, z2, ctx)) + goto err; + if (!group->meth->field_mul(group, z1, z1, x2, ctx)) + goto err; + if (!group->meth->field_mul(group, t2, x1, z1, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_sqr(group, z1, z1, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z1, t1, ctx)) + goto err; + if (!BN_GF2m_add(x1, x1, t2)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} -/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) - * using Montgomery point multiplication algorithm Mxy() in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over +/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) + * using Montgomery point multiplication algorithm Mxy() in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * Returns: * 0 on error * 1 if return value should be the point at infinity * 2 otherwise */ -static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, - BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) - { +static int +gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, + BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) +{ BIGNUM *t3, *t4, *t5; int ret = 0; - - if (BN_is_zero(z1)) - { + + if (BN_is_zero(z1)) { BN_zero(x2); BN_zero(z2); return 1; - } - - if (BN_is_zero(z2)) - { - if (!BN_copy(x2, x)) return 0; - if (!BN_GF2m_add(z2, x, y)) return 0; + } + if (BN_is_zero(z2)) { + if (!BN_copy(x2, x)) + return 0; + if (!BN_GF2m_add(z2, x, y)) + return 0; return 2; - } - + } /* Since Mxy is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t3 = BN_CTX_get(ctx); t4 = BN_CTX_get(ctx); t5 = BN_CTX_get(ctx); - if (t5 == NULL) goto err; + if (t5 == NULL) + goto err; - if (!BN_one(t5)) goto err; + if (!BN_one(t5)) + goto err; - if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; + if (!group->meth->field_mul(group, t3, z1, z2, ctx)) + goto err; - if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; - if (!BN_GF2m_add(z1, z1, x1)) goto err; - if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; - if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; - if (!BN_GF2m_add(z2, z2, x2)) goto err; + if (!group->meth->field_mul(group, z1, z1, x, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_mul(group, z2, z2, x, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z2, x1, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, x2)) + goto err; - if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; - if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; - if (!BN_GF2m_add(t4, t4, y)) goto err; - if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; - if (!BN_GF2m_add(t4, t4, z2)) goto err; + if (!group->meth->field_mul(group, z2, z2, z1, ctx)) + goto err; + if (!group->meth->field_sqr(group, t4, x, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, y)) + goto err; + if (!group->meth->field_mul(group, t4, t4, t3, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, z2)) + goto err; - if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; - if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; - if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; - if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; - if (!BN_GF2m_add(z2, x2, x)) goto err; + if (!group->meth->field_mul(group, t3, t3, x, ctx)) + goto err; + if (!group->meth->field_div(group, t3, t5, t3, ctx)) + goto err; + if (!group->meth->field_mul(group, t4, t3, t4, ctx)) + goto err; + if (!group->meth->field_mul(group, x2, x1, t3, ctx)) + goto err; + if (!BN_GF2m_add(z2, x2, x)) + goto err; - if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; - if (!BN_GF2m_add(z2, z2, y)) goto err; + if (!group->meth->field_mul(group, z2, z2, t4, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, y)) + goto err; ret = 2; - err: +err: BN_CTX_end(ctx); return ret; - } +} /* Computes scalar*point and stores the result in r. * point can not equal r. * Uses a modified algorithm 2P of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * * To protect against side-channel attack the function uses constant time swap, * avoiding conditional branches. */ -static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - const EC_POINT *point, BN_CTX *ctx) - { +static int +ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) +{ BIGNUM *x1, *x2, *z1, *z2; int ret = 0, i; - BN_ULONG mask,word; + BN_ULONG mask, word; - if (r == point) - { + if (r == point) { ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); return 0; - } - + } /* if result should be point at infinity */ - if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || - EC_POINT_is_at_infinity(group, point)) - { + if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || + EC_POINT_is_at_infinity(group, point)) { return EC_POINT_set_to_infinity(group, r); - } - + } /* only support affine coordinates */ - if (!point->Z_is_one) return 0; + if (!point->Z_is_one) + return 0; /* Since point_multiply is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); x1 = BN_CTX_get(ctx); z1 = BN_CTX_get(ctx); - if (z1 == NULL) goto err; + if (z1 == NULL) + goto err; x2 = &r->X; z2 = &r->Y; @@ -255,53 +292,57 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, bn_wexpand(x2, group->field.top); bn_wexpand(z2, group->field.top); - if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ - if (!BN_one(z1)) goto err; /* z1 = 1 */ - if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ - if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ + if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) + goto err; /* x1 = x */ + if (!BN_one(z1)) + goto err; /* z1 = 1 */ + if (!group->meth->field_sqr(group, z2, x1, ctx)) + goto err; /* z2 = x1^2 = x^2 */ + if (!group->meth->field_sqr(group, x2, z2, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->b)) + goto err; /* x2 = x^4 + b */ /* find top most bit and go one past it */ i = scalar->top - 1; mask = BN_TBIT; word = scalar->d[i]; - while (!(word & mask)) mask >>= 1; + while (!(word & mask)) + mask >>= 1; mask >>= 1; /* if top most bit was at word break, go to next word */ - if (!mask) - { + if (!mask) { i--; mask = BN_TBIT; - } - - for (; i >= 0; i--) - { + } + for (; i >= 0; i--) { word = scalar->d[i]; - while (mask) - { + while (mask) { BN_consttime_swap(word & mask, x1, x2, group->field.top); BN_consttime_swap(word & mask, z1, z2, group->field.top); - if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; - if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; + if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) + goto err; + if (!gf2m_Mdouble(group, x1, z1, ctx)) + goto err; BN_consttime_swap(word & mask, x1, x2, group->field.top); BN_consttime_swap(word & mask, z1, z2, group->field.top); mask >>= 1; - } - mask = BN_TBIT; } + mask = BN_TBIT; + } /* convert out of "projective" coordinates */ i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); - if (i == 0) goto err; - else if (i == 1) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; - } - else - { - if (!BN_one(&r->Z)) goto err; + if (i == 0) + goto err; + else if (i == 1) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { + if (!BN_one(&r->Z)) + goto err; r->Z_is_one = 1; - } + } /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ BN_set_negative(&r->X, 0); @@ -309,87 +350,98 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} /* Computes the sum * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] * gracefully ignoring NULL scalar values. */ -int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; size_t i; - EC_POINT *p=NULL; + EC_POINT *p = NULL; EC_POINT *acc = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - - /* This implementation is more efficient than the wNAF implementation for 2 - * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, - * or if we can perform a fast multiplication based on precomputation. + } + /* + * This implementation is more efficient than the wNAF implementation + * for 2 or fewer points. Use the ec_wNAF_mul implementation for 3 + * or more points, or if we can perform a fast multiplication based + * on precomputation. */ - if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) - { + if ((scalar && (num > 1)) || (num > 2) || + (num == 0 && EC_GROUP_have_precompute_mult(group))) { ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); goto err; - } - - if ((p = EC_POINT_new(group)) == NULL) goto err; - if ((acc = EC_POINT_new(group)) == NULL) goto err; + } + if ((p = EC_POINT_new(group)) == NULL) + goto err; + if ((acc = EC_POINT_new(group)) == NULL) + goto err; - if (!EC_POINT_set_to_infinity(group, acc)) goto err; + if (!EC_POINT_set_to_infinity(group, acc)) + goto err; - if (scalar) - { - if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; + if (scalar) { + if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) + goto err; if (BN_is_negative(scalar)) - if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, acc, acc, p, ctx)) goto err; - } - - for (i = 0; i < num; i++) - { - if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } + for (i = 0; i < num; i++) { + if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) + goto err; if (BN_is_negative(scalars[i])) - if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, acc, acc, p, ctx)) goto err; - } + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } - if (!EC_POINT_copy(r, acc)) goto err; + if (!EC_POINT_copy(r, acc)) + goto err; ret = 1; - err: - if (p) EC_POINT_free(p); - if (acc) EC_POINT_free(acc); +err: + if (p) + EC_POINT_free(p); + if (acc) + EC_POINT_free(acc); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Precomputation for point multiplication: fall back to wNAF methods * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ -int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ return ec_wNAF_precompute_mult(group, ctx); - } +} -int ec_GF2m_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GF2m_have_precompute_mult(const EC_GROUP * group) +{ return ec_wNAF_have_precompute_mult(group); - } +} #endif diff --git a/lib/libcrypto/ec/ec2_oct.c b/lib/libcrypto/ec/ec2_oct.c index f1d75e5ddf6..a856a5b1a7b 100644 --- a/lib/libcrypto/ec/ec2_oct.c +++ b/lib/libcrypto/ec/ec2_oct.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -74,11 +74,11 @@ #ifndef OPENSSL_NO_EC2M /* Calculates and sets the affine coordinates of an EC_POINT from the given - * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. + * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. * Note that the simple implementation only uses affine coordinates. * * The method is from the following publication: - * + * * Harper, Menezes, Vanstone: * "Public-Key Cryptosystems with Very Small Key Lengths", * EUROCRYPT '92, Springer-Verlag LNCS 658, @@ -88,9 +88,10 @@ * the same method, but claim no priority date earlier than July 29, 1994 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). */ -int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { +int +ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp, *x, *y, *z; int ret = 0, z0; @@ -98,13 +99,11 @@ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p /* clear error queue */ ERR_clear_error(); - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } y_bit = (y_bit != 0) ? 1 : 0; BN_CTX_start(ctx); @@ -112,59 +111,65 @@ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); z = BN_CTX_get(ctx); - if (z == NULL) goto err; + if (z == NULL) + goto err; - if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; - if (BN_is_zero(x)) - { - if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; - } - else - { - if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; - if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; - if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; - if (!BN_GF2m_add(tmp, x, tmp)) goto err; - if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) - { + if (!BN_GF2m_mod_arr(x, x_, group->poly)) + goto err; + if (BN_is_zero(x)) { + if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) + goto err; + } else { + if (!group->meth->field_sqr(group, tmp, x, ctx)) + goto err; + if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) + goto err; + if (!BN_GF2m_add(tmp, &group->a, tmp)) + goto err; + if (!BN_GF2m_add(tmp, x, tmp)) + goto err; + if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) { unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) - { + + if (ERR_GET_LIB(err) == ERR_LIB_BN && + ERR_GET_REASON(err) == BN_R_NO_SOLUTION) { ERR_clear_error(); ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else + } else ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); goto err; - } + } z0 = (BN_is_odd(z)) ? 1 : 0; - if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; - if (z0 != y_bit) - { - if (!BN_GF2m_add(y, y, x)) goto err; - } + if (!group->meth->field_mul(group, y, x, z, ctx)) + goto err; + if (z0 != y_bit) { + if (!BN_GF2m_add(y, y, x)) + goto err; } + } - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -/* Converts an EC_POINT to an octet string. +/* Converts an EC_POINT to an octet string. * If buf is NULL, the encoded length will be returned. * If the length len of buf is smaller than required an error will be returned. */ -size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX * ctx) +{ size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; @@ -172,131 +177,114 @@ size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, po size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { + } + if (EC_POINT_is_at_infinity(group, point)) { /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { + if (buf != NULL) { + if (len < 1) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); return 0; - } - buf[0] = 0; } - return 1; + buf[0] = 0; } - - + return 1; + } /* ret := required output buffer length */ field_len = (EC_GROUP_get_degree(group) + 7) / 8; - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : + 1 + 2 * field_len; /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { + if (buf != NULL) { + if (len < ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); used_ctx = 1; x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; + if (yxi == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; buf[0] = form; - if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (BN_is_odd(yxi)) buf[0]++; - } - + if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (BN_is_odd(yxi)) + buf[0]++; + } i = 1; - + skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(x, buf + i); i += skip; - if (i != 1 + field_len) - { + if (i != 1 + field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { + } + if (form == POINT_CONVERSION_UNCOMPRESSED || + form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(y, buf + i); i += skip; - } - - if (i != ret) - { + } + if (i != ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } } - + } if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - err: +err: if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return 0; - } +} -/* Converts an octet string representation to an EC_POINT. +/* Converts an octet string representation to an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { +int +ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; @@ -304,104 +292,89 @@ int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, size_t field_len, enc_len; int ret = 0; - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); return 0; - } + } form = buf[0]; y_bit = form & 1; form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) && + (form != POINT_CONVERSION_UNCOMPRESSED) && + (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (form == 0) - { - if (len != 1) - { + } + if (form == 0) { + if (len != 1) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - return EC_POINT_set_to_infinity(group, point); } - + return EC_POINT_set_to_infinity(group, point); + } field_len = (EC_GROUP_get_degree(group) + 7) / 8; - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : + 1 + 2 * field_len; - if (len != enc_len) - { + if (len != enc_len) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; + if (yxi == NULL) + goto err; - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { + } + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (y_bit != BN_is_odd(yxi)) - { + } + if (form == POINT_CONVERSION_HYBRID) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (y_bit != BN_is_odd(yxi)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) { + /* test required by X9.62 */ ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} #endif diff --git a/lib/libcrypto/ec/ec2_smpl.c b/lib/libcrypto/ec/ec2_smpl.c index 5682bfab377..71bacf71dd9 100644 --- a/lib/libcrypto/ec/ec2_smpl.c +++ b/lib/libcrypto/ec/ec2_smpl.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -87,16 +87,16 @@ EC_GF2m_simple_method(void) .group_get_curve = ec_GF2m_simple_group_get_curve, .group_get_degree = ec_GF2m_simple_group_get_degree, .group_check_discriminant = - ec_GF2m_simple_group_check_discriminant, + ec_GF2m_simple_group_check_discriminant, .point_init = ec_GF2m_simple_point_init, .point_finish = ec_GF2m_simple_point_finish, .point_clear_finish = ec_GF2m_simple_point_clear_finish, .point_copy = ec_GF2m_simple_point_copy, .point_set_to_infinity = ec_GF2m_simple_point_set_to_infinity, .point_set_affine_coordinates = - ec_GF2m_simple_point_set_affine_coordinates, + ec_GF2m_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GF2m_simple_point_get_affine_coordinates, + ec_GF2m_simple_point_get_affine_coordinates, .add = ec_GF2m_simple_add, .dbl = ec_GF2m_simple_dbl, .invert = ec_GF2m_simple_invert, @@ -106,7 +106,10 @@ EC_GF2m_simple_method(void) .make_affine = ec_GF2m_simple_make_affine, .points_make_affine = ec_GF2m_simple_points_make_affine, - /* the following three method functions are defined in ec2_mult.c */ + /* + * the following three method functions are defined in + * ec2_mult.c + */ .mul = ec_GF2m_simple_mul, .precompute_mult = ec_GF2m_precompute_mult, .have_precompute_mult = ec_GF2m_have_precompute_mult, @@ -123,31 +126,34 @@ EC_GF2m_simple_method(void) /* Initialize a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_new. */ -int ec_GF2m_simple_group_init(EC_GROUP *group) - { +int +ec_GF2m_simple_group_init(EC_GROUP * group) +{ BN_init(&group->field); BN_init(&group->a); BN_init(&group->b); return 1; - } +} /* Free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_free. */ -void ec_GF2m_simple_group_finish(EC_GROUP *group) - { +void +ec_GF2m_simple_group_finish(EC_GROUP * group) +{ BN_free(&group->field); BN_free(&group->a); BN_free(&group->b); - } +} /* Clear and free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_clear_free. */ -void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) - { +void +ec_GF2m_simple_group_clear_finish(EC_GROUP * group) +{ BN_clear_free(&group->field); BN_clear_free(&group->a); BN_clear_free(&group->b); @@ -157,127 +163,145 @@ void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) group->poly[3] = 0; group->poly[4] = 0; group->poly[5] = -1; - } +} /* Copy a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_copy. */ -int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +ec_GF2m_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ int i; - if (!BN_copy(&dest->field, &src->field)) return 0; - if (!BN_copy(&dest->a, &src->a)) return 0; - if (!BN_copy(&dest->b, &src->b)) return 0; + + if (!BN_copy(&dest->field, &src->field)) + return 0; + if (!BN_copy(&dest->a, &src->a)) + return 0; + if (!BN_copy(&dest->b, &src->b)) + return 0; dest->poly[0] = src->poly[0]; dest->poly[1] = src->poly[1]; dest->poly[2] = src->poly[2]; dest->poly[3] = src->poly[3]; dest->poly[4] = src->poly[4]; dest->poly[5] = src->poly[5]; - if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; - if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; - for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; - for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; + if (bn_wexpand(&dest->a, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + return 0; + if (bn_wexpand(&dest->b, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + return 0; + for (i = dest->a.top; i < dest->a.dmax; i++) + dest->a.d[i] = 0; + for (i = dest->b.top; i < dest->b.dmax; i++) + dest->b.d[i] = 0; return 1; - } +} /* Set the curve parameters of an EC_GROUP structure. */ -int ec_GF2m_simple_group_set_curve(EC_GROUP *group, - const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_set_curve(EC_GROUP * group, + const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0, i; /* group->field */ - if (!BN_copy(&group->field, p)) goto err; + if (!BN_copy(&group->field, p)) + goto err; i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; - if ((i != 5) && (i != 3)) - { + if ((i != 5) && (i != 3)) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); goto err; - } - + } /* group->a */ - if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; - if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; - for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; - + if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) + goto err; + if (bn_wexpand(&group->a, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + goto err; + for (i = group->a.top; i < group->a.dmax; i++) + group->a.d[i] = 0; + /* group->b */ - if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; - if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; - for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; - + if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) + goto err; + if (bn_wexpand(&group->b, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + goto err; + for (i = group->b.top; i < group->b.dmax; i++) + group->b.d[i] = 0; + ret = 1; - err: +err: return ret; - } +} /* Get the curve parameters of an EC_GROUP structure. * If p, a, or b are NULL then there values will not be set but the method will return with success. */ -int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_get_curve(const EC_GROUP *group, + BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) +{ int ret = 0; - - if (p != NULL) - { - if (!BN_copy(p, &group->field)) return 0; - } - if (a != NULL) - { - if (!BN_copy(a, &group->a)) goto err; - } - - if (b != NULL) - { - if (!BN_copy(b, &group->b)) goto err; - } - + if (p != NULL) { + if (!BN_copy(p, &group->field)) + return 0; + } + if (a != NULL) { + if (!BN_copy(a, &group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, &group->b)) + goto err; + } ret = 1; - - err: + +err: return ret; - } +} /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ -int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) - { - return BN_num_bits(&group->field)-1; - } +int +ec_GF2m_simple_group_get_degree(const EC_GROUP * group) +{ + return BN_num_bits(&group->field) - 1; +} /* Checks the discriminant of the curve. - * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) + * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) */ -int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; BIGNUM *b; BN_CTX *new_ctx = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); b = BN_CTX_get(ctx); - if (b == NULL) goto err; + if (b == NULL) + goto err; + + if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) + goto err; - if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; - - /* check the discriminant: - * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) + /* + * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic + * curve <=> b != 0 (mod p) */ - if (BN_is_zero(b)) goto err; + if (BN_is_zero(b)) + goto err; ret = 1; @@ -287,151 +311,157 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Initializes an EC_POINT. */ -int ec_GF2m_simple_point_init(EC_POINT *point) - { +int +ec_GF2m_simple_point_init(EC_POINT * point) +{ BN_init(&point->X); BN_init(&point->Y); BN_init(&point->Z); return 1; - } +} /* Frees an EC_POINT. */ -void ec_GF2m_simple_point_finish(EC_POINT *point) - { +void +ec_GF2m_simple_point_finish(EC_POINT * point) +{ BN_free(&point->X); BN_free(&point->Y); BN_free(&point->Z); - } +} /* Clears and frees an EC_POINT. */ -void ec_GF2m_simple_point_clear_finish(EC_POINT *point) - { +void +ec_GF2m_simple_point_clear_finish(EC_POINT * point) +{ BN_clear_free(&point->X); BN_clear_free(&point->Y); BN_clear_free(&point->Z); point->Z_is_one = 0; - } +} /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ -int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) - { - if (!BN_copy(&dest->X, &src->X)) return 0; - if (!BN_copy(&dest->Y, &src->Y)) return 0; - if (!BN_copy(&dest->Z, &src->Z)) return 0; +int +ec_GF2m_simple_point_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (!BN_copy(&dest->X, &src->X)) + return 0; + if (!BN_copy(&dest->Y, &src->Y)) + return 0; + if (!BN_copy(&dest->Z, &src->Z)) + return 0; dest->Z_is_one = src->Z_is_one; return 1; - } +} -/* Set an EC_POINT to the point at infinity. +/* Set an EC_POINT to the point at infinity. * A point at infinity is represented by having Z=0. */ -int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { +int +ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ point->Z_is_one = 0; BN_zero(&point->Z); return 1; - } +} -/* Set the coordinates of an EC_POINT using affine coordinates. +/* Set the coordinates of an EC_POINT using affine coordinates. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - int ret = 0; - if (x == NULL || y == NULL) - { +int +ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) +{ + int ret = 0; + if (x == NULL || y == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if (!BN_copy(&point->X, x)) goto err; + } + if (!BN_copy(&point->X, x)) + goto err; BN_set_negative(&point->X, 0); - if (!BN_copy(&point->Y, y)) goto err; + if (!BN_copy(&point->Y, y)) + goto err; BN_set_negative(&point->Y, 0); - if (!BN_copy(&point->Z, BN_value_one())) goto err; + if (!BN_copy(&point->Z, BN_value_one())) + goto err; BN_set_negative(&point->Z, 0); point->Z_is_one = 1; ret = 1; - err: +err: return ret; - } +} -/* Gets the affine coordinates of an EC_POINT. +/* Gets the affine coordinates of an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ int ret = 0; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; - } - - if (BN_cmp(&point->Z, BN_value_one())) - { + } + if (BN_cmp(&point->Z, BN_value_one())) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; + } + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; BN_set_negative(x, 0); - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; BN_set_negative(y, 0); - } + } ret = 1; - - err: + +err: return ret; - } +} /* Computes a + b and stores the result in r. r could be a or b, a could be b. * Uses algorithm A.10.2 of IEEE P1363. */ -int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; int ret = 0; - - if (EC_POINT_is_at_infinity(group, a)) - { - if (!EC_POINT_copy(r, b)) return 0; - return 1; - } - if (EC_POINT_is_at_infinity(group, b)) - { - if (!EC_POINT_copy(r, a)) return 0; + if (EC_POINT_is_at_infinity(group, a)) { + if (!EC_POINT_copy(r, b)) + return 0; return 1; - } - - if (ctx == NULL) - { + } + if (EC_POINT_is_at_infinity(group, b)) { + if (!EC_POINT_copy(r, a)) + return 0; + return 1; + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x0 = BN_CTX_get(ctx); y0 = BN_CTX_get(ctx); @@ -441,149 +471,178 @@ int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, co y2 = BN_CTX_get(ctx); s = BN_CTX_get(ctx); t = BN_CTX_get(ctx); - if (t == NULL) goto err; + if (t == NULL) + goto err; - if (a->Z_is_one) - { - if (!BN_copy(x0, &a->X)) goto err; - if (!BN_copy(y0, &a->Y)) goto err; - } - else - { - if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; - } - if (b->Z_is_one) - { - if (!BN_copy(x1, &b->X)) goto err; - if (!BN_copy(y1, &b->Y)) goto err; - } - else - { - if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; - } + if (a->Z_is_one) { + if (!BN_copy(x0, &a->X)) + goto err; + if (!BN_copy(y0, &a->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) + goto err; + } + if (b->Z_is_one) { + if (!BN_copy(x1, &b->X)) + goto err; + if (!BN_copy(y1, &b->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) + goto err; + } - if (BN_GF2m_cmp(x0, x1)) - { - if (!BN_GF2m_add(t, x0, x1)) goto err; - if (!BN_GF2m_add(s, y0, y1)) goto err; - if (!group->meth->field_div(group, s, s, t, ctx)) goto err; - if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, &group->a)) goto err; - if (!BN_GF2m_add(x2, x2, s)) goto err; - if (!BN_GF2m_add(x2, x2, t)) goto err; - } - else - { - if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; + if (BN_GF2m_cmp(x0, x1)) { + if (!BN_GF2m_add(t, x0, x1)) + goto err; + if (!BN_GF2m_add(s, y0, y1)) + goto err; + if (!group->meth->field_div(group, s, s, t, ctx)) + goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->a)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, t)) + goto err; + } else { + if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; ret = 1; goto err; - } - if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; - if (!BN_GF2m_add(s, s, x1)) goto err; - - if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, s)) goto err; - if (!BN_GF2m_add(x2, x2, &group->a)) goto err; } + if (!group->meth->field_div(group, s, y1, x1, ctx)) + goto err; + if (!BN_GF2m_add(s, s, x1)) + goto err; - if (!BN_GF2m_add(y2, x1, x2)) goto err; - if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; - if (!BN_GF2m_add(y2, y2, x2)) goto err; - if (!BN_GF2m_add(y2, y2, y1)) goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->a)) + goto err; + } - if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; + if (!BN_GF2m_add(y2, x1, x2)) + goto err; + if (!group->meth->field_mul(group, y2, y2, s, ctx)) + goto err; + if (!BN_GF2m_add(y2, y2, x2)) + goto err; + if (!BN_GF2m_add(y2, y2, y1)) + goto err; + + if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Computes 2 * a and stores the result in r. r could be a. * Uses algorithm A.10.2 of IEEE P1363. */ -int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { +int +ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ return ec_GF2m_simple_add(group, r, a, a, ctx); - } - +} -int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) /* point is its own inverse */ return 1; - - if (!EC_POINT_make_affine(group, point, ctx)) return 0; + + if (!EC_POINT_make_affine(group, point, ctx)) + return 0; return BN_GF2m_add(&point->Y, &point->X, &point->Y); - } +} /* Indicates whether the given point is the point at infinity. */ -int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { +int +ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ return BN_is_zero(&point->Z); - } +} /* Determines whether the given EC_POINT is an actual point on the curve defined * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: * y^2 + x*y = x^3 + a*x^2 + b. */ -int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) +{ int ret = -1; BN_CTX *new_ctx = NULL; BIGNUM *lh, *y2; - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); if (EC_POINT_is_at_infinity(group, point)) return 1; field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; + field_sqr = group->meth->field_sqr; /* only support affine coordinates */ - if (!point->Z_is_one) return -1; + if (!point->Z_is_one) + return -1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); y2 = BN_CTX_get(ctx); lh = BN_CTX_get(ctx); - if (lh == NULL) goto err; + if (lh == NULL) + goto err; - /* We have a curve defined by a Weierstrass equation - * y^2 + x*y = x^3 + a*x^2 + b. - * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 - * <=> ((x + a) * x + y ) * x + b + y^2 = 0 + /* + * We have a curve defined by a Weierstrass equation y^2 + x*y = x^3 + * + a*x^2 + b. <=> x^3 + a*x^2 + x*y + b + y^2 = 0 <=> ((x + a) * x + * + y ) * x + b + y^2 = 0 */ - if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; - if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; - if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, &group->b)) goto err; - if (!field_sqr(group, y2, &point->Y, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, y2)) goto err; + if (!BN_GF2m_add(lh, &point->X, &group->a)) + goto err; + if (!field_mul(group, lh, lh, &point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, &point->Y)) + goto err; + if (!field_mul(group, lh, lh, &point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, &group->b)) + goto err; + if (!field_sqr(group, y2, &point->Y, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, y2)) + goto err; ret = BN_is_zero(lh); - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Indicates whether two points are equal. @@ -592,118 +651,132 @@ int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_ * 0 equal (in affine coordinates) * 1 not equal */ -int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ BIGNUM *aX, *aY, *bX, *bY; BN_CTX *new_ctx = NULL; int ret = -1; - if (EC_POINT_is_at_infinity(group, a)) - { + if (EC_POINT_is_at_infinity(group, a)) { return EC_POINT_is_at_infinity(group, b) ? 0 : 1; - } - + } if (EC_POINT_is_at_infinity(group, b)) return 1; - - if (a->Z_is_one && b->Z_is_one) - { - return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; - } - if (ctx == NULL) - { + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); aX = BN_CTX_get(ctx); aY = BN_CTX_get(ctx); bX = BN_CTX_get(ctx); bY = BN_CTX_get(ctx); - if (bY == NULL) goto err; + if (bY == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) + goto err; ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Forces the given EC_POINT to internally use affine coordinates. */ -int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; - - if (ctx == NULL) - { + + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - if (!BN_copy(&point->X, x)) goto err; - if (!BN_copy(&point->Y, y)) goto err; - if (!BN_one(&point->Z)) goto err; - - ret = 1; - - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + if (!BN_copy(&point->X, x)) + goto err; + if (!BN_copy(&point->Y, y)) + goto err; + if (!BN_one(&point->Z)) + goto err; + + ret = 1; + +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ -int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ size_t i; - for (i = 0; i < num; i++) - { - if (!group->meth->make_affine(group, points[i], ctx)) return 0; - } + for (i = 0; i < num; i++) { + if (!group->meth->make_affine(group, points[i], ctx)) + return 0; + } return 1; - } +} /* Wrapper to simple binary polynomial field multiplication implementation. */ -int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); - } +} /* Wrapper to simple binary polynomial field squaring implementation. */ -int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); - } +} /* Wrapper to simple binary polynomial field division implementation. */ -int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ return BN_GF2m_mod_div(r, a, b, &group->field, ctx); - } +} #endif diff --git a/lib/libcrypto/ec/ec_ameth.c b/lib/libcrypto/ec/ec_ameth.c index 0e6381f5439..9b52c3cbfc8 100644 --- a/lib/libcrypto/ec/ec_ameth.c +++ b/lib/libcrypto/ec/ec_ameth.c @@ -9,7 +9,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -65,54 +65,51 @@ #endif #include "asn1_locl.h" -static int eckey_param2type(int *pptype, void **ppval, EC_KEY *ec_key) - { - const EC_GROUP *group; +static int +eckey_param2type(int *pptype, void **ppval, EC_KEY * ec_key) +{ + const EC_GROUP *group; int nid; - if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) - { + if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) { ECerr(EC_F_ECKEY_PARAM2TYPE, EC_R_MISSING_PARAMETERS); return 0; } - if (EC_GROUP_get_asn1_flag(group) - && (nid = EC_GROUP_get_curve_name(group))) + if (EC_GROUP_get_asn1_flag(group) && + (nid = EC_GROUP_get_curve_name(group))) { /* we have a 'named curve' => just set the OID */ - { *ppval = OBJ_nid2obj(nid); *pptype = V_ASN1_OBJECT; - } - else /* explicit parameters */ - { + } else { + /* explicit parameters */ ASN1_STRING *pstr = NULL; pstr = ASN1_STRING_new(); if (!pstr) return 0; pstr->length = i2d_ECParameters(ec_key, &pstr->data); - if (pstr->length <= 0) - { + if (pstr->length <= 0) { ASN1_STRING_free(pstr); ECerr(EC_F_ECKEY_PARAM2TYPE, ERR_R_EC_LIB); return 0; - } + } *ppval = pstr; *pptype = V_ASN1_SEQUENCE; - } - return 1; } + return 1; +} -static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) - { +static int +eckey_pub_encode(X509_PUBKEY * pk, const EVP_PKEY * pkey) +{ EC_KEY *ec_key = pkey->pkey.ec; void *pval = NULL; int ptype; unsigned char *penc = NULL, *p; int penclen; - if (!eckey_param2type(&ptype, &pval, ec_key)) - { + if (!eckey_param2type(&ptype, &pval, ec_key)) { ECerr(EC_F_ECKEY_PUB_ENCODE, ERR_R_EC_LIB); return 0; - } + } penclen = i2o_ECPublicKey(ec_key, NULL); if (penclen <= 0) goto err; @@ -124,9 +121,9 @@ static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) if (penclen <= 0) goto err; if (X509_PUBKEY_set0_param(pk, OBJ_nid2obj(EVP_PKEY_EC), - ptype, pval, penc, penclen)) + ptype, pval, penc, penclen)) return 1; - err: +err: if (ptype == V_ASN1_OBJECT) ASN1_OBJECT_free(pval); else @@ -134,37 +131,36 @@ static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) if (penc) free(penc); return 0; - } +} -static EC_KEY *eckey_type2param(int ptype, void *pval) - { +static EC_KEY * +eckey_type2param(int ptype, void *pval) +{ EC_KEY *eckey = NULL; - if (ptype == V_ASN1_SEQUENCE) - { + + if (ptype == V_ASN1_SEQUENCE) { ASN1_STRING *pstr = pval; const unsigned char *pm = NULL; int pmlen; + pm = pstr->data; pmlen = pstr->length; - if (!(eckey = d2i_ECParameters(NULL, &pm, pmlen))) - { + if (!(eckey = d2i_ECParameters(NULL, &pm, pmlen))) { ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); goto ecerr; - } } - else if (ptype == V_ASN1_OBJECT) - { + } else if (ptype == V_ASN1_OBJECT) { ASN1_OBJECT *poid = pval; EC_GROUP *group; - /* type == V_ASN1_OBJECT => the parameters are given - * by an asn1 OID + /* + * type == V_ASN1_OBJECT => the parameters are given by an + * asn1 OID */ - if ((eckey = EC_KEY_new()) == NULL) - { + if ((eckey = EC_KEY_new()) == NULL) { ECerr(EC_F_ECKEY_TYPE2PARAM, ERR_R_MALLOC_FAILURE); goto ecerr; - } + } group = EC_GROUP_new_by_curve_name(OBJ_obj2nid(poid)); if (group == NULL) goto ecerr; @@ -172,23 +168,22 @@ static EC_KEY *eckey_type2param(int ptype, void *pval) if (EC_KEY_set_group(eckey, group) == 0) goto ecerr; EC_GROUP_free(group); - } - else - { + } else { ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); goto ecerr; - } + } return eckey; - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return NULL; - } +} -static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) - { +static int +eckey_pub_decode(EVP_PKEY * pkey, X509_PUBKEY * pubkey) +{ const unsigned char *p = NULL; void *pval; int ptype, pklen; @@ -201,44 +196,42 @@ static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) eckey = eckey_type2param(ptype, pval); - if (!eckey) - { + if (!eckey) { ECerr(EC_F_ECKEY_PUB_DECODE, ERR_R_EC_LIB); return 0; - } - + } /* We have parameters now set public key */ - if (!o2i_ECPublicKey(&eckey, &p, pklen)) - { + if (!o2i_ECPublicKey(&eckey, &p, pklen)) { ECerr(EC_F_ECKEY_PUB_DECODE, EC_R_DECODE_ERROR); goto ecerr; - } - + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return 0; - } +} -static int eckey_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b) - { - int r; +static int +eckey_pub_cmp(const EVP_PKEY * a, const EVP_PKEY * b) +{ + int r; const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec); - const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), - *pb = EC_KEY_get0_public_key(b->pkey.ec); + const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), *pb = EC_KEY_get0_public_key(b->pkey.ec); + r = EC_POINT_cmp(group, pa, pb, NULL); if (r == 0) return 1; if (r == 1) return 0; return -2; - } +} -static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8) - { +static int +eckey_priv_decode(EVP_PKEY * pkey, PKCS8_PRIV_KEY_INFO * p8) +{ const unsigned char *p = NULL; void *pval; int ptype, pklen; @@ -255,100 +248,92 @@ static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8) goto ecliberr; /* We have parameters now set private key */ - if (!d2i_ECPrivateKey(&eckey, &p, pklen)) - { + if (!d2i_ECPrivateKey(&eckey, &p, pklen)) { ECerr(EC_F_ECKEY_PRIV_DECODE, EC_R_DECODE_ERROR); goto ecerr; - } - + } /* calculate public key (if necessary) */ - if (EC_KEY_get0_public_key(eckey) == NULL) - { + if (EC_KEY_get0_public_key(eckey) == NULL) { const BIGNUM *priv_key; const EC_GROUP *group; EC_POINT *pub_key; - /* the public key was not included in the SEC1 private - * key => calculate the public key */ - group = EC_KEY_get0_group(eckey); + /* + * the public key was not included in the SEC1 private key => + * calculate the public key + */ + group = EC_KEY_get0_group(eckey); pub_key = EC_POINT_new(group); - if (pub_key == NULL) - { + if (pub_key == NULL) { ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group))) - { + } + if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group))) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } + } priv_key = EC_KEY_get0_private_key(eckey); - if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL)) - { + if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL)) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - if (EC_KEY_set_public_key(eckey, pub_key) == 0) - { + } + if (EC_KEY_set_public_key(eckey, pub_key) == 0) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - EC_POINT_free(pub_key); } - + EC_POINT_free(pub_key); + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - ecliberr: +ecliberr: ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return 0; - } +} -static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) +static int +eckey_priv_encode(PKCS8_PRIV_KEY_INFO * p8, const EVP_PKEY * pkey) { - EC_KEY *ec_key; - unsigned char *ep, *p; - int eplen, ptype; - void *pval; - unsigned int tmp_flags, old_flags; + EC_KEY *ec_key; + unsigned char *ep, *p; + int eplen, ptype; + void *pval; + unsigned int tmp_flags, old_flags; ec_key = pkey->pkey.ec; - if (!eckey_param2type(&ptype, &pval, ec_key)) - { + if (!eckey_param2type(&ptype, &pval, ec_key)) { ECerr(EC_F_ECKEY_PRIV_ENCODE, EC_R_DECODE_ERROR); return 0; - } - + } /* set the private key */ - /* do not include the parameters in the SEC1 private key - * see PKCS#11 12.11 */ + /* + * do not include the parameters in the SEC1 private key see PKCS#11 + * 12.11 + */ old_flags = EC_KEY_get_enc_flags(ec_key); tmp_flags = old_flags | EC_PKEY_NO_PARAMETERS; EC_KEY_set_enc_flags(ec_key, tmp_flags); eplen = i2d_ECPrivateKey(ec_key, NULL); - if (!eplen) - { + if (!eplen) { EC_KEY_set_enc_flags(ec_key, old_flags); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); return 0; } ep = (unsigned char *) malloc(eplen); - if (!ep) - { + if (!ep) { EC_KEY_set_enc_flags(ec_key, old_flags); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); return 0; } p = ep; - if (!i2d_ECPrivateKey(ec_key, &p)) - { + if (!i2d_ECPrivateKey(ec_key, &p)) { EC_KEY_set_enc_flags(ec_key, old_flags); free(ep); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); @@ -358,49 +343,50 @@ static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) EC_KEY_set_enc_flags(ec_key, old_flags); if (!PKCS8_pkey_set0(p8, OBJ_nid2obj(NID_X9_62_id_ecPublicKey), 0, - ptype, pval, ep, eplen)) + ptype, pval, ep, eplen)) return 0; return 1; } -static int int_ec_size(const EVP_PKEY *pkey) - { +static int +int_ec_size(const EVP_PKEY * pkey) +{ return ECDSA_size(pkey->pkey.ec); - } +} -static int ec_bits(const EVP_PKEY *pkey) - { +static int +ec_bits(const EVP_PKEY * pkey) +{ BIGNUM *order = BN_new(); const EC_GROUP *group; int ret; - if (!order) - { + if (!order) { ERR_clear_error(); return 0; - } + } group = EC_KEY_get0_group(pkey->pkey.ec); - if (!EC_GROUP_get_order(group, order, NULL)) - { + if (!EC_GROUP_get_order(group, order, NULL)) { ERR_clear_error(); return 0; - } - + } ret = BN_num_bits(order); BN_free(order); return ret; - } +} -static int ec_missing_parameters(const EVP_PKEY *pkey) - { +static int +ec_missing_parameters(const EVP_PKEY * pkey) +{ if (EC_KEY_get0_group(pkey->pkey.ec) == NULL) return 1; return 0; - } +} -static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) - { +static int +ec_copy_parameters(EVP_PKEY * to, const EVP_PKEY * from) +{ EC_GROUP *group = EC_GROUP_dup(EC_KEY_get0_group(from->pkey.ec)); if (group == NULL) return 0; @@ -408,79 +394,70 @@ static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) return 0; EC_GROUP_free(group); return 1; - } +} -static int ec_cmp_parameters(const EVP_PKEY *a, const EVP_PKEY *b) - { - const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), - *group_b = EC_KEY_get0_group(b->pkey.ec); +static int +ec_cmp_parameters(const EVP_PKEY * a, const EVP_PKEY * b) +{ + const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), *group_b = EC_KEY_get0_group(b->pkey.ec); if (EC_GROUP_cmp(group_a, group_b, NULL)) return 0; else return 1; - } +} -static void int_ec_free(EVP_PKEY *pkey) - { +static void +int_ec_free(EVP_PKEY * pkey) +{ EC_KEY_free(pkey->pkey.ec); - } +} -static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) - { - unsigned char *buffer=NULL; +static int +do_EC_KEY_print(BIO * bp, const EC_KEY * x, int off, int ktype) +{ + unsigned char *buffer = NULL; const char *ecstr; - size_t buf_len=0, i; - int ret=0, reason=ERR_R_BIO_LIB; - BIGNUM *pub_key=NULL, *order=NULL; - BN_CTX *ctx=NULL; + size_t buf_len = 0, i; + int ret = 0, reason = ERR_R_BIO_LIB; + BIGNUM *pub_key = NULL, *order = NULL; + BN_CTX *ctx = NULL; const EC_GROUP *group; const EC_POINT *public_key; const BIGNUM *priv_key; - - if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) - { + + if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) { reason = ERR_R_PASSED_NULL_PARAMETER; goto err; - } - + } ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - - if (ktype > 0) - { + } + if (ktype > 0) { public_key = EC_KEY_get0_public_key(x); if ((pub_key = EC_POINT_point2bn(group, public_key, - EC_KEY_get_conv_form(x), NULL, ctx)) == NULL) - { + EC_KEY_get_conv_form(x), NULL, ctx)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - if (pub_key) - buf_len = (size_t)BN_num_bytes(pub_key); } - - if (ktype == 2) - { + if (pub_key) + buf_len = (size_t) BN_num_bytes(pub_key); + } + if (ktype == 2) { priv_key = EC_KEY_get0_private_key(x); - if (priv_key && (i = (size_t)BN_num_bytes(priv_key)) > buf_len) + if (priv_key && (i = (size_t) BN_num_bytes(priv_key)) > buf_len) buf_len = i; - } - else + } else priv_key = NULL; - if (ktype > 0) - { + if (ktype > 0) { buf_len += 10; - if ((buffer = malloc(buf_len)) == NULL) - { + if ((buffer = malloc(buf_len)) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } } + } if (ktype == 2) ecstr = "Private-Key"; else if (ktype == 1) @@ -495,9 +472,10 @@ static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) if (!EC_GROUP_get_order(group, order, NULL)) goto err; if (BIO_printf(bp, "%s: (%d bit)\n", ecstr, - BN_num_bits(order)) <= 0) goto err; - - if ((priv_key != NULL) && !ASN1_bn_print(bp, "priv:", priv_key, + BN_num_bits(order)) <= 0) + goto err; + + if ((priv_key != NULL) && !ASN1_bn_print(bp, "priv:", priv_key, buffer, off)) goto err; if ((pub_key != NULL) && !ASN1_bn_print(bp, "pub: ", pub_key, @@ -505,11 +483,11 @@ static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) goto err; if (!ECPKParameters_print(bp, group, off)) goto err; - ret=1; + ret = 1; err: if (!ret) - ECerr(EC_F_DO_EC_KEY_PRINT, reason); - if (pub_key) + ECerr(EC_F_DO_EC_KEY_PRINT, reason); + if (pub_key) BN_free(pub_key); if (order) BN_free(order); @@ -517,71 +495,75 @@ err: BN_CTX_free(ctx); if (buffer != NULL) free(buffer); - return(ret); - } + return (ret); +} -static int eckey_param_decode(EVP_PKEY *pkey, - const unsigned char **pder, int derlen) - { +static int +eckey_param_decode(EVP_PKEY * pkey, + const unsigned char **pder, int derlen) +{ EC_KEY *eckey; - if (!(eckey = d2i_ECParameters(NULL, pder, derlen))) - { + if (!(eckey = d2i_ECParameters(NULL, pder, derlen))) { ECerr(EC_F_ECKEY_PARAM_DECODE, ERR_R_EC_LIB); return 0; - } + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - } +} -static int eckey_param_encode(const EVP_PKEY *pkey, unsigned char **pder) - { +static int +eckey_param_encode(const EVP_PKEY * pkey, unsigned char **pder) +{ return i2d_ECParameters(pkey->pkey.ec, pder); - } +} -static int eckey_param_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_param_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 0); - } +} -static int eckey_pub_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_pub_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 1); - } +} -static int eckey_priv_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_priv_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 2); - } +} -static int old_ec_priv_decode(EVP_PKEY *pkey, - const unsigned char **pder, int derlen) - { +static int +old_ec_priv_decode(EVP_PKEY * pkey, + const unsigned char **pder, int derlen) +{ EC_KEY *ec; - if (!(ec = d2i_ECPrivateKey (NULL, pder, derlen))) - { + if (!(ec = d2i_ECPrivateKey(NULL, pder, derlen))) { ECerr(EC_F_OLD_EC_PRIV_DECODE, EC_R_DECODE_ERROR); return 0; - } + } EVP_PKEY_assign_EC_KEY(pkey, ec); return 1; - } +} -static int old_ec_priv_encode(const EVP_PKEY *pkey, unsigned char **pder) - { +static int +old_ec_priv_encode(const EVP_PKEY * pkey, unsigned char **pder) +{ return i2d_ECPrivateKey(pkey->pkey.ec, pder); - } +} -static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) - { - switch (op) - { - case ASN1_PKEY_CTRL_PKCS7_SIGN: - if (arg1 == 0) - { +static int +ec_pkey_ctrl(EVP_PKEY * pkey, int op, long arg1, void *arg2) +{ + switch (op) { + case ASN1_PKEY_CTRL_PKCS7_SIGN: + if (arg1 == 0) { int snid, hnid; X509_ALGOR *alg1, *alg2; PKCS7_SIGNER_INFO_get0_algs(arg2, NULL, &alg1, &alg2); @@ -591,41 +573,40 @@ static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) if (hnid == NID_undef) return -1; if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) - return -1; + return -1; X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); - } + } return 1; #ifndef OPENSSL_NO_CMS - case ASN1_PKEY_CTRL_CMS_SIGN: - if (arg1 == 0) - { + case ASN1_PKEY_CTRL_CMS_SIGN: + if (arg1 == 0) { int snid, hnid; X509_ALGOR *alg1, *alg2; CMS_SignerInfo_get0_algs(arg2, NULL, NULL, - &alg1, &alg2); + &alg1, &alg2); if (alg1 == NULL || alg1->algorithm == NULL) return -1; hnid = OBJ_obj2nid(alg1->algorithm); if (hnid == NID_undef) return -1; if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) - return -1; + return -1; X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); - } + } return 1; #endif - case ASN1_PKEY_CTRL_DEFAULT_MD_NID: - *(int *)arg2 = NID_sha1; + case ASN1_PKEY_CTRL_DEFAULT_MD_NID: + *(int *) arg2 = NID_sha1; return 2; - default: + default: return -2; - } - } +} + const EVP_PKEY_ASN1_METHOD eckey_asn1_meth = { .pkey_id = EVP_PKEY_EC, .pkey_base_id = EVP_PKEY_EC, diff --git a/lib/libcrypto/ec/ec_asn1.c b/lib/libcrypto/ec/ec_asn1.c index 2bde9a6a3c5..70670a4c750 100644 --- a/lib/libcrypto/ec/ec_asn1.c +++ b/lib/libcrypto/ec/ec_asn1.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -63,12 +63,13 @@ #include -int EC_GROUP_get_basis_type(const EC_GROUP *group) - { - int i=0; +int +EC_GROUP_get_basis_type(const EC_GROUP * group) +{ + int i = 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != - NID_X9_62_characteristic_two_field) + NID_X9_62_characteristic_two_field) /* everything else is currently not supported */ return 0; @@ -82,40 +83,38 @@ int EC_GROUP_get_basis_type(const EC_GROUP *group) else /* everything else is currently not supported */ return 0; - } +} #ifndef OPENSSL_NO_EC2M -int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) - { +int +EC_GROUP_get_trinomial_basis(const EC_GROUP * group, unsigned int *k) +{ if (group == NULL) return 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != NID_X9_62_characteristic_two_field - || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] == 0))) - { + || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] == 0))) { ECerr(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - + } if (k) *k = group->poly[1]; return 1; - } -int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, - unsigned int *k2, unsigned int *k3) - { +} +int +EC_GROUP_get_pentanomial_basis(const EC_GROUP * group, unsigned int *k1, + unsigned int *k2, unsigned int *k3) +{ if (group == NULL) return 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != NID_X9_62_characteristic_two_field - || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] != 0) && (group->poly[3] != 0) && (group->poly[4] == 0))) - { + || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] != 0) && (group->poly[3] != 0) && (group->poly[4] == 0))) { ECerr(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - + } if (k1) *k1 = group->poly[3]; if (k2) @@ -124,7 +123,7 @@ int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, *k3 = group->poly[1]; return 1; - } +} #endif @@ -133,27 +132,27 @@ typedef struct x9_62_pentanomial_st { long k1; long k2; long k3; - } X9_62_PENTANOMIAL; +} X9_62_PENTANOMIAL; typedef struct x9_62_characteristic_two_st { long m; - ASN1_OBJECT *type; - union { + ASN1_OBJECT *type; + union { char *ptr; /* NID_X9_62_onBasis */ - ASN1_NULL *onBasis; + ASN1_NULL *onBasis; /* NID_X9_62_tpBasis */ ASN1_INTEGER *tpBasis; /* NID_X9_62_ppBasis */ X9_62_PENTANOMIAL *ppBasis; /* anything else */ ASN1_TYPE *other; - } p; - } X9_62_CHARACTERISTIC_TWO; + } p; +} X9_62_CHARACTERISTIC_TWO; typedef struct x9_62_fieldid_st { - ASN1_OBJECT *fieldType; - union { + ASN1_OBJECT *fieldType; + union { char *ptr; /* NID_X9_62_prime_field */ ASN1_INTEGER *prime; @@ -161,40 +160,40 @@ typedef struct x9_62_fieldid_st { X9_62_CHARACTERISTIC_TWO *char_two; /* anything else */ ASN1_TYPE *other; - } p; - } X9_62_FIELDID; + } p; +} X9_62_FIELDID; typedef struct x9_62_curve_st { - ASN1_OCTET_STRING *a; - ASN1_OCTET_STRING *b; - ASN1_BIT_STRING *seed; - } X9_62_CURVE; + ASN1_OCTET_STRING *a; + ASN1_OCTET_STRING *b; + ASN1_BIT_STRING *seed; +} X9_62_CURVE; typedef struct ec_parameters_st { - long version; - X9_62_FIELDID *fieldID; - X9_62_CURVE *curve; - ASN1_OCTET_STRING *base; - ASN1_INTEGER *order; - ASN1_INTEGER *cofactor; - } ECPARAMETERS; + long version; + X9_62_FIELDID *fieldID; + X9_62_CURVE *curve; + ASN1_OCTET_STRING *base; + ASN1_INTEGER *order; + ASN1_INTEGER *cofactor; +} ECPARAMETERS; struct ecpk_parameters_st { - int type; + int type; union { - ASN1_OBJECT *named_curve; + ASN1_OBJECT *named_curve; ECPARAMETERS *parameters; - ASN1_NULL *implicitlyCA; + ASN1_NULL *implicitlyCA; } value; - }/* ECPKPARAMETERS */; +} /* ECPKPARAMETERS */ ; /* SEC1 ECPrivateKey */ typedef struct ec_privatekey_st { - long version; + long version; ASN1_OCTET_STRING *privateKey; - ECPKPARAMETERS *parameters; - ASN1_BIT_STRING *publicKey; - } EC_PRIVATEKEY; + ECPKPARAMETERS *parameters; + ASN1_BIT_STRING *publicKey; +} EC_PRIVATEKEY; /* the OpenSSL ASN.1 definitions */ ASN1_SEQUENCE(X9_62_PENTANOMIAL) = { @@ -219,10 +218,8 @@ ASN1_SEQUENCE(X9_62_CHARACTERISTIC_TWO) = { ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, type, ASN1_OBJECT), ASN1_ADB_OBJECT(X9_62_CHARACTERISTIC_TWO) } ASN1_SEQUENCE_END(X9_62_CHARACTERISTIC_TWO) - DECLARE_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) IMPLEMENT_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) - ASN1_ADB_TEMPLATE(fieldID_def) = ASN1_SIMPLE(X9_62_FIELDID, p.other, ASN1_ANY); ASN1_ADB(X9_62_FIELDID) = { @@ -249,7 +246,6 @@ ASN1_SEQUENCE(ECPARAMETERS) = { ASN1_SIMPLE(ECPARAMETERS, order, ASN1_INTEGER), ASN1_OPT(ECPARAMETERS, cofactor, ASN1_INTEGER) } ASN1_SEQUENCE_END(ECPARAMETERS) - DECLARE_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) IMPLEMENT_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) @@ -258,7 +254,6 @@ ASN1_CHOICE(ECPKPARAMETERS) = { ASN1_SIMPLE(ECPKPARAMETERS, value.parameters, ECPARAMETERS), ASN1_SIMPLE(ECPKPARAMETERS, value.implicitlyCA, ASN1_NULL) } ASN1_CHOICE_END(ECPKPARAMETERS) - DECLARE_ASN1_FUNCTIONS_const(ECPKPARAMETERS) DECLARE_ASN1_ENCODE_FUNCTIONS_const(ECPKPARAMETERS, ECPKPARAMETERS) IMPLEMENT_ASN1_FUNCTIONS_const(ECPKPARAMETERS) @@ -269,39 +264,38 @@ ASN1_SEQUENCE(EC_PRIVATEKEY) = { ASN1_EXP_OPT(EC_PRIVATEKEY, parameters, ECPKPARAMETERS, 0), ASN1_EXP_OPT(EC_PRIVATEKEY, publicKey, ASN1_BIT_STRING, 1) } ASN1_SEQUENCE_END(EC_PRIVATEKEY) - DECLARE_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) DECLARE_ASN1_ENCODE_FUNCTIONS_const(EC_PRIVATEKEY, EC_PRIVATEKEY) IMPLEMENT_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) - /* some declarations of internal function */ -/* ec_asn1_group2field() sets the values in a X9_62_FIELDID object */ +/* ec_asn1_group2field() sets the values in a X9_62_FIELDID object */ static int ec_asn1_group2fieldid(const EC_GROUP *, X9_62_FIELDID *); -/* ec_asn1_group2curve() sets the values in a X9_62_CURVE object */ +/* ec_asn1_group2curve() sets the values in a X9_62_CURVE object */ static int ec_asn1_group2curve(const EC_GROUP *, X9_62_CURVE *); /* ec_asn1_parameters2group() creates a EC_GROUP object from a * ECPARAMETERS object */ -static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *); -/* ec_asn1_group2parameters() creates a ECPARAMETERS object from a +static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *); +/* ec_asn1_group2parameters() creates a ECPARAMETERS object from a * EC_GROUP object */ -static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *,ECPARAMETERS *); +static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *, ECPARAMETERS *); /* ec_asn1_pkparameters2group() creates a EC_GROUP object from a * ECPKPARAMETERS object */ -static EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *); -/* ec_asn1_group2pkparameters() creates a ECPKPARAMETERS object from a +static EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *); +/* ec_asn1_group2pkparameters() creates a ECPKPARAMETERS object from a * EC_GROUP object */ -static ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *, - ECPKPARAMETERS *); +static ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *, + ECPKPARAMETERS *); /* the function definitions */ -static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) - { - int ok=0, nid; - BIGNUM *tmp = NULL; - +static int +ec_asn1_group2fieldid(const EC_GROUP * group, X9_62_FIELDID * field) +{ + int ok = 0, nid; + BIGNUM *tmp = NULL; + if (group == NULL || field == NULL) return 0; @@ -313,248 +307,203 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); /* set OID for the field */ - if ((field->fieldType = OBJ_nid2obj(nid)) == NULL) - { + if ((field->fieldType = OBJ_nid2obj(nid)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); goto err; - } - - if (nid == NID_X9_62_prime_field) - { - if ((tmp = BN_new()) == NULL) - { + } + if (nid == NID_X9_62_prime_field) { + if ((tmp = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } + } /* the parameters are specified by the prime number p */ - if (!EC_GROUP_get_curve_GFp(group, tmp, NULL, NULL, NULL)) - { + if (!EC_GROUP_get_curve_GFp(group, tmp, NULL, NULL, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); goto err; - } + } /* set the prime number */ - field->p.prime = BN_to_ASN1_INTEGER(tmp,NULL); - if (field->p.prime == NULL) - { + field->p.prime = BN_to_ASN1_INTEGER(tmp, NULL); + if (field->p.prime == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_ASN1_LIB); goto err; - } } - else /* nid == NID_X9_62_characteristic_two_field */ + } else /* nid == NID_X9_62_characteristic_two_field */ #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_GF2M_NOT_SUPPORTED); goto err; - } + } #else - { - int field_type; + { + int field_type; X9_62_CHARACTERISTIC_TWO *char_two; field->p.char_two = X9_62_CHARACTERISTIC_TWO_new(); char_two = field->p.char_two; - if (char_two == NULL) - { + if (char_two == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - - char_two->m = (long)EC_GROUP_get_degree(group); + } + char_two->m = (long) EC_GROUP_get_degree(group); field_type = EC_GROUP_get_basis_type(group); - if (field_type == 0) - { + if (field_type == 0) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); goto err; - } + } /* set base type OID */ - if ((char_two->type = OBJ_nid2obj(field_type)) == NULL) - { + if ((char_two->type = OBJ_nid2obj(field_type)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); goto err; - } - - if (field_type == NID_X9_62_tpBasis) - { + } + if (field_type == NID_X9_62_tpBasis) { unsigned int k; if (!EC_GROUP_get_trinomial_basis(group, &k)) goto err; char_two->p.tpBasis = ASN1_INTEGER_new(); - if (!char_two->p.tpBasis) - { + if (!char_two->p.tpBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - if (!ASN1_INTEGER_set(char_two->p.tpBasis, (long)k)) - { + } + if (!ASN1_INTEGER_set(char_two->p.tpBasis, (long) k)) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, - ERR_R_ASN1_LIB); + ERR_R_ASN1_LIB); goto err; - } } - else if (field_type == NID_X9_62_ppBasis) - { + } else if (field_type == NID_X9_62_ppBasis) { unsigned int k1, k2, k3; if (!EC_GROUP_get_pentanomial_basis(group, &k1, &k2, &k3)) goto err; char_two->p.ppBasis = X9_62_PENTANOMIAL_new(); - if (!char_two->p.ppBasis) - { + if (!char_two->p.ppBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - - /* set k? values */ - char_two->p.ppBasis->k1 = (long)k1; - char_two->p.ppBasis->k2 = (long)k2; - char_two->p.ppBasis->k3 = (long)k3; } - else /* field_type == NID_X9_62_onBasis */ - { + /* set k? values */ + char_two->p.ppBasis->k1 = (long) k1; + char_two->p.ppBasis->k2 = (long) k2; + char_two->p.ppBasis->k3 = (long) k3; + } else { /* field_type == NID_X9_62_onBasis */ /* for ONB the parameters are (asn1) NULL */ char_two->p.onBasis = ASN1_NULL_new(); - if (!char_two->p.onBasis) - { + if (!char_two->p.onBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } } } + } #endif ok = 1; -err : if (tmp) +err: if (tmp) BN_free(tmp); - return(ok); + return (ok); } -static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) - { - int ok=0, nid; - BIGNUM *tmp_1=NULL, *tmp_2=NULL; - unsigned char *buffer_1=NULL, *buffer_2=NULL, - *a_buf=NULL, *b_buf=NULL; - size_t len_1, len_2; +static int +ec_asn1_group2curve(const EC_GROUP * group, X9_62_CURVE * curve) +{ + int ok = 0, nid; + BIGNUM *tmp_1 = NULL, *tmp_2 = NULL; + unsigned char *buffer_1 = NULL, *buffer_2 = NULL, *a_buf = NULL, + *b_buf = NULL; + size_t len_1, len_2; unsigned char char_zero = 0; if (!group || !curve || !curve->a || !curve->b) return 0; - if ((tmp_1 = BN_new()) == NULL || (tmp_2 = BN_new()) == NULL) - { + if ((tmp_1 = BN_new()) == NULL || (tmp_2 = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); goto err; - } - + } nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); /* get a and b */ - if (nid == NID_X9_62_prime_field) - { - if (!EC_GROUP_get_curve_GFp(group, NULL, tmp_1, tmp_2, NULL)) - { + if (nid == NID_X9_62_prime_field) { + if (!EC_GROUP_get_curve_GFp(group, NULL, tmp_1, tmp_2, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); goto err; - } } + } #ifndef OPENSSL_NO_EC2M - else /* nid == NID_X9_62_characteristic_two_field */ - { - if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) - { + else { /* nid == NID_X9_62_characteristic_two_field */ + if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); goto err; - } } + } #endif - len_1 = (size_t)BN_num_bytes(tmp_1); - len_2 = (size_t)BN_num_bytes(tmp_2); + len_1 = (size_t) BN_num_bytes(tmp_1); + len_2 = (size_t) BN_num_bytes(tmp_2); - if (len_1 == 0) - { + if (len_1 == 0) { /* len_1 == 0 => a == 0 */ a_buf = &char_zero; len_1 = 1; - } - else - { - if ((buffer_1 = malloc(len_1)) == NULL) - { + } else { + if ((buffer_1 = malloc(len_1)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - if ( (len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) - { + } + if ((len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); goto err; - } - a_buf = buffer_1; } + a_buf = buffer_1; + } - if (len_2 == 0) - { + if (len_2 == 0) { /* len_2 == 0 => b == 0 */ b_buf = &char_zero; len_2 = 1; - } - else - { - if ((buffer_2 = malloc(len_2)) == NULL) - { + } else { + if ((buffer_2 = malloc(len_2)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - if ( (len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) - { + } + if ((len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); goto err; - } - b_buf = buffer_2; } - + b_buf = buffer_2; + } + /* set a and b */ if (!M_ASN1_OCTET_STRING_set(curve->a, a_buf, len_1) || - !M_ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) - { + !M_ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); goto err; - } - + } /* set the seed (optional) */ - if (group->seed) - { + if (group->seed) { if (!curve->seed) - if ((curve->seed = ASN1_BIT_STRING_new()) == NULL) - { + if ((curve->seed = ASN1_BIT_STRING_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); goto err; - } - curve->seed->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT|0x07); + } + curve->seed->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); curve->seed->flags |= ASN1_STRING_FLAG_BITS_LEFT; - if (!ASN1_BIT_STRING_set(curve->seed, group->seed, - (int)group->seed_len)) - { + if (!ASN1_BIT_STRING_set(curve->seed, group->seed, + (int) group->seed_len)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); goto err; - } } - else - { - if (curve->seed) - { + } else { + if (curve->seed) { ASN1_BIT_STRING_free(curve->seed); curve->seed = NULL; - } } + } ok = 1; @@ -566,880 +515,729 @@ err: if (buffer_1) BN_free(tmp_1); if (tmp_2) BN_free(tmp_2); - return(ok); - } + return (ok); +} -static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *group, - ECPARAMETERS *param) - { - int ok=0; - size_t len=0; - ECPARAMETERS *ret=NULL; - BIGNUM *tmp=NULL; - unsigned char *buffer=NULL; - const EC_POINT *point=NULL; +static ECPARAMETERS * +ec_asn1_group2parameters(const EC_GROUP * group, ECPARAMETERS * param) +{ + int ok = 0; + size_t len = 0; + ECPARAMETERS *ret = NULL; + BIGNUM *tmp = NULL; + unsigned char *buffer = NULL; + const EC_POINT *point = NULL; point_conversion_form_t form; - if ((tmp = BN_new()) == NULL) - { + if ((tmp = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - - if (param == NULL) - { - if ((ret = ECPARAMETERS_new()) == NULL) - { - ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, - ERR_R_MALLOC_FAILURE); - goto err; - } } - else + if (param == NULL) { + if ((ret = ECPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, + ERR_R_MALLOC_FAILURE); + goto err; + } + } else ret = param; /* set the version (always one) */ - ret->version = (long)0x1; + ret->version = (long) 0x1; /* set the fieldID */ - if (!ec_asn1_group2fieldid(group, ret->fieldID)) - { + if (!ec_asn1_group2fieldid(group, ret->fieldID)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - + } /* set the curve */ - if (!ec_asn1_group2curve(group, ret->curve)) - { + if (!ec_asn1_group2curve(group, ret->curve)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - + } /* set the base point */ - if ((point = EC_GROUP_get0_generator(group)) == NULL) - { + if ((point = EC_GROUP_get0_generator(group)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, EC_R_UNDEFINED_GENERATOR); goto err; - } - + } form = EC_GROUP_get_point_conversion_form(group); len = EC_POINT_point2oct(group, point, form, NULL, len, NULL); - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - if ((buffer = malloc(len)) == NULL) - { + } + if ((buffer = malloc(len)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - if (!EC_POINT_point2oct(group, point, form, buffer, len, NULL)) - { + } + if (!EC_POINT_point2oct(group, point, form, buffer, len, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - if (ret->base == NULL && (ret->base = ASN1_OCTET_STRING_new()) == NULL) - { + } + if (ret->base == NULL && (ret->base = ASN1_OCTET_STRING_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - if (!ASN1_OCTET_STRING_set(ret->base, buffer, len)) - { + } + if (!ASN1_OCTET_STRING_set(ret->base, buffer, len)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } - + } /* set the order */ - if (!EC_GROUP_get_order(group, tmp, NULL)) - { + if (!EC_GROUP_get_order(group, tmp, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } + } ret->order = BN_to_ASN1_INTEGER(tmp, ret->order); - if (ret->order == NULL) - { + if (ret->order == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } - + } /* set the cofactor (optional) */ - if (EC_GROUP_get_cofactor(group, tmp, NULL)) - { + if (EC_GROUP_get_cofactor(group, tmp, NULL)) { ret->cofactor = BN_to_ASN1_INTEGER(tmp, ret->cofactor); - if (ret->cofactor == NULL) - { + if (ret->cofactor == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } } - + } ok = 1; -err : if(!ok) - { +err: if (!ok) { if (ret && !param) ECPARAMETERS_free(ret); ret = NULL; - } + } if (tmp) BN_free(tmp); if (buffer) free(buffer); - return(ret); - } + return (ret); +} -ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *group, - ECPKPARAMETERS *params) - { - int ok = 1, tmp; +ECPKPARAMETERS * +ec_asn1_group2pkparameters(const EC_GROUP * group, ECPKPARAMETERS * params) +{ + int ok = 1, tmp; ECPKPARAMETERS *ret = params; - if (ret == NULL) - { - if ((ret = ECPKPARAMETERS_new()) == NULL) - { - ECerr(EC_F_EC_ASN1_GROUP2PKPARAMETERS, - ERR_R_MALLOC_FAILURE); + if (ret == NULL) { + if ((ret = ECPKPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2PKPARAMETERS, + ERR_R_MALLOC_FAILURE); return NULL; - } } - else - { + } else { if (ret->type == 0 && ret->value.named_curve) ASN1_OBJECT_free(ret->value.named_curve); else if (ret->type == 1 && ret->value.parameters) ECPARAMETERS_free(ret->value.parameters); - } + } - if (EC_GROUP_get_asn1_flag(group)) - { - /* use the asn1 OID to describe the - * the elliptic curve parameters + if (EC_GROUP_get_asn1_flag(group)) { + /* + * use the asn1 OID to describe the the elliptic curve + * parameters */ tmp = EC_GROUP_get_curve_name(group); - if (tmp) - { + if (tmp) { ret->type = 0; if ((ret->value.named_curve = OBJ_nid2obj(tmp)) == NULL) ok = 0; - } - else + } else /* we don't kmow the nid => ERROR */ ok = 0; - } - else - { + } else { /* use the ECPARAMETERS structure */ ret->type = 1; if ((ret->value.parameters = ec_asn1_group2parameters( - group, NULL)) == NULL) + group, NULL)) == NULL) ok = 0; - } + } - if (!ok) - { + if (!ok) { ECPKPARAMETERS_free(ret); return NULL; - } - return ret; } + return ret; +} -static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) - { - int ok = 0, tmp; - EC_GROUP *ret = NULL; - BIGNUM *p = NULL, *a = NULL, *b = NULL; - EC_POINT *point=NULL; - long field_bits; - - if (!params->fieldID || !params->fieldID->fieldType || - !params->fieldID->p.ptr) - { +static EC_GROUP * +ec_asn1_parameters2group(const ECPARAMETERS * params) +{ + int ok = 0, tmp; + EC_GROUP *ret = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL; + EC_POINT *point = NULL; + long field_bits; + + if (!params->fieldID || !params->fieldID->fieldType || + !params->fieldID->p.ptr) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - + } /* now extract the curve parameters a and b */ - if (!params->curve || !params->curve->a || + if (!params->curve || !params->curve->a || !params->curve->a->data || !params->curve->b || - !params->curve->b->data) - { + !params->curve->b->data) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } a = BN_bin2bn(params->curve->a->data, params->curve->a->length, NULL); - if (a == NULL) - { + if (a == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_BN_LIB); goto err; - } + } b = BN_bin2bn(params->curve->b->data, params->curve->b->length, NULL); - if (b == NULL) - { + if (b == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_BN_LIB); goto err; - } - + } /* get the field parameters */ tmp = OBJ_obj2nid(params->fieldID->fieldType); if (tmp == NID_X9_62_characteristic_two_field) #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_GF2M_NOT_SUPPORTED); goto err; - } + } #else - { + { X9_62_CHARACTERISTIC_TWO *char_two; char_two = params->fieldID->p.char_two; field_bits = char_two->m; - if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) - { + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_FIELD_TOO_LARGE); goto err; - } - - if ((p = BN_new()) == NULL) - { + } + if ((p = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_MALLOC_FAILURE); goto err; - } - + } /* get the base type */ tmp = OBJ_obj2nid(char_two->type); - if (tmp == NID_X9_62_tpBasis) - { + if (tmp == NID_X9_62_tpBasis) { long tmp_long; - if (!char_two->p.tpBasis) - { + if (!char_two->p.tpBasis) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - + } tmp_long = ASN1_INTEGER_get(char_two->p.tpBasis); - if (!(char_two->m > tmp_long && tmp_long > 0)) - { + if (!(char_two->m > tmp_long && tmp_long > 0)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_TRINOMIAL_BASIS); goto err; - } - + } /* create the polynomial */ - if (!BN_set_bit(p, (int)char_two->m)) + if (!BN_set_bit(p, (int) char_two->m)) goto err; - if (!BN_set_bit(p, (int)tmp_long)) + if (!BN_set_bit(p, (int) tmp_long)) goto err; if (!BN_set_bit(p, 0)) goto err; - } - else if (tmp == NID_X9_62_ppBasis) - { + } else if (tmp == NID_X9_62_ppBasis) { X9_62_PENTANOMIAL *penta; penta = char_two->p.ppBasis; - if (!penta) - { + if (!penta) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - - if (!(char_two->m > penta->k3 && penta->k3 > penta->k2 && penta->k2 > penta->k1 && penta->k1 > 0)) - { + } + if (!(char_two->m > penta->k3 && penta->k3 > penta->k2 && penta->k2 > penta->k1 && penta->k1 > 0)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_PENTANOMIAL_BASIS); goto err; - } - - /* create the polynomial */ - if (!BN_set_bit(p, (int)char_two->m)) goto err; - if (!BN_set_bit(p, (int)penta->k1)) goto err; - if (!BN_set_bit(p, (int)penta->k2)) goto err; - if (!BN_set_bit(p, (int)penta->k3)) goto err; - if (!BN_set_bit(p, 0)) goto err; } - else if (tmp == NID_X9_62_onBasis) - { + /* create the polynomial */ + if (!BN_set_bit(p, (int) char_two->m)) + goto err; + if (!BN_set_bit(p, (int) penta->k1)) + goto err; + if (!BN_set_bit(p, (int) penta->k2)) + goto err; + if (!BN_set_bit(p, (int) penta->k3)) + goto err; + if (!BN_set_bit(p, 0)) + goto err; + } else if (tmp == NID_X9_62_onBasis) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_NOT_IMPLEMENTED); goto err; - } - else /* error */ - { + } else { /* error */ ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GF2m(p, a, b, NULL); - } + } #endif - else if (tmp == NID_X9_62_prime_field) - { + else if (tmp == NID_X9_62_prime_field) { /* we have a curve over a prime field */ /* extract the prime number */ - if (!params->fieldID->p.prime) - { + if (!params->fieldID->p.prime) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } p = ASN1_INTEGER_to_BN(params->fieldID->p.prime, NULL); - if (p == NULL) - { + if (p == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); goto err; - } - - if (BN_is_negative(p) || BN_is_zero(p)) - { + } + if (BN_is_negative(p) || BN_is_zero(p)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_FIELD); goto err; - } - + } field_bits = BN_num_bits(p); - if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) - { + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_FIELD_TOO_LARGE); goto err; - } - + } /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GFp(p, a, b, NULL); - } - else - { + } else { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_FIELD); goto err; - } + } - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } /* extract seed (optional) */ - if (params->curve->seed != NULL) - { + if (params->curve->seed != NULL) { if (ret->seed != NULL) free(ret->seed); - if (!(ret->seed = malloc(params->curve->seed->length))) - { - ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, - ERR_R_MALLOC_FAILURE); + if (!(ret->seed = malloc(params->curve->seed->length))) { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, + ERR_R_MALLOC_FAILURE); goto err; - } - memcpy(ret->seed, params->curve->seed->data, - params->curve->seed->length); - ret->seed_len = params->curve->seed->length; } - - if (!params->order || !params->base || !params->base->data) - { + memcpy(ret->seed, params->curve->seed->data, + params->curve->seed->length); + ret->seed_len = params->curve->seed->length; + } + if (!params->order || !params->base || !params->base->data) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - - if ((point = EC_POINT_new(ret)) == NULL) goto err; + } + if ((point = EC_POINT_new(ret)) == NULL) + goto err; /* set the point conversion form */ EC_GROUP_set_point_conversion_form(ret, (point_conversion_form_t) - (params->base->data[0] & ~0x01)); + (params->base->data[0] & ~0x01)); /* extract the ec point */ - if (!EC_POINT_oct2point(ret, point, params->base->data, - params->base->length, NULL)) - { + if (!EC_POINT_oct2point(ret, point, params->base->data, + params->base->length, NULL)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } /* extract the order */ - if ((a = ASN1_INTEGER_to_BN(params->order, a)) == NULL) - { + if ((a = ASN1_INTEGER_to_BN(params->order, a)) == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); goto err; - } - if (BN_is_negative(a) || BN_is_zero(a)) - { + } + if (BN_is_negative(a) || BN_is_zero(a)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_GROUP_ORDER); goto err; - } - if (BN_num_bits(a) > (int)field_bits + 1) /* Hasse bound */ - { + } + if (BN_num_bits(a) > (int) field_bits + 1) { /* Hasse bound */ ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_GROUP_ORDER); goto err; - } - + } /* extract the cofactor (optional) */ - if (params->cofactor == NULL) - { - if (b) - { + if (params->cofactor == NULL) { + if (b) { BN_free(b); b = NULL; - } } - else - if ((b = ASN1_INTEGER_to_BN(params->cofactor, b)) == NULL) - { - ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); - goto err; - } + } else if ((b = ASN1_INTEGER_to_BN(params->cofactor, b)) == NULL) { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); + goto err; + } /* set the generator, order and cofactor (if present) */ - if (!EC_GROUP_set_generator(ret, point, a, b)) - { + if (!EC_GROUP_set_generator(ret, point, a, b)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } ok = 1; -err: if (!ok) - { - if (ret) +err: if (!ok) { + if (ret) EC_GROUP_clear_free(ret); ret = NULL; - } - - if (p) + } + if (p) BN_free(p); - if (a) + if (a) BN_free(a); - if (b) + if (b) BN_free(b); - if (point) + if (point) EC_POINT_free(point); - return(ret); + return (ret); } -EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *params) - { - EC_GROUP *ret=NULL; - int tmp=0; +EC_GROUP * +ec_asn1_pkparameters2group(const ECPKPARAMETERS * params) +{ + EC_GROUP *ret = NULL; + int tmp = 0; - if (params == NULL) - { - ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, - EC_R_MISSING_PARAMETERS); + if (params == NULL) { + ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, + EC_R_MISSING_PARAMETERS); return NULL; - } - - if (params->type == 0) - { /* the curve is given by an OID */ + } + if (params->type == 0) {/* the curve is given by an OID */ tmp = OBJ_obj2nid(params->value.named_curve); - if ((ret = EC_GROUP_new_by_curve_name(tmp)) == NULL) - { - ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, - EC_R_EC_GROUP_NEW_BY_NAME_FAILURE); + if ((ret = EC_GROUP_new_by_curve_name(tmp)) == NULL) { + ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, + EC_R_EC_GROUP_NEW_BY_NAME_FAILURE); return NULL; - } - EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_NAMED_CURVE); } - else if (params->type == 1) - { /* the parameters are given by a ECPARAMETERS - * structure */ + EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_NAMED_CURVE); + } else if (params->type == 1) { /* the parameters are given by a + * ECPARAMETERS structure */ ret = ec_asn1_parameters2group(params->value.parameters); - if (!ret) - { + if (!ret) { ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, ERR_R_EC_LIB); return NULL; - } - EC_GROUP_set_asn1_flag(ret, 0x0); } - else if (params->type == 2) - { /* implicitlyCA */ + EC_GROUP_set_asn1_flag(ret, 0x0); + } else if (params->type == 2) { /* implicitlyCA */ return NULL; - } - else - { + } else { ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, EC_R_ASN1_ERROR); return NULL; - } + } return ret; - } +} /* EC_GROUP <-> DER encoding of ECPKPARAMETERS */ -EC_GROUP *d2i_ECPKParameters(EC_GROUP **a, const unsigned char **in, long len) - { - EC_GROUP *group = NULL; - ECPKPARAMETERS *params = NULL; +EC_GROUP * +d2i_ECPKParameters(EC_GROUP ** a, const unsigned char **in, long len) +{ + EC_GROUP *group = NULL; + ECPKPARAMETERS *params = NULL; - if ((params = d2i_ECPKPARAMETERS(NULL, in, len)) == NULL) - { + if ((params = d2i_ECPKPARAMETERS(NULL, in, len)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_D2I_ECPKPARAMETERS_FAILURE); ECPKPARAMETERS_free(params); return NULL; - } - - if ((group = ec_asn1_pkparameters2group(params)) == NULL) - { + } + if ((group = ec_asn1_pkparameters2group(params)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_PKPARAMETERS2GROUP_FAILURE); ECPKPARAMETERS_free(params); - return NULL; - } - - + return NULL; + } if (a && *a) EC_GROUP_clear_free(*a); if (a) *a = group; ECPKPARAMETERS_free(params); - return(group); - } + return (group); +} -int i2d_ECPKParameters(const EC_GROUP *a, unsigned char **out) - { - int ret=0; - ECPKPARAMETERS *tmp = ec_asn1_group2pkparameters(a, NULL); - if (tmp == NULL) - { +int +i2d_ECPKParameters(const EC_GROUP * a, unsigned char **out) +{ + int ret = 0; + ECPKPARAMETERS *tmp = ec_asn1_group2pkparameters(a, NULL); + if (tmp == NULL) { ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_GROUP2PKPARAMETERS_FAILURE); return 0; - } - if ((ret = i2d_ECPKPARAMETERS(tmp, out)) == 0) - { + } + if ((ret = i2d_ECPKPARAMETERS(tmp, out)) == 0) { ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_I2D_ECPKPARAMETERS_FAILURE); ECPKPARAMETERS_free(tmp); return 0; - } - ECPKPARAMETERS_free(tmp); - return(ret); } + ECPKPARAMETERS_free(tmp); + return (ret); +} /* some EC_KEY functions */ -EC_KEY *d2i_ECPrivateKey(EC_KEY **a, const unsigned char **in, long len) - { - int ok=0; - EC_KEY *ret=NULL; - EC_PRIVATEKEY *priv_key=NULL; +EC_KEY * +d2i_ECPrivateKey(EC_KEY ** a, const unsigned char **in, long len) +{ + int ok = 0; + EC_KEY *ret = NULL; + EC_PRIVATEKEY *priv_key = NULL; - if ((priv_key = EC_PRIVATEKEY_new()) == NULL) - { + if ((priv_key = EC_PRIVATEKEY_new()) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); return NULL; - } - - if ((priv_key = d2i_EC_PRIVATEKEY(&priv_key, in, len)) == NULL) - { + } + if ((priv_key = d2i_EC_PRIVATEKEY(&priv_key, in, len)) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); EC_PRIVATEKEY_free(priv_key); return NULL; - } - - if (a == NULL || *a == NULL) - { - if ((ret = EC_KEY_new()) == NULL) - { + } + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } + } if (a) *a = ret; - } - else + } else ret = *a; - if (priv_key->parameters) - { + if (priv_key->parameters) { if (ret->group) EC_GROUP_clear_free(ret->group); ret->group = ec_asn1_pkparameters2group(priv_key->parameters); - } - - if (ret->group == NULL) - { + } + if (ret->group == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - + } ret->version = priv_key->version; - if (priv_key->privateKey) - { + if (priv_key->privateKey) { ret->priv_key = BN_bin2bn( - M_ASN1_STRING_data(priv_key->privateKey), - M_ASN1_STRING_length(priv_key->privateKey), - ret->priv_key); - if (ret->priv_key == NULL) - { + M_ASN1_STRING_data(priv_key->privateKey), + M_ASN1_STRING_length(priv_key->privateKey), + ret->priv_key); + if (ret->priv_key == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, - ERR_R_BN_LIB); + ERR_R_BN_LIB); goto err; - } } - else - { - ECerr(EC_F_D2I_ECPRIVATEKEY, - EC_R_MISSING_PRIVATE_KEY); + } else { + ECerr(EC_F_D2I_ECPRIVATEKEY, + EC_R_MISSING_PRIVATE_KEY); goto err; - } + } - if (priv_key->publicKey) - { + if (priv_key->publicKey) { const unsigned char *pub_oct; size_t pub_oct_len; if (ret->pub_key) EC_POINT_clear_free(ret->pub_key); ret->pub_key = EC_POINT_new(ret->group); - if (ret->pub_key == NULL) - { + if (ret->pub_key == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - pub_oct = M_ASN1_STRING_data(priv_key->publicKey); + } + pub_oct = M_ASN1_STRING_data(priv_key->publicKey); pub_oct_len = M_ASN1_STRING_length(priv_key->publicKey); /* save the point conversion form */ - ret->conv_form = (point_conversion_form_t)(pub_oct[0] & ~0x01); + ret->conv_form = (point_conversion_form_t) (pub_oct[0] & ~0x01); if (!EC_POINT_oct2point(ret->group, ret->pub_key, - pub_oct, pub_oct_len, NULL)) - { + pub_oct, pub_oct_len, NULL)) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } } - + } ok = 1; err: - if (!ok) - { + if (!ok) { if (ret) EC_KEY_free(ret); ret = NULL; - } - + } if (priv_key) EC_PRIVATEKEY_free(priv_key); - return(ret); - } + return (ret); +} -int i2d_ECPrivateKey(EC_KEY *a, unsigned char **out) - { - int ret=0, ok=0; - unsigned char *buffer=NULL; - size_t buf_len=0, tmp_len; - EC_PRIVATEKEY *priv_key=NULL; +int +i2d_ECPrivateKey(EC_KEY * a, unsigned char **out) +{ + int ret = 0, ok = 0; + unsigned char *buffer = NULL; + size_t buf_len = 0, tmp_len; + EC_PRIVATEKEY *priv_key = NULL; - if (a == NULL || a->group == NULL || a->priv_key == NULL) - { + if (a == NULL || a->group == NULL || a->priv_key == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_PASSED_NULL_PARAMETER); + ERR_R_PASSED_NULL_PARAMETER); goto err; - } - - if ((priv_key = EC_PRIVATEKEY_new()) == NULL) - { + } + if ((priv_key = EC_PRIVATEKEY_new()) == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - + } priv_key->version = a->version; - buf_len = (size_t)BN_num_bytes(a->priv_key); + buf_len = (size_t) BN_num_bytes(a->priv_key); buffer = malloc(buf_len); - if (buffer == NULL) - { + if (buffer == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - - if (!BN_bn2bin(a->priv_key, buffer)) - { + } + if (!BN_bn2bin(a->priv_key, buffer)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_BN_LIB); goto err; - } - - if (!M_ASN1_OCTET_STRING_set(priv_key->privateKey, buffer, buf_len)) - { + } + if (!M_ASN1_OCTET_STRING_set(priv_key->privateKey, buffer, buf_len)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_ASN1_LIB); goto err; - } - - if (!(a->enc_flag & EC_PKEY_NO_PARAMETERS)) - { + } + if (!(a->enc_flag & EC_PKEY_NO_PARAMETERS)) { if ((priv_key->parameters = ec_asn1_group2pkparameters( - a->group, priv_key->parameters)) == NULL) - { + a->group, priv_key->parameters)) == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } } - - if (!(a->enc_flag & EC_PKEY_NO_PUBKEY)) - { + } + if (!(a->enc_flag & EC_PKEY_NO_PUBKEY)) { priv_key->publicKey = M_ASN1_BIT_STRING_new(); - if (priv_key->publicKey == NULL) - { + if (priv_key->publicKey == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - - tmp_len = EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, NULL, 0, NULL); + } + tmp_len = EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, NULL, 0, NULL); - if (tmp_len > buf_len) - { + if (tmp_len > buf_len) { unsigned char *tmp_buffer = realloc(buffer, tmp_len); - if (!tmp_buffer) - { + if (!tmp_buffer) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); goto err; - } + } buffer = tmp_buffer; buf_len = tmp_len; - } - - if (!EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, buffer, buf_len, NULL)) - { + } + if (!EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, buffer, buf_len, NULL)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - - priv_key->publicKey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT|0x07); + } + priv_key->publicKey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); priv_key->publicKey->flags |= ASN1_STRING_FLAG_BITS_LEFT; - if (!M_ASN1_BIT_STRING_set(priv_key->publicKey, buffer, - buf_len)) - { + if (!M_ASN1_BIT_STRING_set(priv_key->publicKey, buffer, + buf_len)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_ASN1_LIB); goto err; - } } - - if ((ret = i2d_EC_PRIVATEKEY(priv_key, out)) == 0) - { + } + if ((ret = i2d_EC_PRIVATEKEY(priv_key, out)) == 0) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - ok=1; + } + ok = 1; err: if (buffer) free(buffer); if (priv_key) EC_PRIVATEKEY_free(priv_key); - return(ok?ret:0); - } + return (ok ? ret : 0); +} -int i2d_ECParameters(EC_KEY *a, unsigned char **out) - { - if (a == NULL) - { +int +i2d_ECParameters(EC_KEY * a, unsigned char **out) +{ + if (a == NULL) { ECerr(EC_F_I2D_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - return i2d_ECPKParameters(a->group, out); } + return i2d_ECPKParameters(a->group, out); +} -EC_KEY *d2i_ECParameters(EC_KEY **a, const unsigned char **in, long len) - { - EC_KEY *ret; +EC_KEY * +d2i_ECParameters(EC_KEY ** a, const unsigned char **in, long len) +{ + EC_KEY *ret; - if (in == NULL || *in == NULL) - { + if (in == NULL || *in == NULL) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } - - if (a == NULL || *a == NULL) - { - if ((ret = EC_KEY_new()) == NULL) - { + } + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_MALLOC_FAILURE); return NULL; - } + } if (a) *a = ret; - } - else + } else ret = *a; - if (!d2i_ECPKParameters(&ret->group, in, len)) - { + if (!d2i_ECPKParameters(&ret->group, in, len)) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_EC_LIB); return NULL; - } - - return ret; } + return ret; +} -EC_KEY *o2i_ECPublicKey(EC_KEY **a, const unsigned char **in, long len) - { - EC_KEY *ret=NULL; +EC_KEY * +o2i_ECPublicKey(EC_KEY ** a, const unsigned char **in, long len) +{ + EC_KEY *ret = NULL; - if (a == NULL || (*a) == NULL || (*a)->group == NULL) - { - /* sorry, but a EC_GROUP-structur is necessary - * to set the public key */ + if (a == NULL || (*a) == NULL || (*a)->group == NULL) { + /* + * sorry, but a EC_GROUP-structur is necessary to set the + * public key + */ ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } + } ret = *a; - if (ret->pub_key == NULL && - (ret->pub_key = EC_POINT_new(ret->group)) == NULL) - { + if (ret->pub_key == NULL && + (ret->pub_key = EC_POINT_new(ret->group)) == NULL) { ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_MALLOC_FAILURE); return 0; - } - if (!EC_POINT_oct2point(ret->group, ret->pub_key, *in, len, NULL)) - { + } + if (!EC_POINT_oct2point(ret->group, ret->pub_key, *in, len, NULL)) { ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_EC_LIB); return 0; - } + } /* save the point conversion form */ - ret->conv_form = (point_conversion_form_t)(*in[0] & ~0x01); + ret->conv_form = (point_conversion_form_t) (*in[0] & ~0x01); *in += len; return ret; - } +} -int i2o_ECPublicKey(EC_KEY *a, unsigned char **out) - { - size_t buf_len=0; +int +i2o_ECPublicKey(EC_KEY * a, unsigned char **out) +{ + size_t buf_len = 0; int new_buffer = 0; - if (a == NULL) - { + if (a == NULL) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - buf_len = EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, NULL, 0, NULL); + } + buf_len = EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, NULL, 0, NULL); if (out == NULL || buf_len == 0) - /* out == NULL => just return the length of the octet string */ + /* out == NULL => just return the length of the octet string */ return buf_len; - if (*out == NULL) - { - if ((*out = malloc(buf_len)) == NULL) - { + if (*out == NULL) { + if ((*out = malloc(buf_len)) == NULL) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_MALLOC_FAILURE); return 0; - } - new_buffer = 1; } - if (!EC_POINT_point2oct(a->group, a->pub_key, a->conv_form, - *out, buf_len, NULL)) - { + new_buffer = 1; + } + if (!EC_POINT_point2oct(a->group, a->pub_key, a->conv_form, + *out, buf_len, NULL)) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_EC_LIB); free(*out); *out = NULL; return 0; - } + } if (!new_buffer) *out += buf_len; return buf_len; - } +} diff --git a/lib/libcrypto/ec/ec_check.c b/lib/libcrypto/ec/ec_check.c index 0e316b4b3ff..8f533d5ff8a 100644 --- a/lib/libcrypto/ec/ec_check.c +++ b/lib/libcrypto/ec/ec_check.c @@ -7,7 +7,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -56,60 +56,54 @@ #include "ec_lcl.h" #include -int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx) - { +int +EC_GROUP_check(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; BIGNUM *order; BN_CTX *new_ctx = NULL; EC_POINT *point = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GROUP_CHECK, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); - if ((order = BN_CTX_get(ctx)) == NULL) goto err; + if ((order = BN_CTX_get(ctx)) == NULL) + goto err; /* check the discriminant */ - if (!EC_GROUP_check_discriminant(group, ctx)) - { + if (!EC_GROUP_check_discriminant(group, ctx)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_DISCRIMINANT_IS_ZERO); goto err; - } - + } /* check the generator */ - if (group->generator == NULL) - { + if (group->generator == NULL) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_GENERATOR); goto err; - } - if (!EC_POINT_is_on_curve(group, group->generator, ctx)) - { + } + if (!EC_POINT_is_on_curve(group, group->generator, ctx)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } /* check the order of the generator */ - if ((point = EC_POINT_new(group)) == NULL) goto err; - if (!EC_GROUP_get_order(group, order, ctx)) goto err; - if (BN_is_zero(order)) - { + if ((point = EC_POINT_new(group)) == NULL) + goto err; + if (!EC_GROUP_get_order(group, order, ctx)) + goto err; + if (BN_is_zero(order)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_ORDER); goto err; - } - - if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx)) goto err; - if (!EC_POINT_is_at_infinity(group, point)) - { + } + if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx)) + goto err; + if (!EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_INVALID_GROUP_ORDER); goto err; - } - + } ret = 1; err: @@ -120,4 +114,4 @@ err: if (point) EC_POINT_free(point); return ret; - } +} diff --git a/lib/libcrypto/ec/ec_curve.c b/lib/libcrypto/ec/ec_curve.c index 23bc3ab94e1..daaa8edd7eb 100644 --- a/lib/libcrypto/ec/ec_curve.c +++ b/lib/libcrypto/ec/ec_curve.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -58,13 +58,13 @@ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * - * Portions of the attached software ("Contribution") are developed by + * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the OpenSSL open source * license provided above. * - * The elliptic curve binary polynomial software is originally written by + * The elliptic curve binary polynomial software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. * */ @@ -75,1692 +75,2075 @@ #include typedef struct { - int field_type, /* either NID_X9_62_prime_field or + int field_type, /* either NID_X9_62_prime_field or * NID_X9_62_characteristic_two_field */ - seed_len, - param_len; + seed_len, param_len; unsigned int cofactor; /* promoted to BN_ULONG */ } EC_CURVE_DATA; /* the nist prime curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_NIST_PRIME_192 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0x30,0x45,0xAE,0x6F,0xC8,0x42,0x2F,0x64,0xED,0x57, /* seed */ - 0x95,0x28,0xD3,0x81,0x20,0xEA,0xE1,0x21,0x96,0xD5, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0x64,0x21,0x05,0x19,0xE5,0x9C,0x80,0xE7,0x0F,0xA7, /* b */ - 0xE9,0xAB,0x72,0x24,0x30,0x49,0xFE,0xB8,0xDE,0xEC, - 0xC1,0x46,0xB9,0xB1, - 0x18,0x8D,0xA8,0x0E,0xB0,0x30,0x90,0xF6,0x7C,0xBF, /* x */ - 0x20,0xEB,0x43,0xA1,0x88,0x00,0xF4,0xFF,0x0A,0xFD, - 0x82,0xFF,0x10,0x12, - 0x07,0x19,0x2b,0x95,0xff,0xc8,0xda,0x78,0x63,0x10, /* y */ - 0x11,0xed,0x6b,0x24,0xcd,0xd5,0x73,0xf9,0x77,0xa1, - 0x1e,0x79,0x48,0x11, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x99,0xDE,0xF8,0x36,0x14,0x6B,0xC9,0xB1, - 0xB4,0xD2,0x28,0x31 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+28*6]; } - _EC_NIST_PRIME_224 = { - { NID_X9_62_prime_field,20,28,1 }, - { 0xBD,0x71,0x34,0x47,0x99,0xD5,0xC7,0xFC,0xDC,0x45, /* seed */ - 0xB5,0x9F,0xA3,0xB9,0xAB,0x8F,0x6A,0x94,0x8B,0xC5, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, - 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, - 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, - 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+48*6]; } - _EC_NIST_PRIME_384 = { - { NID_X9_62_prime_field,20,48,1 }, - { 0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00, /* seed */ - 0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFC, - 0xB3,0x31,0x2F,0xA7,0xE2,0x3E,0xE7,0xE4,0x98,0x8E, /* b */ - 0x05,0x6B,0xE3,0xF8,0x2D,0x19,0x18,0x1D,0x9C,0x6E, - 0xFE,0x81,0x41,0x12,0x03,0x14,0x08,0x8F,0x50,0x13, - 0x87,0x5A,0xC6,0x56,0x39,0x8D,0x8A,0x2E,0xD1,0x9D, - 0x2A,0x85,0xC8,0xED,0xD3,0xEC,0x2A,0xEF, - 0xAA,0x87,0xCA,0x22,0xBE,0x8B,0x05,0x37,0x8E,0xB1, /* x */ - 0xC7,0x1E,0xF3,0x20,0xAD,0x74,0x6E,0x1D,0x3B,0x62, - 0x8B,0xA7,0x9B,0x98,0x59,0xF7,0x41,0xE0,0x82,0x54, - 0x2A,0x38,0x55,0x02,0xF2,0x5D,0xBF,0x55,0x29,0x6C, - 0x3A,0x54,0x5E,0x38,0x72,0x76,0x0A,0xB7, - 0x36,0x17,0xde,0x4a,0x96,0x26,0x2c,0x6f,0x5d,0x9e, /* y */ - 0x98,0xbf,0x92,0x92,0xdc,0x29,0xf8,0xf4,0x1d,0xbd, - 0x28,0x9a,0x14,0x7c,0xe9,0xda,0x31,0x13,0xb5,0xf0, - 0xb8,0xc0,0x0a,0x60,0xb1,0xce,0x1d,0x7e,0x81,0x9d, - 0x7a,0x43,0x1d,0x7c,0x90,0xea,0x0e,0x5f, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xC7,0x63,0x4D,0x81,0xF4,0x37, - 0x2D,0xDF,0x58,0x1A,0x0D,0xB2,0x48,0xB0,0xA7,0x7A, - 0xEC,0xEC,0x19,0x6A,0xCC,0xC5,0x29,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+66*6]; } - _EC_NIST_PRIME_521 = { - { NID_X9_62_prime_field,20,66,1 }, - { 0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC, /* seed */ - 0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA, - - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, - 0x00,0x51,0x95,0x3E,0xB9,0x61,0x8E,0x1C,0x9A,0x1F, /* b */ - 0x92,0x9A,0x21,0xA0,0xB6,0x85,0x40,0xEE,0xA2,0xDA, - 0x72,0x5B,0x99,0xB3,0x15,0xF3,0xB8,0xB4,0x89,0x91, - 0x8E,0xF1,0x09,0xE1,0x56,0x19,0x39,0x51,0xEC,0x7E, - 0x93,0x7B,0x16,0x52,0xC0,0xBD,0x3B,0xB1,0xBF,0x07, - 0x35,0x73,0xDF,0x88,0x3D,0x2C,0x34,0xF1,0xEF,0x45, - 0x1F,0xD4,0x6B,0x50,0x3F,0x00, - 0x00,0xC6,0x85,0x8E,0x06,0xB7,0x04,0x04,0xE9,0xCD, /* x */ - 0x9E,0x3E,0xCB,0x66,0x23,0x95,0xB4,0x42,0x9C,0x64, - 0x81,0x39,0x05,0x3F,0xB5,0x21,0xF8,0x28,0xAF,0x60, - 0x6B,0x4D,0x3D,0xBA,0xA1,0x4B,0x5E,0x77,0xEF,0xE7, - 0x59,0x28,0xFE,0x1D,0xC1,0x27,0xA2,0xFF,0xA8,0xDE, - 0x33,0x48,0xB3,0xC1,0x85,0x6A,0x42,0x9B,0xF9,0x7E, - 0x7E,0x31,0xC2,0xE5,0xBD,0x66, - 0x01,0x18,0x39,0x29,0x6a,0x78,0x9a,0x3b,0xc0,0x04, /* y */ - 0x5c,0x8a,0x5f,0xb4,0x2c,0x7d,0x1b,0xd9,0x98,0xf5, - 0x44,0x49,0x57,0x9b,0x44,0x68,0x17,0xaf,0xbd,0x17, - 0x27,0x3e,0x66,0x2c,0x97,0xee,0x72,0x99,0x5e,0xf4, - 0x26,0x40,0xc5,0x50,0xb9,0x01,0x3f,0xad,0x07,0x61, - 0x35,0x3c,0x70,0x86,0xa2,0x72,0xc2,0x40,0x88,0xbe, - 0x94,0x76,0x9f,0xd1,0x66,0x50, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFA,0x51,0x86,0x87,0x83,0xBF,0x2F, - 0x96,0x6B,0x7F,0xCC,0x01,0x48,0xF7,0x09,0xA5,0xD0, - 0x3B,0xB5,0xC9,0xB8,0x89,0x9C,0x47,0xAE,0xBB,0x6F, - 0xB7,0x1E,0x91,0x38,0x64,0x09 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_NIST_PRIME_192 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0x30, 0x45, 0xAE, 0x6F, 0xC8, 0x42, 0x2F, 0x64, 0xED, 0x57, /* seed */ + 0x95, 0x28, 0xD3, 0x81, 0x20, 0xEA, 0xE1, 0x21, 0x96, 0xD5, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0x64, 0x21, 0x05, 0x19, 0xE5, 0x9C, 0x80, 0xE7, 0x0F, 0xA7, /* b */ + 0xE9, 0xAB, 0x72, 0x24, 0x30, 0x49, 0xFE, 0xB8, 0xDE, 0xEC, + 0xC1, 0x46, 0xB9, 0xB1, + 0x18, 0x8D, 0xA8, 0x0E, 0xB0, 0x30, 0x90, 0xF6, 0x7C, 0xBF, /* x */ + 0x20, 0xEB, 0x43, 0xA1, 0x88, 0x00, 0xF4, 0xFF, 0x0A, 0xFD, + 0x82, 0xFF, 0x10, 0x12, + 0x07, 0x19, 0x2b, 0x95, 0xff, 0xc8, 0xda, 0x78, 0x63, 0x10, /* y */ + 0x11, 0xed, 0x6b, 0x24, 0xcd, 0xd5, 0x73, 0xf9, 0x77, 0xa1, + 0x1e, 0x79, 0x48, 0x11, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x99, 0xDE, 0xF8, 0x36, 0x14, 0x6B, 0xC9, 0xB1, + 0xB4, 0xD2, 0x28, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 28 * 6]; +} + _EC_NIST_PRIME_224 = { + { + NID_X9_62_prime_field, 20, 28, 1 + }, + { + 0xBD, 0x71, 0x34, 0x47, 0x99, 0xD5, 0xC7, 0xFC, 0xDC, 0x45, /* seed */ + 0xB5, 0x9F, 0xA3, 0xB9, 0xAB, 0x8F, 0x6A, 0x94, 0x8B, 0xC5, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4, + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21, + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, + 0x13, 0xDD, 0x29, 0x45, 0x5C, 0x5C, 0x2A, 0x3D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 48 * 6]; +} + _EC_NIST_PRIME_384 = { + { + NID_X9_62_prime_field, 20, 48, 1 + }, + { + 0xA3, 0x35, 0x92, 0x6A, 0xA3, 0x19, 0xA2, 0x7A, 0x1D, 0x00, /* seed */ + 0x89, 0x6A, 0x67, 0x73, 0xA4, 0x82, 0x7A, 0xCD, 0xAC, 0x73, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC, + 0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, /* b */ + 0x05, 0x6B, 0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, + 0xFE, 0x81, 0x41, 0x12, 0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, + 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D, 0x8A, 0x2E, 0xD1, 0x9D, + 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF, + 0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, /* x */ + 0xC7, 0x1E, 0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, + 0x8B, 0xA7, 0x9B, 0x98, 0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, + 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D, 0xBF, 0x55, 0x29, 0x6C, + 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7, + 0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, /* y */ + 0x98, 0xbf, 0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, + 0x28, 0x9a, 0x14, 0x7c, 0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, + 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce, 0x1d, 0x7e, 0x81, 0x9d, + 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, + 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2, 0x48, 0xB0, 0xA7, 0x7A, + 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 66 * 6]; +} + _EC_NIST_PRIME_521 = { + { + NID_X9_62_prime_field, 20, 66, 1 + }, + { + 0xD0, 0x9E, 0x88, 0x00, 0x29, 0x1C, 0xB8, 0x53, 0x96, 0xCC, /* seed */ + 0x67, 0x17, 0x39, 0x32, 0x84, 0xAA, 0xA0, 0xDA, 0x64, 0xBA, + + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + 0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, /* b */ + 0x92, 0x9A, 0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, + 0x72, 0x5B, 0x99, 0xB3, 0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, + 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19, 0x39, 0x51, 0xEC, 0x7E, + 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1, 0xBF, 0x07, + 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45, + 0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00, + 0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, /* x */ + 0x9E, 0x3E, 0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, + 0x81, 0x39, 0x05, 0x3F, 0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, + 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B, 0x5E, 0x77, 0xEF, 0xE7, + 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF, 0xA8, 0xDE, + 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E, + 0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66, + 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x04, /* y */ + 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, + 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, + 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, + 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, + 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, + 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86, 0x87, 0x83, 0xBF, 0x2F, + 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09, 0xA5, 0xD0, + 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F, + 0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09 + } +}; /* the x9.62 prime curves (minus the nist prime curves) */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_PRIME_192V2 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0x31,0xA9,0x2E,0xE2,0x02,0x9F,0xD1,0x0D,0x90,0x1B, /* seed */ - 0x11,0x3E,0x99,0x07,0x10,0xF0,0xD2,0x1A,0xC6,0xB6, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0xCC,0x22,0xD6,0xDF,0xB9,0x5C,0x6B,0x25,0xE4,0x9C, /* b */ - 0x0D,0x63,0x64,0xA4,0xE5,0x98,0x0C,0x39,0x3A,0xA2, - 0x16,0x68,0xD9,0x53, - 0xEE,0xA2,0xBA,0xE7,0xE1,0x49,0x78,0x42,0xF2,0xDE, /* x */ - 0x77,0x69,0xCF,0xE9,0xC9,0x89,0xC0,0x72,0xAD,0x69, - 0x6F,0x48,0x03,0x4A, - 0x65,0x74,0xd1,0x1d,0x69,0xb6,0xec,0x7a,0x67,0x2b, /* y */ - 0xb8,0x2a,0x08,0x3d,0xf2,0xf2,0xb0,0x84,0x7d,0xe9, - 0x70,0xb2,0xde,0x15, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFE,0x5F,0xB1,0xA7,0x24,0xDC,0x80,0x41,0x86, - 0x48,0xD8,0xDD,0x31 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_PRIME_192V3 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0xC4,0x69,0x68,0x44,0x35,0xDE,0xB3,0x78,0xC4,0xB6, /* seed */ - 0x5C,0xA9,0x59,0x1E,0x2A,0x57,0x63,0x05,0x9A,0x2E, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0x22,0x12,0x3D,0xC2,0x39,0x5A,0x05,0xCA,0xA7,0x42, /* b */ - 0x3D,0xAE,0xCC,0xC9,0x47,0x60,0xA7,0xD4,0x62,0x25, - 0x6B,0xD5,0x69,0x16, - 0x7D,0x29,0x77,0x81,0x00,0xC6,0x5A,0x1D,0xA1,0x78, /* x */ - 0x37,0x16,0x58,0x8D,0xCE,0x2B,0x8B,0x4A,0xEE,0x8E, - 0x22,0x8F,0x18,0x96, - 0x38,0xa9,0x0f,0x22,0x63,0x73,0x37,0x33,0x4b,0x49, /* y */ - 0xdc,0xb6,0x6a,0x6d,0xc8,0xf9,0x97,0x8a,0xca,0x76, - 0x48,0xa9,0x43,0xb0, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7A,0x62,0xD0,0x31,0xC8,0x3F,0x42,0x94, - 0xF6,0x40,0xEC,0x13 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V1 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0xE4,0x3B,0xB4,0x60,0xF0,0xB8,0x0C,0xC0,0xC0,0xB0, /* seed */ - 0x75,0x79,0x8E,0x94,0x80,0x60,0xF8,0x32,0x1B,0x7D, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x6B,0x01,0x6C,0x3B,0xDC,0xF1,0x89,0x41,0xD0,0xD6, /* b */ - 0x54,0x92,0x14,0x75,0xCA,0x71,0xA9,0xDB,0x2F,0xB2, - 0x7D,0x1D,0x37,0x79,0x61,0x85,0xC2,0x94,0x2C,0x0A, - - 0x0F,0xFA,0x96,0x3C,0xDC,0xA8,0x81,0x6C,0xCC,0x33, /* x */ - 0xB8,0x64,0x2B,0xED,0xF9,0x05,0xC3,0xD3,0x58,0x57, - 0x3D,0x3F,0x27,0xFB,0xBD,0x3B,0x3C,0xB9,0xAA,0xAF, - - 0x7d,0xeb,0xe8,0xe4,0xe9,0x0a,0x5d,0xae,0x6e,0x40, /* y */ - 0x54,0xca,0x53,0x0b,0xa0,0x46,0x54,0xb3,0x68,0x18, - 0xce,0x22,0x6b,0x39,0xfc,0xcb,0x7b,0x02,0xf1,0xae, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0x9E,0x5E,0x9A,0x9F,0x5D, - 0x90,0x71,0xFB,0xD1,0x52,0x26,0x88,0x90,0x9D,0x0B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V2 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0xE8,0xB4,0x01,0x16,0x04,0x09,0x53,0x03,0xCA,0x3B, /* seed */ - 0x80,0x99,0x98,0x2B,0xE0,0x9F,0xCB,0x9A,0xE6,0x16, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x61,0x7F,0xAB,0x68,0x32,0x57,0x6C,0xBB,0xFE,0xD5, /* b */ - 0x0D,0x99,0xF0,0x24,0x9C,0x3F,0xEE,0x58,0xB9,0x4B, - 0xA0,0x03,0x8C,0x7A,0xE8,0x4C,0x8C,0x83,0x2F,0x2C, - - 0x38,0xAF,0x09,0xD9,0x87,0x27,0x70,0x51,0x20,0xC9, /* x */ - 0x21,0xBB,0x5E,0x9E,0x26,0x29,0x6A,0x3C,0xDC,0xF2, - 0xF3,0x57,0x57,0xA0,0xEA,0xFD,0x87,0xB8,0x30,0xE7, - - 0x5b,0x01,0x25,0xe4,0xdb,0xea,0x0e,0xc7,0x20,0x6d, /* y */ - 0xa0,0xfc,0x01,0xd9,0xb0,0x81,0x32,0x9f,0xb5,0x55, - 0xde,0x6e,0xf4,0x60,0x23,0x7d,0xff,0x8b,0xe4,0xba, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x80,0x00,0x00,0xCF,0xA7,0xE8,0x59,0x43, - 0x77,0xD4,0x14,0xC0,0x38,0x21,0xBC,0x58,0x20,0x63 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V3 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0x7D,0x73,0x74,0x16,0x8F,0xFE,0x34,0x71,0xB6,0x0A, /* seed */ - 0x85,0x76,0x86,0xA1,0x94,0x75,0xD3,0xBF,0xA2,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x25,0x57,0x05,0xFA,0x2A,0x30,0x66,0x54,0xB1,0xF4, /* b */ - 0xCB,0x03,0xD6,0xA7,0x50,0xA3,0x0C,0x25,0x01,0x02, - 0xD4,0x98,0x87,0x17,0xD9,0xBA,0x15,0xAB,0x6D,0x3E, - - 0x67,0x68,0xAE,0x8E,0x18,0xBB,0x92,0xCF,0xCF,0x00, /* x */ - 0x5C,0x94,0x9A,0xA2,0xC6,0xD9,0x48,0x53,0xD0,0xE6, - 0x60,0xBB,0xF8,0x54,0xB1,0xC9,0x50,0x5F,0xE9,0x5A, - - 0x16,0x07,0xe6,0x89,0x8f,0x39,0x0c,0x06,0xbc,0x1d, /* y */ - 0x55,0x2b,0xad,0x22,0x6f,0x3b,0x6f,0xcf,0xe4,0x8b, - 0x6e,0x81,0x84,0x99,0xaf,0x18,0xe3,0xed,0x6c,0xf3, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0x97,0x5D,0xEB,0x41,0xB3, - 0xA6,0x05,0x7C,0x3C,0x43,0x21,0x46,0x52,0x65,0x51 } - }; - - -static const struct { EC_CURVE_DATA h; unsigned char data[20+32*6]; } - _EC_X9_62_PRIME_256V1 = { - { NID_X9_62_prime_field,20,32,1 }, - { 0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66, /* seed */ - 0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90, - - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFC, - 0x5A,0xC6,0x35,0xD8,0xAA,0x3A,0x93,0xE7,0xB3,0xEB, /* b */ - 0xBD,0x55,0x76,0x98,0x86,0xBC,0x65,0x1D,0x06,0xB0, - 0xCC,0x53,0xB0,0xF6,0x3B,0xCE,0x3C,0x3E,0x27,0xD2, - 0x60,0x4B, - 0x6B,0x17,0xD1,0xF2,0xE1,0x2C,0x42,0x47,0xF8,0xBC, /* x */ - 0xE6,0xE5,0x63,0xA4,0x40,0xF2,0x77,0x03,0x7D,0x81, - 0x2D,0xEB,0x33,0xA0,0xF4,0xA1,0x39,0x45,0xD8,0x98, - 0xC2,0x96, - 0x4f,0xe3,0x42,0xe2,0xfe,0x1a,0x7f,0x9b,0x8e,0xe7, /* y */ - 0xeb,0x4a,0x7c,0x0f,0x9e,0x16,0x2b,0xce,0x33,0x57, - 0x6b,0x31,0x5e,0xce,0xcb,0xb6,0x40,0x68,0x37,0xbf, - 0x51,0xf5, - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xBC,0xE6,0xFA,0xAD, - 0xA7,0x17,0x9E,0x84,0xF3,0xB9,0xCA,0xC2,0xFC,0x63, - 0x25,0x51 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_PRIME_192V2 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0x31, 0xA9, 0x2E, 0xE2, 0x02, 0x9F, 0xD1, 0x0D, 0x90, 0x1B, /* seed */ + 0x11, 0x3E, 0x99, 0x07, 0x10, 0xF0, 0xD2, 0x1A, 0xC6, 0xB6, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0xCC, 0x22, 0xD6, 0xDF, 0xB9, 0x5C, 0x6B, 0x25, 0xE4, 0x9C, /* b */ + 0x0D, 0x63, 0x64, 0xA4, 0xE5, 0x98, 0x0C, 0x39, 0x3A, 0xA2, + 0x16, 0x68, 0xD9, 0x53, + 0xEE, 0xA2, 0xBA, 0xE7, 0xE1, 0x49, 0x78, 0x42, 0xF2, 0xDE, /* x */ + 0x77, 0x69, 0xCF, 0xE9, 0xC9, 0x89, 0xC0, 0x72, 0xAD, 0x69, + 0x6F, 0x48, 0x03, 0x4A, + 0x65, 0x74, 0xd1, 0x1d, 0x69, 0xb6, 0xec, 0x7a, 0x67, 0x2b, /* y */ + 0xb8, 0x2a, 0x08, 0x3d, 0xf2, 0xf2, 0xb0, 0x84, 0x7d, 0xe9, + 0x70, 0xb2, 0xde, 0x15, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFE, 0x5F, 0xB1, 0xA7, 0x24, 0xDC, 0x80, 0x41, 0x86, + 0x48, 0xD8, 0xDD, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_PRIME_192V3 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0xC4, 0x69, 0x68, 0x44, 0x35, 0xDE, 0xB3, 0x78, 0xC4, 0xB6, /* seed */ + 0x5C, 0xA9, 0x59, 0x1E, 0x2A, 0x57, 0x63, 0x05, 0x9A, 0x2E, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0x22, 0x12, 0x3D, 0xC2, 0x39, 0x5A, 0x05, 0xCA, 0xA7, 0x42, /* b */ + 0x3D, 0xAE, 0xCC, 0xC9, 0x47, 0x60, 0xA7, 0xD4, 0x62, 0x25, + 0x6B, 0xD5, 0x69, 0x16, + 0x7D, 0x29, 0x77, 0x81, 0x00, 0xC6, 0x5A, 0x1D, 0xA1, 0x78, /* x */ + 0x37, 0x16, 0x58, 0x8D, 0xCE, 0x2B, 0x8B, 0x4A, 0xEE, 0x8E, + 0x22, 0x8F, 0x18, 0x96, + 0x38, 0xa9, 0x0f, 0x22, 0x63, 0x73, 0x37, 0x33, 0x4b, 0x49, /* y */ + 0xdc, 0xb6, 0x6a, 0x6d, 0xc8, 0xf9, 0x97, 0x8a, 0xca, 0x76, + 0x48, 0xa9, 0x43, 0xb0, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7A, 0x62, 0xD0, 0x31, 0xC8, 0x3F, 0x42, 0x94, + 0xF6, 0x40, 0xEC, 0x13 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V1 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0xE4, 0x3B, 0xB4, 0x60, 0xF0, 0xB8, 0x0C, 0xC0, 0xC0, 0xB0, /* seed */ + 0x75, 0x79, 0x8E, 0x94, 0x80, 0x60, 0xF8, 0x32, 0x1B, 0x7D, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x6B, 0x01, 0x6C, 0x3B, 0xDC, 0xF1, 0x89, 0x41, 0xD0, 0xD6, /* b */ + 0x54, 0x92, 0x14, 0x75, 0xCA, 0x71, 0xA9, 0xDB, 0x2F, 0xB2, + 0x7D, 0x1D, 0x37, 0x79, 0x61, 0x85, 0xC2, 0x94, 0x2C, 0x0A, + + 0x0F, 0xFA, 0x96, 0x3C, 0xDC, 0xA8, 0x81, 0x6C, 0xCC, 0x33, /* x */ + 0xB8, 0x64, 0x2B, 0xED, 0xF9, 0x05, 0xC3, 0xD3, 0x58, 0x57, + 0x3D, 0x3F, 0x27, 0xFB, 0xBD, 0x3B, 0x3C, 0xB9, 0xAA, 0xAF, + + 0x7d, 0xeb, 0xe8, 0xe4, 0xe9, 0x0a, 0x5d, 0xae, 0x6e, 0x40, /* y */ + 0x54, 0xca, 0x53, 0x0b, 0xa0, 0x46, 0x54, 0xb3, 0x68, 0x18, + 0xce, 0x22, 0x6b, 0x39, 0xfc, 0xcb, 0x7b, 0x02, 0xf1, 0xae, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0x9E, 0x5E, 0x9A, 0x9F, 0x5D, + 0x90, 0x71, 0xFB, 0xD1, 0x52, 0x26, 0x88, 0x90, 0x9D, 0x0B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V2 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0xE8, 0xB4, 0x01, 0x16, 0x04, 0x09, 0x53, 0x03, 0xCA, 0x3B, /* seed */ + 0x80, 0x99, 0x98, 0x2B, 0xE0, 0x9F, 0xCB, 0x9A, 0xE6, 0x16, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x61, 0x7F, 0xAB, 0x68, 0x32, 0x57, 0x6C, 0xBB, 0xFE, 0xD5, /* b */ + 0x0D, 0x99, 0xF0, 0x24, 0x9C, 0x3F, 0xEE, 0x58, 0xB9, 0x4B, + 0xA0, 0x03, 0x8C, 0x7A, 0xE8, 0x4C, 0x8C, 0x83, 0x2F, 0x2C, + + 0x38, 0xAF, 0x09, 0xD9, 0x87, 0x27, 0x70, 0x51, 0x20, 0xC9, /* x */ + 0x21, 0xBB, 0x5E, 0x9E, 0x26, 0x29, 0x6A, 0x3C, 0xDC, 0xF2, + 0xF3, 0x57, 0x57, 0xA0, 0xEA, 0xFD, 0x87, 0xB8, 0x30, 0xE7, + + 0x5b, 0x01, 0x25, 0xe4, 0xdb, 0xea, 0x0e, 0xc7, 0x20, 0x6d, /* y */ + 0xa0, 0xfc, 0x01, 0xd9, 0xb0, 0x81, 0x32, 0x9f, 0xb5, 0x55, + 0xde, 0x6e, 0xf4, 0x60, 0x23, 0x7d, 0xff, 0x8b, 0xe4, 0xba, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x80, 0x00, 0x00, 0xCF, 0xA7, 0xE8, 0x59, 0x43, + 0x77, 0xD4, 0x14, 0xC0, 0x38, 0x21, 0xBC, 0x58, 0x20, 0x63 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V3 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0x7D, 0x73, 0x74, 0x16, 0x8F, 0xFE, 0x34, 0x71, 0xB6, 0x0A, /* seed */ + 0x85, 0x76, 0x86, 0xA1, 0x94, 0x75, 0xD3, 0xBF, 0xA2, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x25, 0x57, 0x05, 0xFA, 0x2A, 0x30, 0x66, 0x54, 0xB1, 0xF4, /* b */ + 0xCB, 0x03, 0xD6, 0xA7, 0x50, 0xA3, 0x0C, 0x25, 0x01, 0x02, + 0xD4, 0x98, 0x87, 0x17, 0xD9, 0xBA, 0x15, 0xAB, 0x6D, 0x3E, + + 0x67, 0x68, 0xAE, 0x8E, 0x18, 0xBB, 0x92, 0xCF, 0xCF, 0x00, /* x */ + 0x5C, 0x94, 0x9A, 0xA2, 0xC6, 0xD9, 0x48, 0x53, 0xD0, 0xE6, + 0x60, 0xBB, 0xF8, 0x54, 0xB1, 0xC9, 0x50, 0x5F, 0xE9, 0x5A, + + 0x16, 0x07, 0xe6, 0x89, 0x8f, 0x39, 0x0c, 0x06, 0xbc, 0x1d, /* y */ + 0x55, 0x2b, 0xad, 0x22, 0x6f, 0x3b, 0x6f, 0xcf, 0xe4, 0x8b, + 0x6e, 0x81, 0x84, 0x99, 0xaf, 0x18, 0xe3, 0xed, 0x6c, 0xf3, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0x97, 0x5D, 0xEB, 0x41, 0xB3, + 0xA6, 0x05, 0x7C, 0x3C, 0x43, 0x21, 0x46, 0x52, 0x65, 0x51 + } +}; + + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 32 * 6]; +} + _EC_X9_62_PRIME_256V1 = { + { + NID_X9_62_prime_field, 20, 32, 1 + }, + { + 0xC4, 0x9D, 0x36, 0x08, 0x86, 0xE7, 0x04, 0x93, 0x6A, 0x66, /* seed */ + 0x78, 0xE1, 0x13, 0x9D, 0x26, 0xB7, 0x81, 0x9F, 0x7E, 0x90, + + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFC, + 0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, /* b */ + 0xBD, 0x55, 0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, + 0xCC, 0x53, 0xB0, 0xF6, 0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, + 0x60, 0x4B, + 0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, /* x */ + 0xE6, 0xE5, 0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, + 0x2D, 0xEB, 0x33, 0xA0, 0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, + 0xC2, 0x96, + 0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, 0x8e, 0xe7, /* y */ + 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, 0x2b, 0xce, 0x33, 0x57, + 0x6b, 0x31, 0x5e, 0xce, 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, + 0x51, 0xf5, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, + 0xA7, 0x17, 0x9E, 0x84, 0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, + 0x25, 0x51 + } +}; /* the secg prime curves (minus the nist and x9.62 prime curves) */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } - _EC_SECG_PRIME_112R1 = { - { NID_X9_62_prime_field,20,14,1 }, - { 0x00,0xF5,0x0B,0x02,0x8E,0x4D,0x69,0x6E,0x67,0x68, /* seed */ - 0x75,0x61,0x51,0x75,0x29,0x04,0x72,0x78,0x3F,0xB1, - - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ - 0xBE,0xAD,0x20,0x8B, - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* a */ - 0xBE,0xAD,0x20,0x88, - 0x65,0x9E,0xF8,0xBA,0x04,0x39,0x16,0xEE,0xDE,0x89, /* b */ - 0x11,0x70,0x2B,0x22, - 0x09,0x48,0x72,0x39,0x99,0x5A,0x5E,0xE7,0x6B,0x55, /* x */ - 0xF9,0xC2,0xF0,0x98, - 0xa8,0x9c,0xe5,0xaf,0x87,0x24,0xc0,0xa2,0x3e,0x0e, /* y */ - 0x0f,0xf7,0x75,0x00, - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x76,0x28,0xDF, /* order */ - 0xAC,0x65,0x61,0xC5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } - _EC_SECG_PRIME_112R2 = { - { NID_X9_62_prime_field,20,14,4 }, - { 0x00,0x27,0x57,0xA1,0x11,0x4D,0x69,0x6E,0x67,0x68, /* seed */ - 0x75,0x61,0x51,0x75,0x53,0x16,0xC0,0x5E,0x0B,0xD4, - - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ - 0xBE,0xAD,0x20,0x8B, - 0x61,0x27,0xC2,0x4C,0x05,0xF3,0x8A,0x0A,0xAA,0xF6, /* a */ - 0x5C,0x0E,0xF0,0x2C, - 0x51,0xDE,0xF1,0x81,0x5D,0xB5,0xED,0x74,0xFC,0xC3, /* b */ - 0x4C,0x85,0xD7,0x09, - 0x4B,0xA3,0x0A,0xB5,0xE8,0x92,0xB4,0xE1,0x64,0x9D, /* x */ - 0xD0,0x92,0x86,0x43, - 0xad,0xcd,0x46,0xf5,0x88,0x2e,0x37,0x47,0xde,0xf3, /* y */ - 0x6e,0x95,0x6e,0x97, - 0x36,0xDF,0x0A,0xAF,0xD8,0xB8,0xD7,0x59,0x7C,0xA1, /* order */ - 0x05,0x20,0xD0,0x4B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } - _EC_SECG_PRIME_128R1 = { - { NID_X9_62_prime_field,20,16,1 }, - { 0x00,0x0E,0x0D,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0x0C,0xC0,0x3A,0x44,0x73,0xD0,0x36,0x79, - - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, - 0xE8,0x75,0x79,0xC1,0x10,0x79,0xF4,0x3D,0xD8,0x24, /* b */ - 0x99,0x3C,0x2C,0xEE,0x5E,0xD3, - 0x16,0x1F,0xF7,0x52,0x8B,0x89,0x9B,0x2D,0x0C,0x28, /* x */ - 0x60,0x7C,0xA5,0x2C,0x5B,0x86, - 0xcf,0x5a,0xc8,0x39,0x5b,0xaf,0xeb,0x13,0xc0,0x2d, /* y */ - 0xa2,0x92,0xdd,0xed,0x7a,0x83, - 0xFF,0xFF,0xFF,0xFE,0x00,0x00,0x00,0x00,0x75,0xA3, /* order */ - 0x0D,0x1B,0x90,0x38,0xA1,0x15 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } - _EC_SECG_PRIME_128R2 = { - { NID_X9_62_prime_field,20,16,4 }, - { 0x00,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75, /* seed */ - 0x12,0xD8,0xF0,0x34,0x31,0xFC,0xE6,0x3B,0x88,0xF4, - - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xD6,0x03,0x19,0x98,0xD1,0xB3,0xBB,0xFE,0xBF,0x59, /* a */ - 0xCC,0x9B,0xBF,0xF9,0xAE,0xE1, - 0x5E,0xEE,0xFC,0xA3,0x80,0xD0,0x29,0x19,0xDC,0x2C, /* b */ - 0x65,0x58,0xBB,0x6D,0x8A,0x5D, - 0x7B,0x6A,0xA5,0xD8,0x5E,0x57,0x29,0x83,0xE6,0xFB, /* x */ - 0x32,0xA7,0xCD,0xEB,0xC1,0x40, - 0x27,0xb6,0x91,0x6a,0x89,0x4d,0x3a,0xee,0x71,0x06, /* y */ - 0xfe,0x80,0x5f,0xc3,0x4b,0x44, - 0x3F,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xBE,0x00, /* order */ - 0x24,0x72,0x06,0x13,0xB5,0xA3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_SECG_PRIME_160K1 = { - { NID_X9_62_prime_field,0,21,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x73, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x07, - 0x00,0x3B,0x4C,0x38,0x2C,0xE3,0x7A,0xA1,0x92,0xA4, /* x */ - 0x01,0x9E,0x76,0x30,0x36,0xF4,0xF5,0xDD,0x4D,0x7E, - 0xBB, - 0x00,0x93,0x8c,0xf9,0x35,0x31,0x8f,0xdc,0xed,0x6b, /* y */ - 0xc2,0x82,0x86,0x53,0x17,0x33,0xc3,0xf0,0x3c,0x4f, - 0xee, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xB8,0xFA,0x16,0xDF,0xAB,0x9A,0xCA,0x16,0xB6, - 0xB3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_SECG_PRIME_160R1 = { - { NID_X9_62_prime_field,20,21,1 }, - { 0x10,0x53,0xCD,0xE4,0x2C,0x14,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x53,0x3B,0xF3,0xF8,0x33,0x45, - - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, - 0xFF, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, - 0xFC, - 0x00,0x1C,0x97,0xBE,0xFC,0x54,0xBD,0x7A,0x8B,0x65, /* b */ - 0xAC,0xF8,0x9F,0x81,0xD4,0xD4,0xAD,0xC5,0x65,0xFA, - 0x45, - 0x00,0x4A,0x96,0xB5,0x68,0x8E,0xF5,0x73,0x28,0x46, /* x */ - 0x64,0x69,0x89,0x68,0xC3,0x8B,0xB9,0x13,0xCB,0xFC, - 0x82, - 0x00,0x23,0xa6,0x28,0x55,0x31,0x68,0x94,0x7d,0x59, /* y */ - 0xdc,0xc9,0x12,0x04,0x23,0x51,0x37,0x7a,0xc5,0xfb, - 0x32, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xF4,0xC8,0xF9,0x27,0xAE,0xD3,0xCA,0x75,0x22, - 0x57 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_SECG_PRIME_160R2 = { - { NID_X9_62_prime_field,20,21,1 }, - { 0xB9,0x9B,0x99,0xB0,0x99,0xB3,0x23,0xE0,0x27,0x09, /* seed */ - 0xA4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x51, - - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x73, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x70, - 0x00,0xB4,0xE1,0x34,0xD3,0xFB,0x59,0xEB,0x8B,0xAB, /* b */ - 0x57,0x27,0x49,0x04,0x66,0x4D,0x5A,0xF5,0x03,0x88, - 0xBA, - 0x00,0x52,0xDC,0xB0,0x34,0x29,0x3A,0x11,0x7E,0x1F, /* x */ - 0x4F,0xF1,0x1B,0x30,0xF7,0x19,0x9D,0x31,0x44,0xCE, - 0x6D, - 0x00,0xfe,0xaf,0xfe,0xf2,0xe3,0x31,0xf2,0x96,0xe0, /* y */ - 0x71,0xfa,0x0d,0xf9,0x98,0x2c,0xfe,0xa7,0xd4,0x3f, - 0x2e, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x35,0x1E,0xE7,0x86,0xA8,0x18,0xF3,0xA1,0xA1, - 0x6B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_SECG_PRIME_192K1 = { - { NID_X9_62_prime_field,0,24,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xFF,0xFF,0xEE,0x37, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x03, - 0xDB,0x4F,0xF1,0x0E,0xC0,0x57,0xE9,0xAE,0x26,0xB0, /* x */ - 0x7D,0x02,0x80,0xB7,0xF4,0x34,0x1D,0xA5,0xD1,0xB1, - 0xEA,0xE0,0x6C,0x7D, - 0x9b,0x2f,0x2f,0x6d,0x9c,0x56,0x28,0xa7,0x84,0x41, /* y */ - 0x63,0xd0,0x15,0xbe,0x86,0x34,0x40,0x82,0xaa,0x88, - 0xd9,0x5e,0x2f,0x9d, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFE,0x26,0xF2,0xFC,0x17,0x0F,0x69,0x46,0x6A, - 0x74,0xDE,0xFD,0x8D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+29*6]; } - _EC_SECG_PRIME_224K1 = { - { NID_X9_62_prime_field,0,29,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xE5,0x6D, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x05, - 0x00,0xA1,0x45,0x5B,0x33,0x4D,0xF0,0x99,0xDF,0x30, /* x */ - 0xFC,0x28,0xA1,0x69,0xA4,0x67,0xE9,0xE4,0x70,0x75, - 0xA9,0x0F,0x7E,0x65,0x0E,0xB6,0xB7,0xA4,0x5C, - 0x00,0x7e,0x08,0x9f,0xed,0x7f,0xba,0x34,0x42,0x82, /* y */ - 0xca,0xfb,0xd6,0xf7,0xe3,0x19,0xf7,0xc0,0xb0,0xbd, - 0x59,0xe2,0xca,0x4b,0xdb,0x55,0x6d,0x61,0xa5, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x01,0xDC,0xE8,0xD2,0xEC,0x61, - 0x84,0xCA,0xF0,0xA9,0x71,0x76,0x9F,0xB1,0xF7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_SECG_PRIME_256K1 = { - { NID_X9_62_prime_field,0,32,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF, - 0xFC,0x2F, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x07, - 0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0, /* x */ - 0x62,0x95,0xCE,0x87,0x0B,0x07,0x02,0x9B,0xFC,0xDB, - 0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, - 0x17,0x98, - 0x48,0x3a,0xda,0x77,0x26,0xa3,0xc4,0x65,0x5d,0xa4, /* y */ - 0xfb,0xfc,0x0e,0x11,0x08,0xa8,0xfd,0x17,0xb4,0x48, - 0xa6,0x85,0x54,0x19,0x9c,0x47,0xd0,0x8f,0xfb,0x10, - 0xd4,0xb8, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6, - 0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,0x8C,0xD0,0x36, - 0x41,0x41 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} + _EC_SECG_PRIME_112R1 = { + { + NID_X9_62_prime_field, 20, 14, 1 + }, + { + 0x00, 0xF5, 0x0B, 0x02, 0x8E, 0x4D, 0x69, 0x6E, 0x67, 0x68, /* seed */ + 0x75, 0x61, 0x51, 0x75, 0x29, 0x04, 0x72, 0x78, 0x3F, 0xB1, + + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* p */ + 0xBE, 0xAD, 0x20, 0x8B, + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* a */ + 0xBE, 0xAD, 0x20, 0x88, + 0x65, 0x9E, 0xF8, 0xBA, 0x04, 0x39, 0x16, 0xEE, 0xDE, 0x89, /* b */ + 0x11, 0x70, 0x2B, 0x22, + 0x09, 0x48, 0x72, 0x39, 0x99, 0x5A, 0x5E, 0xE7, 0x6B, 0x55, /* x */ + 0xF9, 0xC2, 0xF0, 0x98, + 0xa8, 0x9c, 0xe5, 0xaf, 0x87, 0x24, 0xc0, 0xa2, 0x3e, 0x0e, /* y */ + 0x0f, 0xf7, 0x75, 0x00, + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x76, 0x28, 0xDF, /* order */ + 0xAC, 0x65, 0x61, 0xC5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} + _EC_SECG_PRIME_112R2 = { + { + NID_X9_62_prime_field, 20, 14, 4 + }, + { + 0x00, 0x27, 0x57, 0xA1, 0x11, 0x4D, 0x69, 0x6E, 0x67, 0x68, /* seed */ + 0x75, 0x61, 0x51, 0x75, 0x53, 0x16, 0xC0, 0x5E, 0x0B, 0xD4, + + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* p */ + 0xBE, 0xAD, 0x20, 0x8B, + 0x61, 0x27, 0xC2, 0x4C, 0x05, 0xF3, 0x8A, 0x0A, 0xAA, 0xF6, /* a */ + 0x5C, 0x0E, 0xF0, 0x2C, + 0x51, 0xDE, 0xF1, 0x81, 0x5D, 0xB5, 0xED, 0x74, 0xFC, 0xC3, /* b */ + 0x4C, 0x85, 0xD7, 0x09, + 0x4B, 0xA3, 0x0A, 0xB5, 0xE8, 0x92, 0xB4, 0xE1, 0x64, 0x9D, /* x */ + 0xD0, 0x92, 0x86, 0x43, + 0xad, 0xcd, 0x46, 0xf5, 0x88, 0x2e, 0x37, 0x47, 0xde, 0xf3, /* y */ + 0x6e, 0x95, 0x6e, 0x97, + 0x36, 0xDF, 0x0A, 0xAF, 0xD8, 0xB8, 0xD7, 0x59, 0x7C, 0xA1, /* order */ + 0x05, 0x20, 0xD0, 0x4B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} + _EC_SECG_PRIME_128R1 = { + { + NID_X9_62_prime_field, 20, 16, 1 + }, + { + 0x00, 0x0E, 0x0D, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0x0C, 0xC0, 0x3A, 0x44, 0x73, 0xD0, 0x36, 0x79, + + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + 0xE8, 0x75, 0x79, 0xC1, 0x10, 0x79, 0xF4, 0x3D, 0xD8, 0x24, /* b */ + 0x99, 0x3C, 0x2C, 0xEE, 0x5E, 0xD3, + 0x16, 0x1F, 0xF7, 0x52, 0x8B, 0x89, 0x9B, 0x2D, 0x0C, 0x28, /* x */ + 0x60, 0x7C, 0xA5, 0x2C, 0x5B, 0x86, + 0xcf, 0x5a, 0xc8, 0x39, 0x5b, 0xaf, 0xeb, 0x13, 0xc0, 0x2d, /* y */ + 0xa2, 0x92, 0xdd, 0xed, 0x7a, 0x83, + 0xFF, 0xFF, 0xFF, 0xFE, 0x00, 0x00, 0x00, 0x00, 0x75, 0xA3, /* order */ + 0x0D, 0x1B, 0x90, 0x38, 0xA1, 0x15 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} + _EC_SECG_PRIME_128R2 = { + { + NID_X9_62_prime_field, 20, 16, 4 + }, + { + 0x00, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, /* seed */ + 0x12, 0xD8, 0xF0, 0x34, 0x31, 0xFC, 0xE6, 0x3B, 0x88, 0xF4, + + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xD6, 0x03, 0x19, 0x98, 0xD1, 0xB3, 0xBB, 0xFE, 0xBF, 0x59, /* a */ + 0xCC, 0x9B, 0xBF, 0xF9, 0xAE, 0xE1, + 0x5E, 0xEE, 0xFC, 0xA3, 0x80, 0xD0, 0x29, 0x19, 0xDC, 0x2C, /* b */ + 0x65, 0x58, 0xBB, 0x6D, 0x8A, 0x5D, + 0x7B, 0x6A, 0xA5, 0xD8, 0x5E, 0x57, 0x29, 0x83, 0xE6, 0xFB, /* x */ + 0x32, 0xA7, 0xCD, 0xEB, 0xC1, 0x40, + 0x27, 0xb6, 0x91, 0x6a, 0x89, 0x4d, 0x3a, 0xee, 0x71, 0x06, /* y */ + 0xfe, 0x80, 0x5f, 0xc3, 0x4b, 0x44, + 0x3F, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xBE, 0x00, /* order */ + 0x24, 0x72, 0x06, 0x13, 0xB5, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_SECG_PRIME_160K1 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x73, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x07, + 0x00, 0x3B, 0x4C, 0x38, 0x2C, 0xE3, 0x7A, 0xA1, 0x92, 0xA4, /* x */ + 0x01, 0x9E, 0x76, 0x30, 0x36, 0xF4, 0xF5, 0xDD, 0x4D, 0x7E, + 0xBB, + 0x00, 0x93, 0x8c, 0xf9, 0x35, 0x31, 0x8f, 0xdc, 0xed, 0x6b, /* y */ + 0xc2, 0x82, 0x86, 0x53, 0x17, 0x33, 0xc3, 0xf0, 0x3c, 0x4f, + 0xee, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xB8, 0xFA, 0x16, 0xDF, 0xAB, 0x9A, 0xCA, 0x16, 0xB6, + 0xB3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_SECG_PRIME_160R1 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + 0x10, 0x53, 0xCD, 0xE4, 0x2C, 0x14, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x53, 0x3B, 0xF3, 0xF8, 0x33, 0x45, + + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, + 0xFF, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, + 0xFC, + 0x00, 0x1C, 0x97, 0xBE, 0xFC, 0x54, 0xBD, 0x7A, 0x8B, 0x65, /* b */ + 0xAC, 0xF8, 0x9F, 0x81, 0xD4, 0xD4, 0xAD, 0xC5, 0x65, 0xFA, + 0x45, + 0x00, 0x4A, 0x96, 0xB5, 0x68, 0x8E, 0xF5, 0x73, 0x28, 0x46, /* x */ + 0x64, 0x69, 0x89, 0x68, 0xC3, 0x8B, 0xB9, 0x13, 0xCB, 0xFC, + 0x82, + 0x00, 0x23, 0xa6, 0x28, 0x55, 0x31, 0x68, 0x94, 0x7d, 0x59, /* y */ + 0xdc, 0xc9, 0x12, 0x04, 0x23, 0x51, 0x37, 0x7a, 0xc5, 0xfb, + 0x32, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xF4, 0xC8, 0xF9, 0x27, 0xAE, 0xD3, 0xCA, 0x75, 0x22, + 0x57 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_SECG_PRIME_160R2 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + 0xB9, 0x9B, 0x99, 0xB0, 0x99, 0xB3, 0x23, 0xE0, 0x27, 0x09, /* seed */ + 0xA4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x51, + + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x73, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x70, + 0x00, 0xB4, 0xE1, 0x34, 0xD3, 0xFB, 0x59, 0xEB, 0x8B, 0xAB, /* b */ + 0x57, 0x27, 0x49, 0x04, 0x66, 0x4D, 0x5A, 0xF5, 0x03, 0x88, + 0xBA, + 0x00, 0x52, 0xDC, 0xB0, 0x34, 0x29, 0x3A, 0x11, 0x7E, 0x1F, /* x */ + 0x4F, 0xF1, 0x1B, 0x30, 0xF7, 0x19, 0x9D, 0x31, 0x44, 0xCE, + 0x6D, + 0x00, 0xfe, 0xaf, 0xfe, 0xf2, 0xe3, 0x31, 0xf2, 0x96, 0xe0, /* y */ + 0x71, 0xfa, 0x0d, 0xf9, 0x98, 0x2c, 0xfe, 0xa7, 0xd4, 0x3f, + 0x2e, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x35, 0x1E, 0xE7, 0x86, 0xA8, 0x18, 0xF3, 0xA1, 0xA1, + 0x6B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_SECG_PRIME_192K1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xFF, 0xFF, 0xEE, 0x37, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x03, + 0xDB, 0x4F, 0xF1, 0x0E, 0xC0, 0x57, 0xE9, 0xAE, 0x26, 0xB0, /* x */ + 0x7D, 0x02, 0x80, 0xB7, 0xF4, 0x34, 0x1D, 0xA5, 0xD1, 0xB1, + 0xEA, 0xE0, 0x6C, 0x7D, + 0x9b, 0x2f, 0x2f, 0x6d, 0x9c, 0x56, 0x28, 0xa7, 0x84, 0x41, /* y */ + 0x63, 0xd0, 0x15, 0xbe, 0x86, 0x34, 0x40, 0x82, 0xaa, 0x88, + 0xd9, 0x5e, 0x2f, 0x9d, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFE, 0x26, 0xF2, 0xFC, 0x17, 0x0F, 0x69, 0x46, 0x6A, + 0x74, 0xDE, 0xFD, 0x8D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 29 * 6]; +} + _EC_SECG_PRIME_224K1 = { + { + NID_X9_62_prime_field, 0, 29, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xE5, 0x6D, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x05, + 0x00, 0xA1, 0x45, 0x5B, 0x33, 0x4D, 0xF0, 0x99, 0xDF, 0x30, /* x */ + 0xFC, 0x28, 0xA1, 0x69, 0xA4, 0x67, 0xE9, 0xE4, 0x70, 0x75, + 0xA9, 0x0F, 0x7E, 0x65, 0x0E, 0xB6, 0xB7, 0xA4, 0x5C, + 0x00, 0x7e, 0x08, 0x9f, 0xed, 0x7f, 0xba, 0x34, 0x42, 0x82, /* y */ + 0xca, 0xfb, 0xd6, 0xf7, 0xe3, 0x19, 0xf7, 0xc0, 0xb0, 0xbd, + 0x59, 0xe2, 0xca, 0x4b, 0xdb, 0x55, 0x6d, 0x61, 0xa5, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x01, 0xDC, 0xE8, 0xD2, 0xEC, 0x61, + 0x84, 0xCA, 0xF0, 0xA9, 0x71, 0x76, 0x9F, 0xB1, 0xF7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_SECG_PRIME_256K1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, + 0xFC, 0x2F, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x07, + 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, /* x */ + 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, + 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, + 0x17, 0x98, + 0x48, 0x3a, 0xda, 0x77, 0x26, 0xa3, 0xc4, 0x65, 0x5d, 0xa4, /* y */ + 0xfb, 0xfc, 0x0e, 0x11, 0x08, 0xa8, 0xfd, 0x17, 0xb4, 0x48, + 0xa6, 0x85, 0x54, 0x19, 0x9c, 0x47, 0xd0, 0x8f, 0xfb, 0x10, + 0xd4, 0xb8, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, + 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, + 0x41, 0x41 + } +}; /* some wap/wtls curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } - _EC_WTLS_8 = { - { NID_X9_62_prime_field,0,15,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFD,0xE7, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x03, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x02, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xEC,0xEA, /* order */ - 0x55,0x1A,0xD8,0x37,0xE9 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_WTLS_9 = { - { NID_X9_62_prime_field,0,21,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFC,0x80, - 0x8F, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x03, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x02, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xCD,0xC9,0x8A,0xE0,0xE2,0xDE,0x57,0x4A,0xBF, - 0x33 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_WTLS_12 = { - { NID_X9_62_prime_field,0,28,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, - 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, - 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, - 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} + _EC_WTLS_8 = { + { + NID_X9_62_prime_field, 0, 15, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFD, 0xE7, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x02, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xEC, 0xEA, /* order */ + 0x55, 0x1A, 0xD8, 0x37, 0xE9 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_WTLS_9 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, 0x80, + 0x8F, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x02, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xCD, 0xC9, 0x8A, 0xE0, 0xE2, 0xDE, 0x57, 0x4A, 0xBF, + 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_WTLS_12 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4, + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21, + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, + 0x13, 0xDD, 0x29, 0x45, 0x5C, 0x5C, 0x2A, 0x3D + } +}; #ifndef OPENSSL_NO_EC2M /* characteristic two curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } - _EC_SECG_CHAR2_113R1 = { - { NID_X9_62_characteristic_two_field,20,15,2 }, - { 0x10,0xE7,0x23,0xAB,0x14,0xD6,0x96,0xE6,0x76,0x87, /* seed */ - 0x56,0x15,0x17,0x56,0xFE,0xBF,0x8F,0xCB,0x49,0xA9, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x30,0x88,0x25,0x0C,0xA6,0xE7,0xC7,0xFE,0x64, /* a */ - 0x9C,0xE8,0x58,0x20,0xF7, - 0x00,0xE8,0xBE,0xE4,0xD3,0xE2,0x26,0x07,0x44,0x18, /* b */ - 0x8B,0xE0,0xE9,0xC7,0x23, - 0x00,0x9D,0x73,0x61,0x6F,0x35,0xF4,0xAB,0x14,0x07, /* x */ - 0xD7,0x35,0x62,0xC1,0x0F, - 0x00,0xA5,0x28,0x30,0x27,0x79,0x58,0xEE,0x84,0xD1, /* y */ - 0x31,0x5E,0xD3,0x18,0x86, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0xD9,0xCC, /* order */ - 0xEC,0x8A,0x39,0xE5,0x6F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } - _EC_SECG_CHAR2_113R2 = { - { NID_X9_62_characteristic_two_field,20,15,2 }, - { 0x10,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, /* seed */ - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x5D, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x68,0x99,0x18,0xDB,0xEC,0x7E,0x5A,0x0D,0xD6, /* a */ - 0xDF,0xC0,0xAA,0x55,0xC7, - 0x00,0x95,0xE9,0xA9,0xEC,0x9B,0x29,0x7B,0xD4,0xBF, /* b */ - 0x36,0xE0,0x59,0x18,0x4F, - 0x01,0xA5,0x7A,0x6A,0x7B,0x26,0xCA,0x5E,0xF5,0x2F, /* x */ - 0xCD,0xB8,0x16,0x47,0x97, - 0x00,0xB3,0xAD,0xC9,0x4E,0xD1,0xFE,0x67,0x4C,0x06, /* y */ - 0xE6,0x95,0xBA,0xBA,0x1D, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x08,0x78, /* order */ - 0x9B,0x24,0x96,0xAF,0x93 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } - _EC_SECG_CHAR2_131R1 = { - { NID_X9_62_characteristic_two_field,20,17,2 }, - { 0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,0x98, /* seed */ - 0x5B,0xD3,0xAD,0xBA,0xDA,0x21,0xB4,0x3A,0x97,0xE2, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, - 0x07,0xA1,0x1B,0x09,0xA7,0x6B,0x56,0x21,0x44,0x41, /* a */ - 0x8F,0xF3,0xFF,0x8C,0x25,0x70,0xB8, - 0x02,0x17,0xC0,0x56,0x10,0x88,0x4B,0x63,0xB9,0xC6, /* b */ - 0xC7,0x29,0x16,0x78,0xF9,0xD3,0x41, - 0x00,0x81,0xBA,0xF9,0x1F,0xDF,0x98,0x33,0xC4,0x0F, /* x */ - 0x9C,0x18,0x13,0x43,0x63,0x83,0x99, - 0x07,0x8C,0x6E,0x7E,0xA3,0x8C,0x00,0x1F,0x73,0xC8, /* y */ - 0x13,0x4B,0x1B,0x4E,0xF9,0xE1,0x50, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x02,0x31, /* order */ - 0x23,0x95,0x3A,0x94,0x64,0xB5,0x4D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } - _EC_SECG_CHAR2_131R2 = { - { NID_X9_62_characteristic_two_field,20,17,2 }, - { 0x98,0x5B,0xD3,0xAD,0xBA,0xD4,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x5A,0x21,0xB4,0x3A,0x97,0xE3, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, - 0x03,0xE5,0xA8,0x89,0x19,0xD7,0xCA,0xFC,0xBF,0x41, /* a */ - 0x5F,0x07,0xC2,0x17,0x65,0x73,0xB2, - 0x04,0xB8,0x26,0x6A,0x46,0xC5,0x56,0x57,0xAC,0x73, /* b */ - 0x4C,0xE3,0x8F,0x01,0x8F,0x21,0x92, - 0x03,0x56,0xDC,0xD8,0xF2,0xF9,0x50,0x31,0xAD,0x65, /* x */ - 0x2D,0x23,0x95,0x1B,0xB3,0x66,0xA8, - 0x06,0x48,0xF0,0x6D,0x86,0x79,0x40,0xA5,0x36,0x6D, /* y */ - 0x9E,0x26,0x5D,0xE9,0xEB,0x24,0x0F, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x69, /* order */ - 0x54,0xA2,0x33,0x04,0x9B,0xA9,0x8F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_NIST_CHAR2_163K = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x02,0xFE,0x13,0xC0,0x53,0x7B,0xBC,0x11,0xAC,0xAA, /* x */ - 0x07,0xD7,0x93,0xDE,0x4E,0x6D,0x5E,0x5C,0x94,0xEE, - 0xE8, - 0x02,0x89,0x07,0x0F,0xB0,0x5D,0x38,0xFF,0x58,0x32, /* y */ - 0x1F,0x2E,0x80,0x05,0x36,0xD5,0x38,0xCC,0xDA,0xA3, - 0xD9, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x02,0x01,0x08,0xA2,0xE0,0xCC,0x0D,0x99,0xF8,0xA5, - 0xEF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_SECG_CHAR2_163R1 = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} + _EC_SECG_CHAR2_113R1 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + 0x10, 0xE7, 0x23, 0xAB, 0x14, 0xD6, 0x96, 0xE6, 0x76, 0x87, /* seed */ + 0x56, 0x15, 0x17, 0x56, 0xFE, 0xBF, 0x8F, 0xCB, 0x49, 0xA9, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x30, 0x88, 0x25, 0x0C, 0xA6, 0xE7, 0xC7, 0xFE, 0x64, /* a */ + 0x9C, 0xE8, 0x58, 0x20, 0xF7, + 0x00, 0xE8, 0xBE, 0xE4, 0xD3, 0xE2, 0x26, 0x07, 0x44, 0x18, /* b */ + 0x8B, 0xE0, 0xE9, 0xC7, 0x23, + 0x00, 0x9D, 0x73, 0x61, 0x6F, 0x35, 0xF4, 0xAB, 0x14, 0x07, /* x */ + 0xD7, 0x35, 0x62, 0xC1, 0x0F, + 0x00, 0xA5, 0x28, 0x30, 0x27, 0x79, 0x58, 0xEE, 0x84, 0xD1, /* y */ + 0x31, 0x5E, 0xD3, 0x18, 0x86, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xD9, 0xCC, /* order */ + 0xEC, 0x8A, 0x39, 0xE5, 0x6F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} + _EC_SECG_CHAR2_113R2 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + 0x10, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, /* seed */ + 0xF4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x5D, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x68, 0x99, 0x18, 0xDB, 0xEC, 0x7E, 0x5A, 0x0D, 0xD6, /* a */ + 0xDF, 0xC0, 0xAA, 0x55, 0xC7, + 0x00, 0x95, 0xE9, 0xA9, 0xEC, 0x9B, 0x29, 0x7B, 0xD4, 0xBF, /* b */ + 0x36, 0xE0, 0x59, 0x18, 0x4F, + 0x01, 0xA5, 0x7A, 0x6A, 0x7B, 0x26, 0xCA, 0x5E, 0xF5, 0x2F, /* x */ + 0xCD, 0xB8, 0x16, 0x47, 0x97, + 0x00, 0xB3, 0xAD, 0xC9, 0x4E, 0xD1, 0xFE, 0x67, 0x4C, 0x06, /* y */ + 0xE6, 0x95, 0xBA, 0xBA, 0x1D, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x08, 0x78, /* order */ + 0x9B, 0x24, 0x96, 0xAF, 0x93 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} + _EC_SECG_CHAR2_131R1 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, 0x98, /* seed */ + 0x5B, 0xD3, 0xAD, 0xBA, 0xDA, 0x21, 0xB4, 0x3A, 0x97, 0xE2, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x0D, + 0x07, 0xA1, 0x1B, 0x09, 0xA7, 0x6B, 0x56, 0x21, 0x44, 0x41, /* a */ + 0x8F, 0xF3, 0xFF, 0x8C, 0x25, 0x70, 0xB8, + 0x02, 0x17, 0xC0, 0x56, 0x10, 0x88, 0x4B, 0x63, 0xB9, 0xC6, /* b */ + 0xC7, 0x29, 0x16, 0x78, 0xF9, 0xD3, 0x41, + 0x00, 0x81, 0xBA, 0xF9, 0x1F, 0xDF, 0x98, 0x33, 0xC4, 0x0F, /* x */ + 0x9C, 0x18, 0x13, 0x43, 0x63, 0x83, 0x99, + 0x07, 0x8C, 0x6E, 0x7E, 0xA3, 0x8C, 0x00, 0x1F, 0x73, 0xC8, /* y */ + 0x13, 0x4B, 0x1B, 0x4E, 0xF9, 0xE1, 0x50, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x31, /* order */ + 0x23, 0x95, 0x3A, 0x94, 0x64, 0xB5, 0x4D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} + _EC_SECG_CHAR2_131R2 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + 0x98, 0x5B, 0xD3, 0xAD, 0xBA, 0xD4, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x5A, 0x21, 0xB4, 0x3A, 0x97, 0xE3, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x0D, + 0x03, 0xE5, 0xA8, 0x89, 0x19, 0xD7, 0xCA, 0xFC, 0xBF, 0x41, /* a */ + 0x5F, 0x07, 0xC2, 0x17, 0x65, 0x73, 0xB2, + 0x04, 0xB8, 0x26, 0x6A, 0x46, 0xC5, 0x56, 0x57, 0xAC, 0x73, /* b */ + 0x4C, 0xE3, 0x8F, 0x01, 0x8F, 0x21, 0x92, + 0x03, 0x56, 0xDC, 0xD8, 0xF2, 0xF9, 0x50, 0x31, 0xAD, 0x65, /* x */ + 0x2D, 0x23, 0x95, 0x1B, 0xB3, 0x66, 0xA8, + 0x06, 0x48, 0xF0, 0x6D, 0x86, 0x79, 0x40, 0xA5, 0x36, 0x6D, /* y */ + 0x9E, 0x26, 0x5D, 0xE9, 0xEB, 0x24, 0x0F, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x69, /* order */ + 0x54, 0xA2, 0x33, 0x04, 0x9B, 0xA9, 0x8F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_NIST_CHAR2_163K = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x02, 0xFE, 0x13, 0xC0, 0x53, 0x7B, 0xBC, 0x11, 0xAC, 0xAA, /* x */ + 0x07, 0xD7, 0x93, 0xDE, 0x4E, 0x6D, 0x5E, 0x5C, 0x94, 0xEE, + 0xE8, + 0x02, 0x89, 0x07, 0x0F, 0xB0, 0x5D, 0x38, 0xFF, 0x58, 0x32, /* y */ + 0x1F, 0x2E, 0x80, 0x05, 0x36, 0xD5, 0x38, 0xCC, 0xDA, 0xA3, + 0xD9, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x02, 0x01, 0x08, 0xA2, 0xE0, 0xCC, 0x0D, 0x99, 0xF8, 0xA5, + 0xEF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_SECG_CHAR2_163R1 = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ #if 0 /* The algorithm used to derive the curve parameters from * the seed used here is slightly different than the * algorithm described in X9.62 . */ - 0x24,0xB7,0xB1,0x37,0xC8,0xA1,0x4D,0x69,0x6E,0x67, - 0x68,0x75,0x61,0x51,0x75,0x6F,0xD0,0xDA,0x2E,0x5C, + 0x24, 0xB7, 0xB1, 0x37, 0xC8, 0xA1, 0x4D, 0x69, 0x6E, 0x67, + 0x68, 0x75, 0x61, 0x51, 0x75, 0x6F, 0xD0, 0xDA, 0x2E, 0x5C, #endif - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x07,0xB6,0x88,0x2C,0xAA,0xEF,0xA8,0x4F,0x95,0x54, /* a */ - 0xFF,0x84,0x28,0xBD,0x88,0xE2,0x46,0xD2,0x78,0x2A, - 0xE2, - 0x07,0x13,0x61,0x2D,0xCD,0xDC,0xB4,0x0A,0xAB,0x94, /* b */ - 0x6B,0xDA,0x29,0xCA,0x91,0xF7,0x3A,0xF9,0x58,0xAF, - 0xD9, - 0x03,0x69,0x97,0x96,0x97,0xAB,0x43,0x89,0x77,0x89, /* x */ - 0x56,0x67,0x89,0x56,0x7F,0x78,0x7A,0x78,0x76,0xA6, - 0x54, - 0x00,0x43,0x5E,0xDB,0x42,0xEF,0xAF,0xB2,0x98,0x9D, /* y */ - 0x51,0xFE,0xFC,0xE3,0xC8,0x09,0x88,0xF4,0x1F,0xF8, - 0x83, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0x48,0xAA,0xB6,0x89,0xC2,0x9C,0xA7,0x10,0x27, - 0x9B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_NIST_CHAR2_163B = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x07, 0xB6, 0x88, 0x2C, 0xAA, 0xEF, 0xA8, 0x4F, 0x95, 0x54, /* a */ + 0xFF, 0x84, 0x28, 0xBD, 0x88, 0xE2, 0x46, 0xD2, 0x78, 0x2A, + 0xE2, + 0x07, 0x13, 0x61, 0x2D, 0xCD, 0xDC, 0xB4, 0x0A, 0xAB, 0x94, /* b */ + 0x6B, 0xDA, 0x29, 0xCA, 0x91, 0xF7, 0x3A, 0xF9, 0x58, 0xAF, + 0xD9, + 0x03, 0x69, 0x97, 0x96, 0x97, 0xAB, 0x43, 0x89, 0x77, 0x89, /* x */ + 0x56, 0x67, 0x89, 0x56, 0x7F, 0x78, 0x7A, 0x78, 0x76, 0xA6, + 0x54, + 0x00, 0x43, 0x5E, 0xDB, 0x42, 0xEF, 0xAF, 0xB2, 0x98, 0x9D, /* y */ + 0x51, 0xFE, 0xFC, 0xE3, 0xC8, 0x09, 0x88, 0xF4, 0x1F, 0xF8, + 0x83, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0x48, 0xAA, 0xB6, 0x89, 0xC2, 0x9C, 0xA7, 0x10, 0x27, + 0x9B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_NIST_CHAR2_163B = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ #if 0 /* The seed here was used to created the curve parameters in normal * basis representation (and not the polynomial representation used here) */ - 0x85,0xE2,0x5B,0xFE,0x5C,0x86,0x22,0x6C,0xDB,0x12, - 0x01,0x6F,0x75,0x53,0xF9,0xD0,0xE6,0x93,0xA2,0x68, + 0x85, 0xE2, 0x5B, 0xFE, 0x5C, 0x86, 0x22, 0x6C, 0xDB, 0x12, + 0x01, 0x6F, 0x75, 0x53, 0xF9, 0xD0, 0xE6, 0x93, 0xA2, 0x68, #endif - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x02,0x0A,0x60,0x19,0x07,0xB8,0xC9,0x53,0xCA,0x14, /* b */ - 0x81,0xEB,0x10,0x51,0x2F,0x78,0x74,0x4A,0x32,0x05, - 0xFD, - 0x03,0xF0,0xEB,0xA1,0x62,0x86,0xA2,0xD5,0x7E,0xA0, /* x */ - 0x99,0x11,0x68,0xD4,0x99,0x46,0x37,0xE8,0x34,0x3E, - 0x36, - 0x00,0xD5,0x1F,0xBC,0x6C,0x71,0xA0,0x09,0x4F,0xA2, /* y */ - 0xCD,0xD5,0x45,0xB1,0x1C,0x5C,0x0C,0x79,0x73,0x24, - 0xF1, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x02,0x92,0xFE,0x77,0xE7,0x0C,0x12,0xA4,0x23,0x4C, - 0x33 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } - _EC_SECG_CHAR2_193R1 = { - { NID_X9_62_characteristic_two_field,20,25,2 }, - { 0x10,0x3F,0xAE,0xC7,0x4D,0x69,0x6E,0x67,0x68,0x75, /* seed */ - 0x61,0x51,0x75,0x77,0x7F,0xC5,0xB1,0x91,0xEF,0x30, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x80,0x01, - 0x00,0x17,0x85,0x8F,0xEB,0x7A,0x98,0x97,0x51,0x69, /* a */ - 0xE1,0x71,0xF7,0x7B,0x40,0x87,0xDE,0x09,0x8A,0xC8, - 0xA9,0x11,0xDF,0x7B,0x01, - 0x00,0xFD,0xFB,0x49,0xBF,0xE6,0xC3,0xA8,0x9F,0xAC, /* b */ - 0xAD,0xAA,0x7A,0x1E,0x5B,0xBC,0x7C,0xC1,0xC2,0xE5, - 0xD8,0x31,0x47,0x88,0x14, - 0x01,0xF4,0x81,0xBC,0x5F,0x0F,0xF8,0x4A,0x74,0xAD, /* x */ - 0x6C,0xDF,0x6F,0xDE,0xF4,0xBF,0x61,0x79,0x62,0x53, - 0x72,0xD8,0xC0,0xC5,0xE1, - 0x00,0x25,0xE3,0x99,0xF2,0x90,0x37,0x12,0xCC,0xF3, /* y */ - 0xEA,0x9E,0x3A,0x1A,0xD1,0x7F,0xB0,0xB3,0x20,0x1B, - 0x6A,0xF7,0xCE,0x1B,0x05, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0xC7,0xF3,0x4A,0x77,0x8F,0x44,0x3A, - 0xCC,0x92,0x0E,0xBA,0x49 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } - _EC_SECG_CHAR2_193R2 = { - { NID_X9_62_characteristic_two_field,20,25,2 }, - { 0x10,0xB7,0xB4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15, /* seed */ - 0x17,0x51,0x37,0xC8,0xA1,0x6F,0xD0,0xDA,0x22,0x11, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x80,0x01, - 0x01,0x63,0xF3,0x5A,0x51,0x37,0xC2,0xCE,0x3E,0xA6, /* a */ - 0xED,0x86,0x67,0x19,0x0B,0x0B,0xC4,0x3E,0xCD,0x69, - 0x97,0x77,0x02,0x70,0x9B, - 0x00,0xC9,0xBB,0x9E,0x89,0x27,0xD4,0xD6,0x4C,0x37, /* b */ - 0x7E,0x2A,0xB2,0x85,0x6A,0x5B,0x16,0xE3,0xEF,0xB7, - 0xF6,0x1D,0x43,0x16,0xAE, - 0x00,0xD9,0xB6,0x7D,0x19,0x2E,0x03,0x67,0xC8,0x03, /* x */ - 0xF3,0x9E,0x1A,0x7E,0x82,0xCA,0x14,0xA6,0x51,0x35, - 0x0A,0xAE,0x61,0x7E,0x8F, - 0x01,0xCE,0x94,0x33,0x56,0x07,0xC3,0x04,0xAC,0x29, /* y */ - 0xE7,0xDE,0xFB,0xD9,0xCA,0x01,0xF5,0x96,0xF9,0x27, - 0x22,0x4C,0xDE,0xCF,0x6C, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x01,0x5A,0xAB,0x56,0x1B,0x00,0x54,0x13, - 0xCC,0xD4,0xEE,0x99,0xD5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } - _EC_NIST_CHAR2_233K = { - { NID_X9_62_characteristic_two_field,0,30,4 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x01,0x72,0x32,0xBA,0x85,0x3A,0x7E,0x73,0x1A,0xF1, /* x */ - 0x29,0xF2,0x2F,0xF4,0x14,0x95,0x63,0xA4,0x19,0xC2, - 0x6B,0xF5,0x0A,0x4C,0x9D,0x6E,0xEF,0xAD,0x61,0x26, - - 0x01,0xDB,0x53,0x7D,0xEC,0xE8,0x19,0xB7,0xF7,0x0F, /* y */ - 0x55,0x5A,0x67,0xC4,0x27,0xA8,0xCD,0x9B,0xF1,0x8A, - 0xEB,0x9B,0x56,0xE0,0xC1,0x10,0x56,0xFA,0xE6,0xA3, - - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x06,0x9D,0x5B,0xB9,0x15, - 0xBC,0xD4,0x6E,0xFB,0x1A,0xD5,0xF1,0x73,0xAB,0xDF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_NIST_CHAR2_233B = { - { NID_X9_62_characteristic_two_field,20,30,2 }, - { 0x74,0xD5,0x9F,0xF0,0x7F,0x6B,0x41,0x3D,0x0E,0xA1, /* seed */ - 0x4B,0x34,0x4B,0x20,0xA2,0xDB,0x04,0x9B,0x50,0xC3, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x66,0x64,0x7E,0xDE,0x6C,0x33,0x2C,0x7F,0x8C, /* b */ - 0x09,0x23,0xBB,0x58,0x21,0x3B,0x33,0x3B,0x20,0xE9, - 0xCE,0x42,0x81,0xFE,0x11,0x5F,0x7D,0x8F,0x90,0xAD, - - 0x00,0xFA,0xC9,0xDF,0xCB,0xAC,0x83,0x13,0xBB,0x21, /* x */ - 0x39,0xF1,0xBB,0x75,0x5F,0xEF,0x65,0xBC,0x39,0x1F, - 0x8B,0x36,0xF8,0xF8,0xEB,0x73,0x71,0xFD,0x55,0x8B, - - 0x01,0x00,0x6A,0x08,0xA4,0x19,0x03,0x35,0x06,0x78, /* y */ - 0xE5,0x85,0x28,0xBE,0xBF,0x8A,0x0B,0xEF,0xF8,0x67, - 0xA7,0xCA,0x36,0x71,0x6F,0x7E,0x01,0xF8,0x10,0x52, - - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x13,0xE9,0x74,0xE7,0x2F, - 0x8A,0x69,0x22,0x03,0x1D,0x26,0x03,0xCF,0xE0,0xD7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } - _EC_SECG_CHAR2_239K1 = { - { NID_X9_62_characteristic_two_field,0,30,4 }, - { /* no seed */ - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x29,0xA0,0xB6,0xA8,0x87,0xA9,0x83,0xE9,0x73,0x09, /* x */ - 0x88,0xA6,0x87,0x27,0xA8,0xB2,0xD1,0x26,0xC4,0x4C, - 0xC2,0xCC,0x7B,0x2A,0x65,0x55,0x19,0x30,0x35,0xDC, - - 0x76,0x31,0x08,0x04,0xF1,0x2E,0x54,0x9B,0xDB,0x01, /* y */ - 0x1C,0x10,0x30,0x89,0xE7,0x35,0x10,0xAC,0xB2,0x75, - 0xFC,0x31,0x2A,0x5D,0xC6,0xB7,0x65,0x53,0xF0,0xCA, - - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x5A,0x79,0xFE,0xC6,0x7C, - 0xB6,0xE9,0x1F,0x1C,0x1D,0xA8,0x00,0xE4,0x78,0xA5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+36*6]; } - _EC_NIST_CHAR2_283K = { - { NID_X9_62_characteristic_two_field,0,36,4 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x10,0xA1, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x01, - 0x05,0x03,0x21,0x3F,0x78,0xCA,0x44,0x88,0x3F,0x1A, /* x */ - 0x3B,0x81,0x62,0xF1,0x88,0xE5,0x53,0xCD,0x26,0x5F, - 0x23,0xC1,0x56,0x7A,0x16,0x87,0x69,0x13,0xB0,0xC2, - 0xAC,0x24,0x58,0x49,0x28,0x36, - 0x01,0xCC,0xDA,0x38,0x0F,0x1C,0x9E,0x31,0x8D,0x90, /* y */ - 0xF9,0x5D,0x07,0xE5,0x42,0x6F,0xE8,0x7E,0x45,0xC0, - 0xE8,0x18,0x46,0x98,0xE4,0x59,0x62,0x36,0x4E,0x34, - 0x11,0x61,0x77,0xDD,0x22,0x59, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE9,0xAE, - 0x2E,0xD0,0x75,0x77,0x26,0x5D,0xFF,0x7F,0x94,0x45, - 0x1E,0x06,0x1E,0x16,0x3C,0x61 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+36*6]; } - _EC_NIST_CHAR2_283B = { - { NID_X9_62_characteristic_two_field,20,36,2 }, - { 0x77,0xE2,0xB0,0x73,0x70,0xEB,0x0F,0x83,0x2A,0x6D, /* no seed */ - 0xD5,0xB6,0x2D,0xFC,0x88,0xCD,0x06,0xBB,0x84,0xBE, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x10,0xA1, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x01, - 0x02,0x7B,0x68,0x0A,0xC8,0xB8,0x59,0x6D,0xA5,0xA4, /* b */ - 0xAF,0x8A,0x19,0xA0,0x30,0x3F,0xCA,0x97,0xFD,0x76, - 0x45,0x30,0x9F,0xA2,0xA5,0x81,0x48,0x5A,0xF6,0x26, - 0x3E,0x31,0x3B,0x79,0xA2,0xF5, - 0x05,0xF9,0x39,0x25,0x8D,0xB7,0xDD,0x90,0xE1,0x93, /* x */ - 0x4F,0x8C,0x70,0xB0,0xDF,0xEC,0x2E,0xED,0x25,0xB8, - 0x55,0x7E,0xAC,0x9C,0x80,0xE2,0xE1,0x98,0xF8,0xCD, - 0xBE,0xCD,0x86,0xB1,0x20,0x53, - 0x03,0x67,0x68,0x54,0xFE,0x24,0x14,0x1C,0xB9,0x8F, /* y */ - 0xE6,0xD4,0xB2,0x0D,0x02,0xB4,0x51,0x6F,0xF7,0x02, - 0x35,0x0E,0xDD,0xB0,0x82,0x67,0x79,0xC8,0x13,0xF0, - 0xDF,0x45,0xBE,0x81,0x12,0xF4, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xEF,0x90, - 0x39,0x96,0x60,0xFC,0x93,0x8A,0x90,0x16,0x5B,0x04, - 0x2A,0x7C,0xEF,0xAD,0xB3,0x07 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+52*6]; } - _EC_NIST_CHAR2_409K = { - { NID_X9_62_characteristic_two_field,0,52,4 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x60,0xF0,0x5F,0x65,0x8F,0x49,0xC1,0xAD,0x3A, /* x */ - 0xB1,0x89,0x0F,0x71,0x84,0x21,0x0E,0xFD,0x09,0x87, - 0xE3,0x07,0xC8,0x4C,0x27,0xAC,0xCF,0xB8,0xF9,0xF6, - 0x7C,0xC2,0xC4,0x60,0x18,0x9E,0xB5,0xAA,0xAA,0x62, - 0xEE,0x22,0x2E,0xB1,0xB3,0x55,0x40,0xCF,0xE9,0x02, - 0x37,0x46, - 0x01,0xE3,0x69,0x05,0x0B,0x7C,0x4E,0x42,0xAC,0xBA, /* y */ - 0x1D,0xAC,0xBF,0x04,0x29,0x9C,0x34,0x60,0x78,0x2F, - 0x91,0x8E,0xA4,0x27,0xE6,0x32,0x51,0x65,0xE9,0xEA, - 0x10,0xE3,0xDA,0x5F,0x6C,0x42,0xE9,0xC5,0x52,0x15, - 0xAA,0x9C,0xA2,0x7A,0x58,0x63,0xEC,0x48,0xD8,0xE0, - 0x28,0x6B, - 0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0x5F,0x83,0xB2, - 0xD4,0xEA,0x20,0x40,0x0E,0xC4,0x55,0x7D,0x5E,0xD3, - 0xE3,0xE7,0xCA,0x5B,0x4B,0x5C,0x83,0xB8,0xE0,0x1E, - 0x5F,0xCF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+52*6]; } - _EC_NIST_CHAR2_409B = { - { NID_X9_62_characteristic_two_field,20,52,2 }, - { 0x40,0x99,0xB5,0xA4,0x57,0xF9,0xD6,0x9F,0x79,0x21, /* seed */ - 0x3D,0x09,0x4C,0x4B,0xCD,0x4D,0x42,0x62,0x21,0x0B, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x21,0xA5,0xC2,0xC8,0xEE,0x9F,0xEB,0x5C,0x4B, /* b */ - 0x9A,0x75,0x3B,0x7B,0x47,0x6B,0x7F,0xD6,0x42,0x2E, - 0xF1,0xF3,0xDD,0x67,0x47,0x61,0xFA,0x99,0xD6,0xAC, - 0x27,0xC8,0xA9,0xA1,0x97,0xB2,0x72,0x82,0x2F,0x6C, - 0xD5,0x7A,0x55,0xAA,0x4F,0x50,0xAE,0x31,0x7B,0x13, - 0x54,0x5F, - 0x01,0x5D,0x48,0x60,0xD0,0x88,0xDD,0xB3,0x49,0x6B, /* x */ - 0x0C,0x60,0x64,0x75,0x62,0x60,0x44,0x1C,0xDE,0x4A, - 0xF1,0x77,0x1D,0x4D,0xB0,0x1F,0xFE,0x5B,0x34,0xE5, - 0x97,0x03,0xDC,0x25,0x5A,0x86,0x8A,0x11,0x80,0x51, - 0x56,0x03,0xAE,0xAB,0x60,0x79,0x4E,0x54,0xBB,0x79, - 0x96,0xA7, - 0x00,0x61,0xB1,0xCF,0xAB,0x6B,0xE5,0xF3,0x2B,0xBF, /* y */ - 0xA7,0x83,0x24,0xED,0x10,0x6A,0x76,0x36,0xB9,0xC5, - 0xA7,0xBD,0x19,0x8D,0x01,0x58,0xAA,0x4F,0x54,0x88, - 0xD0,0x8F,0x38,0x51,0x4F,0x1F,0xDF,0x4B,0x4F,0x40, - 0xD2,0x18,0x1B,0x36,0x81,0xC3,0x64,0xBA,0x02,0x73, - 0xC7,0x06, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xE2,0xAA,0xD6, - 0xA6,0x12,0xF3,0x33,0x07,0xBE,0x5F,0xA4,0x7C,0x3C, - 0x9E,0x05,0x2F,0x83,0x81,0x64,0xCD,0x37,0xD9,0xA2, - 0x11,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+72*6]; } - _EC_NIST_CHAR2_571K = { - { NID_X9_62_characteristic_two_field,0,72,4 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x25, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x02,0x6E,0xB7,0xA8,0x59,0x92,0x3F,0xBC,0x82,0x18, /* x */ - 0x96,0x31,0xF8,0x10,0x3F,0xE4,0xAC,0x9C,0xA2,0x97, - 0x00,0x12,0xD5,0xD4,0x60,0x24,0x80,0x48,0x01,0x84, - 0x1C,0xA4,0x43,0x70,0x95,0x84,0x93,0xB2,0x05,0xE6, - 0x47,0xDA,0x30,0x4D,0xB4,0xCE,0xB0,0x8C,0xBB,0xD1, - 0xBA,0x39,0x49,0x47,0x76,0xFB,0x98,0x8B,0x47,0x17, - 0x4D,0xCA,0x88,0xC7,0xE2,0x94,0x52,0x83,0xA0,0x1C, - 0x89,0x72, - 0x03,0x49,0xDC,0x80,0x7F,0x4F,0xBF,0x37,0x4F,0x4A, /* y */ - 0xEA,0xDE,0x3B,0xCA,0x95,0x31,0x4D,0xD5,0x8C,0xEC, - 0x9F,0x30,0x7A,0x54,0xFF,0xC6,0x1E,0xFC,0x00,0x6D, - 0x8A,0x2C,0x9D,0x49,0x79,0xC0,0xAC,0x44,0xAE,0xA7, - 0x4F,0xBE,0xBB,0xB9,0xF7,0x72,0xAE,0xDC,0xB6,0x20, - 0xB0,0x1A,0x7B,0xA7,0xAF,0x1B,0x32,0x04,0x30,0xC8, - 0x59,0x19,0x84,0xF6,0x01,0xCD,0x4C,0x14,0x3E,0xF1, - 0xC7,0xA3, - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x13,0x18,0x50,0xE1, - 0xF1,0x9A,0x63,0xE4,0xB3,0x91,0xA8,0xDB,0x91,0x7F, - 0x41,0x38,0xB6,0x30,0xD8,0x4B,0xE5,0xD6,0x39,0x38, - 0x1E,0x91,0xDE,0xB4,0x5C,0xFE,0x77,0x8F,0x63,0x7C, - 0x10,0x01 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+72*6]; } - _EC_NIST_CHAR2_571B = { - { NID_X9_62_characteristic_two_field,20,72,2 }, - { 0x2A,0xA0,0x58,0xF7,0x3A,0x0E,0x33,0xAB,0x48,0x6B, /* seed */ - 0x0F,0x61,0x04,0x10,0xC5,0x3A,0x7F,0x13,0x23,0x10, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x25, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x02,0xF4,0x0E,0x7E,0x22,0x21,0xF2,0x95,0xDE,0x29, /* b */ - 0x71,0x17,0xB7,0xF3,0xD6,0x2F,0x5C,0x6A,0x97,0xFF, - 0xCB,0x8C,0xEF,0xF1,0xCD,0x6B,0xA8,0xCE,0x4A,0x9A, - 0x18,0xAD,0x84,0xFF,0xAB,0xBD,0x8E,0xFA,0x59,0x33, - 0x2B,0xE7,0xAD,0x67,0x56,0xA6,0x6E,0x29,0x4A,0xFD, - 0x18,0x5A,0x78,0xFF,0x12,0xAA,0x52,0x0E,0x4D,0xE7, - 0x39,0xBA,0xCA,0x0C,0x7F,0xFE,0xFF,0x7F,0x29,0x55, - 0x72,0x7A, - 0x03,0x03,0x00,0x1D,0x34,0xB8,0x56,0x29,0x6C,0x16, /* x */ - 0xC0,0xD4,0x0D,0x3C,0xD7,0x75,0x0A,0x93,0xD1,0xD2, - 0x95,0x5F,0xA8,0x0A,0xA5,0xF4,0x0F,0xC8,0xDB,0x7B, - 0x2A,0xBD,0xBD,0xE5,0x39,0x50,0xF4,0xC0,0xD2,0x93, - 0xCD,0xD7,0x11,0xA3,0x5B,0x67,0xFB,0x14,0x99,0xAE, - 0x60,0x03,0x86,0x14,0xF1,0x39,0x4A,0xBF,0xA3,0xB4, - 0xC8,0x50,0xD9,0x27,0xE1,0xE7,0x76,0x9C,0x8E,0xEC, - 0x2D,0x19, - 0x03,0x7B,0xF2,0x73,0x42,0xDA,0x63,0x9B,0x6D,0xCC, /* y */ - 0xFF,0xFE,0xB7,0x3D,0x69,0xD7,0x8C,0x6C,0x27,0xA6, - 0x00,0x9C,0xBB,0xCA,0x19,0x80,0xF8,0x53,0x39,0x21, - 0xE8,0xA6,0x84,0x42,0x3E,0x43,0xBA,0xB0,0x8A,0x57, - 0x62,0x91,0xAF,0x8F,0x46,0x1B,0xB2,0xA8,0xB3,0x53, - 0x1D,0x2F,0x04,0x85,0xC1,0x9B,0x16,0xE2,0xF1,0x51, - 0x6E,0x23,0xDD,0x3C,0x1A,0x48,0x27,0xAF,0x1B,0x8A, - 0xC1,0x5B, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE6,0x61,0xCE,0x18, - 0xFF,0x55,0x98,0x73,0x08,0x05,0x9B,0x18,0x68,0x23, - 0x85,0x1E,0xC7,0xDD,0x9C,0xA1,0x16,0x1D,0xE9,0x3D, - 0x51,0x74,0xD6,0x6E,0x83,0x82,0xE9,0xBB,0x2F,0xE8, - 0x4E,0x47 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V1 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0xD2,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x54, /* seed */ - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x07,0x25,0x46,0xB5,0x43,0x52,0x34,0xA4,0x22,0xE0, /* a */ - 0x78,0x96,0x75,0xF4,0x32,0xC8,0x94,0x35,0xDE,0x52, - 0x42, - 0x00,0xC9,0x51,0x7D,0x06,0xD5,0x24,0x0D,0x3C,0xFF, /* b */ - 0x38,0xC7,0x4B,0x20,0xB6,0xCD,0x4D,0x6F,0x9D,0xD4, - 0xD9, - 0x07,0xAF,0x69,0x98,0x95,0x46,0x10,0x3D,0x79,0x32, /* x */ - 0x9F,0xCC,0x3D,0x74,0x88,0x0F,0x33,0xBB,0xE8,0x03, - 0xCB, - 0x01,0xEC,0x23,0x21,0x1B,0x59,0x66,0xAD,0xEA,0x1D, /* y */ - 0x3F,0x87,0xF7,0xEA,0x58,0x48,0xAE,0xF0,0xB7,0xCA, - 0x9F, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xE6,0x0F,0xC8,0x82,0x1C,0xC7,0x4D,0xAE,0xAF, - 0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V2 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x01,0x08,0xB3,0x9E,0x77,0xC4,0xB1,0x08,0xBE,0xD9, /* a */ - 0x81,0xED,0x0E,0x89,0x0E,0x11,0x7C,0x51,0x1C,0xF0, - 0x72, - 0x06,0x67,0xAC,0xEB,0x38,0xAF,0x4E,0x48,0x8C,0x40, /* b */ - 0x74,0x33,0xFF,0xAE,0x4F,0x1C,0x81,0x16,0x38,0xDF, - 0x20, - 0x00,0x24,0x26,0x6E,0x4E,0xB5,0x10,0x6D,0x0A,0x96, /* x */ - 0x4D,0x92,0xC4,0x86,0x0E,0x26,0x71,0xDB,0x9B,0x6C, - 0xC5, - 0x07,0x9F,0x68,0x4D,0xDF,0x66,0x84,0xC5,0xCD,0x25, /* y */ - 0x8B,0x38,0x90,0x02,0x1B,0x23,0x86,0xDF,0xD1,0x9F, - 0xC5, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFD,0xF6,0x4D,0xE1,0x15,0x1A,0xDB,0xB7,0x8F,0x10, - 0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V3 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0x50,0xCB,0xF1,0xD9,0x5C,0xA9,0x4D,0x69,0x6E,0x67, /* seed */ - 0x68,0x75,0x61,0x51,0x75,0xF1,0x6A,0x36,0xA3,0xB8, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x07,0xA5,0x26,0xC6,0x3D,0x3E,0x25,0xA2,0x56,0xA0, /* a */ - 0x07,0x69,0x9F,0x54,0x47,0xE3,0x2A,0xE4,0x56,0xB5, - 0x0E, - 0x03,0xF7,0x06,0x17,0x98,0xEB,0x99,0xE2,0x38,0xFD, /* b */ - 0x6F,0x1B,0xF9,0x5B,0x48,0xFE,0xEB,0x48,0x54,0x25, - 0x2B, - 0x02,0xF9,0xF8,0x7B,0x7C,0x57,0x4D,0x0B,0xDE,0xCF, /* x */ - 0x8A,0x22,0xE6,0x52,0x47,0x75,0xF9,0x8C,0xDE,0xBD, - 0xCB, - 0x05,0xB9,0x35,0x59,0x0C,0x15,0x5E,0x17,0xEA,0x48, /* y */ - 0xEB,0x3F,0xF3,0x71,0x8B,0x89,0x3D,0xF5,0x9A,0x05, - 0xD0, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFE,0x1A,0xEE,0x14,0x0F,0x11,0x0A,0xFF,0x96,0x13, - 0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+23*6]; } - _EC_X9_62_CHAR2_176V1 = { - { NID_X9_62_characteristic_two_field,0,23,0xFF6E }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00, - 0x00,0x00,0x07, - 0x00,0xE4,0xE6,0xDB,0x29,0x95,0x06,0x5C,0x40,0x7D, /* a */ - 0x9D,0x39,0xB8,0xD0,0x96,0x7B,0x96,0x70,0x4B,0xA8, - 0xE9,0xC9,0x0B, - 0x00,0x5D,0xDA,0x47,0x0A,0xBE,0x64,0x14,0xDE,0x8E, /* b */ - 0xC1,0x33,0xAE,0x28,0xE9,0xBB,0xD7,0xFC,0xEC,0x0A, - 0xE0,0xFF,0xF2, - 0x00,0x8D,0x16,0xC2,0x86,0x67,0x98,0xB6,0x00,0xF9, /* x */ - 0xF0,0x8B,0xB4,0xA8,0xE8,0x60,0xF3,0x29,0x8C,0xE0, - 0x4A,0x57,0x98, - 0x00,0x6F,0xA4,0x53,0x9C,0x2D,0xAD,0xDD,0xD6,0xBA, /* y */ - 0xB5,0x16,0x7D,0x61,0xB4,0x36,0xE1,0xD9,0x2B,0xB1, - 0x6A,0x56,0x2C, - 0x00,0x00,0x01,0x00,0x92,0x53,0x73,0x97,0xEC,0xA4, /* order */ - 0xF6,0x14,0x57,0x99,0xD6,0x2B,0x0A,0x19,0xCE,0x06, - 0xFE,0x26,0xAD } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V1 = { - { NID_X9_62_characteristic_two_field,20,24,2 }, - { 0x4E,0x13,0xCA,0x54,0x27,0x44,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x55,0x2F,0x27,0x9A,0x8C,0x84, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x28,0x66,0x53,0x7B,0x67,0x67,0x52,0x63,0x6A,0x68, /* a */ - 0xF5,0x65,0x54,0xE1,0x26,0x40,0x27,0x6B,0x64,0x9E, - 0xF7,0x52,0x62,0x67, - 0x2E,0x45,0xEF,0x57,0x1F,0x00,0x78,0x6F,0x67,0xB0, /* b */ - 0x08,0x1B,0x94,0x95,0xA3,0xD9,0x54,0x62,0xF5,0xDE, - 0x0A,0xA1,0x85,0xEC, - 0x36,0xB3,0xDA,0xF8,0xA2,0x32,0x06,0xF9,0xC4,0xF2, /* x */ - 0x99,0xD7,0xB2,0x1A,0x9C,0x36,0x91,0x37,0xF2,0xC8, - 0x4A,0xE1,0xAA,0x0D, - 0x76,0x5B,0xE7,0x34,0x33,0xB3,0xF9,0x5E,0x33,0x29, /* y */ - 0x32,0xE7,0x0E,0xA2,0x45,0xCA,0x24,0x18,0xEA,0x0E, - 0xF9,0x80,0x18,0xFB, - 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x04,0xA2,0x0E,0x90,0xC3,0x90,0x67,0xC8, - 0x93,0xBB,0xB9,0xA5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V2 = { - { NID_X9_62_characteristic_two_field,20,24,4 }, - { 0x08,0x71,0xEF,0x2F,0xEF,0x24,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0xBE,0xE0,0xD9,0x5C,0x15, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x40,0x10,0x28,0x77,0x4D,0x77,0x77,0xC7,0xB7,0x66, /* a */ - 0x6D,0x13,0x66,0xEA,0x43,0x20,0x71,0x27,0x4F,0x89, - 0xFF,0x01,0xE7,0x18, - 0x06,0x20,0x04,0x8D,0x28,0xBC,0xBD,0x03,0xB6,0x24, /* b */ - 0x9C,0x99,0x18,0x2B,0x7C,0x8C,0xD1,0x97,0x00,0xC3, - 0x62,0xC4,0x6A,0x01, - 0x38,0x09,0xB2,0xB7,0xCC,0x1B,0x28,0xCC,0x5A,0x87, /* x */ - 0x92,0x6A,0xAD,0x83,0xFD,0x28,0x78,0x9E,0x81,0xE2, - 0xC9,0xE3,0xBF,0x10, - 0x17,0x43,0x43,0x86,0x62,0x6D,0x14,0xF3,0xDB,0xF0, /* y */ - 0x17,0x60,0xD9,0x21,0x3A,0x3E,0x1C,0xF3,0x7A,0xEC, - 0x43,0x7D,0x66,0x8A, - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x50,0x50,0x8C,0xB8,0x9F,0x65,0x28,0x24, - 0xE0,0x6B,0x81,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V3 = { - { NID_X9_62_characteristic_two_field,20,24,6 }, - { 0xE0,0x53,0x51,0x2D,0xC6,0x84,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x50,0x67,0xAE,0x78,0x6D,0x1F, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x6C,0x01,0x07,0x47,0x56,0x09,0x91,0x22,0x22,0x10, /* a */ - 0x56,0x91,0x1C,0x77,0xD7,0x7E,0x77,0xA7,0x77,0xE7, - 0xE7,0xE7,0x7F,0xCB, - 0x71,0xFE,0x1A,0xF9,0x26,0xCF,0x84,0x79,0x89,0xEF, /* b */ - 0xEF,0x8D,0xB4,0x59,0xF6,0x63,0x94,0xD9,0x0F,0x32, - 0xAD,0x3F,0x15,0xE8, - 0x37,0x5D,0x4C,0xE2,0x4F,0xDE,0x43,0x44,0x89,0xDE, /* x */ - 0x87,0x46,0xE7,0x17,0x86,0x01,0x50,0x09,0xE6,0x6E, - 0x38,0xA9,0x26,0xDD, - 0x54,0x5A,0x39,0x17,0x61,0x96,0x57,0x5D,0x98,0x59, /* y */ - 0x99,0x36,0x6E,0x6A,0xD3,0x4C,0xE0,0xA7,0x7C,0xD7, - 0x12,0x7B,0x06,0xBE, - 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ - 0x55,0x55,0x61,0x0C,0x0B,0x19,0x68,0x12,0xBF,0xB6, - 0x28,0x8A,0x3E,0xA3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+27*6]; } - _EC_X9_62_CHAR2_208W1 = { - { NID_X9_62_characteristic_two_field,0,27,0xFE48 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x07, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0xC8,0x61,0x9E,0xD4,0x5A,0x62,0xE6,0x21,0x2E, /* b */ - 0x11,0x60,0x34,0x9E,0x2B,0xFA,0x84,0x44,0x39,0xFA, - 0xFC,0x2A,0x3F,0xD1,0x63,0x8F,0x9E, - 0x00,0x89,0xFD,0xFB,0xE4,0xAB,0xE1,0x93,0xDF,0x95, /* x */ - 0x59,0xEC,0xF0,0x7A,0xC0,0xCE,0x78,0x55,0x4E,0x27, - 0x84,0xEB,0x8C,0x1E,0xD1,0xA5,0x7A, - 0x00,0x0F,0x55,0xB5,0x1A,0x06,0xE7,0x8E,0x9A,0xC3, /* y */ - 0x8A,0x03,0x5F,0xF5,0x20,0xD8,0xB0,0x17,0x81,0xBE, - 0xB1,0xA6,0xBB,0x08,0x61,0x7D,0xE3, - 0x00,0x00,0x01,0x01,0xBA,0xF9,0x5C,0x97,0x23,0xC5, /* order */ - 0x7B,0x6C,0x21,0xDA,0x2E,0xFF,0x2D,0x5E,0xD5,0x88, - 0xBD,0xD5,0x71,0x7E,0x21,0x2F,0x9D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V1 = { - { NID_X9_62_characteristic_two_field,20,30,4 }, - { 0xD3,0x4B,0x9A,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0xCA,0x71,0xB9,0x20,0xBF,0xEF,0xB0,0x5D, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x32,0x01,0x08,0x57,0x07,0x7C,0x54,0x31,0x12,0x3A, /* a */ - 0x46,0xB8,0x08,0x90,0x67,0x56,0xF5,0x43,0x42,0x3E, - 0x8D,0x27,0x87,0x75,0x78,0x12,0x57,0x78,0xAC,0x76, - - 0x79,0x04,0x08,0xF2,0xEE,0xDA,0xF3,0x92,0xB0,0x12, /* b */ - 0xED,0xEF,0xB3,0x39,0x2F,0x30,0xF4,0x32,0x7C,0x0C, - 0xA3,0xF3,0x1F,0xC3,0x83,0xC4,0x22,0xAA,0x8C,0x16, - - 0x57,0x92,0x70,0x98,0xFA,0x93,0x2E,0x7C,0x0A,0x96, /* x */ - 0xD3,0xFD,0x5B,0x70,0x6E,0xF7,0xE5,0xF5,0xC1,0x56, - 0xE1,0x6B,0x7E,0x7C,0x86,0x03,0x85,0x52,0xE9,0x1D, - - 0x61,0xD8,0xEE,0x50,0x77,0xC3,0x3F,0xEC,0xF6,0xF1, /* y */ - 0xA1,0x6B,0x26,0x8D,0xE4,0x69,0xC3,0xC7,0x74,0x4E, - 0xA9,0xA9,0x71,0x64,0x9F,0xC7,0xA9,0x61,0x63,0x05, - - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x0F,0x4D,0x42,0xFF,0xE1, - 0x49,0x2A,0x49,0x93,0xF1,0xCA,0xD6,0x66,0xE4,0x47 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V2 = { - { NID_X9_62_characteristic_two_field,20,30,6 }, - { 0x2A,0xA6,0x98,0x2F,0xDF,0xA4,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x5D,0x26,0x67,0x27,0x27,0x7D, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x42,0x30,0x01,0x77,0x57,0xA7,0x67,0xFA,0xE4,0x23, /* a */ - 0x98,0x56,0x9B,0x74,0x63,0x25,0xD4,0x53,0x13,0xAF, - 0x07,0x66,0x26,0x64,0x79,0xB7,0x56,0x54,0xE6,0x5F, - - 0x50,0x37,0xEA,0x65,0x41,0x96,0xCF,0xF0,0xCD,0x82, /* b */ - 0xB2,0xC1,0x4A,0x2F,0xCF,0x2E,0x3F,0xF8,0x77,0x52, - 0x85,0xB5,0x45,0x72,0x2F,0x03,0xEA,0xCD,0xB7,0x4B, - - 0x28,0xF9,0xD0,0x4E,0x90,0x00,0x69,0xC8,0xDC,0x47, /* x */ - 0xA0,0x85,0x34,0xFE,0x76,0xD2,0xB9,0x00,0xB7,0xD7, - 0xEF,0x31,0xF5,0x70,0x9F,0x20,0x0C,0x4C,0xA2,0x05, - - 0x56,0x67,0x33,0x4C,0x45,0xAF,0xF3,0xB5,0xA0,0x3B, /* y */ - 0xAD,0x9D,0xD7,0x5E,0x2C,0x71,0xA9,0x93,0x62,0x56, - 0x7D,0x54,0x53,0xF7,0xFA,0x6E,0x22,0x7E,0xC8,0x33, - - 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ - 0x55,0x55,0x55,0x55,0x55,0x3C,0x6F,0x28,0x85,0x25, - 0x9C,0x31,0xE3,0xFC,0xDF,0x15,0x46,0x24,0x52,0x2D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V3 = { - { NID_X9_62_characteristic_two_field,20,30,0xA }, - { 0x9E,0x07,0x6F,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0xE1,0x1E,0x9F,0xDD,0x77,0xF9,0x20,0x41, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x01,0x23,0x87,0x74,0x66,0x6A,0x67,0x76,0x6D,0x66, /* a */ - 0x76,0xF7,0x78,0xE6,0x76,0xB6,0x69,0x99,0x17,0x66, - 0x66,0xE6,0x87,0x66,0x6D,0x87,0x66,0xC6,0x6A,0x9F, - - 0x6A,0x94,0x19,0x77,0xBA,0x9F,0x6A,0x43,0x51,0x99, /* b */ - 0xAC,0xFC,0x51,0x06,0x7E,0xD5,0x87,0xF5,0x19,0xC5, - 0xEC,0xB5,0x41,0xB8,0xE4,0x41,0x11,0xDE,0x1D,0x40, - - 0x70,0xF6,0xE9,0xD0,0x4D,0x28,0x9C,0x4E,0x89,0x91, /* x */ - 0x3C,0xE3,0x53,0x0B,0xFD,0xE9,0x03,0x97,0x7D,0x42, - 0xB1,0x46,0xD5,0x39,0xBF,0x1B,0xDE,0x4E,0x9C,0x92, - - 0x2E,0x5A,0x0E,0xAF,0x6E,0x5E,0x13,0x05,0xB9,0x00, /* y */ - 0x4D,0xCE,0x5C,0x0E,0xD7,0xFE,0x59,0xA3,0x56,0x08, - 0xF3,0x38,0x37,0xC8,0x16,0xD8,0x0B,0x79,0xF4,0x61, - - 0x0C,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC, /* order */ - 0xCC,0xCC,0xCC,0xCC,0xCC,0xAC,0x49,0x12,0xD2,0xD9, - 0xDF,0x90,0x3E,0xF9,0x88,0x8B,0x8A,0x0E,0x4C,0xFF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+35*6]; } - _EC_X9_62_CHAR2_272W1 = { - { NID_X9_62_characteristic_two_field,0,35,0xFF06 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00, - 0x00,0x00,0x00,0x00,0x0B, - 0x00,0x91,0xA0,0x91,0xF0,0x3B,0x5F,0xBA,0x4A,0xB2, /* a */ - 0xCC,0xF4,0x9C,0x4E,0xDD,0x22,0x0F,0xB0,0x28,0x71, - 0x2D,0x42,0xBE,0x75,0x2B,0x2C,0x40,0x09,0x4D,0xBA, - 0xCD,0xB5,0x86,0xFB,0x20, - 0x00,0x71,0x67,0xEF,0xC9,0x2B,0xB2,0xE3,0xCE,0x7C, /* b */ - 0x8A,0xAA,0xFF,0x34,0xE1,0x2A,0x9C,0x55,0x70,0x03, - 0xD7,0xC7,0x3A,0x6F,0xAF,0x00,0x3F,0x99,0xF6,0xCC, - 0x84,0x82,0xE5,0x40,0xF7, - 0x00,0x61,0x08,0xBA,0xBB,0x2C,0xEE,0xBC,0xF7,0x87, /* x */ - 0x05,0x8A,0x05,0x6C,0xBE,0x0C,0xFE,0x62,0x2D,0x77, - 0x23,0xA2,0x89,0xE0,0x8A,0x07,0xAE,0x13,0xEF,0x0D, - 0x10,0xD1,0x71,0xDD,0x8D, - 0x00,0x10,0xC7,0x69,0x57,0x16,0x85,0x1E,0xEF,0x6B, /* y */ - 0xA7,0xF6,0x87,0x2E,0x61,0x42,0xFB,0xD2,0x41,0xB8, - 0x30,0xFF,0x5E,0xFC,0xAC,0xEC,0xCA,0xB0,0x5E,0x02, - 0x00,0x5D,0xDE,0x9D,0x23, - 0x00,0x00,0x01,0x00,0xFA,0xF5,0x13,0x54,0xE0,0xE3, /* order */ - 0x9E,0x48,0x92,0xDF,0x6E,0x31,0x9C,0x72,0xC8,0x16, - 0x16,0x03,0xFA,0x45,0xAA,0x7B,0x99,0x8A,0x16,0x7B, - 0x8F,0x1E,0x62,0x95,0x21 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+39*6]; } - _EC_X9_62_CHAR2_304W1 = { - { NID_X9_62_characteristic_two_field,0,39,0xFE2E }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x07, - 0x00,0xFD,0x0D,0x69,0x31,0x49,0xA1,0x18,0xF6,0x51, /* a */ - 0xE6,0xDC,0xE6,0x80,0x20,0x85,0x37,0x7E,0x5F,0x88, - 0x2D,0x1B,0x51,0x0B,0x44,0x16,0x00,0x74,0xC1,0x28, - 0x80,0x78,0x36,0x5A,0x03,0x96,0xC8,0xE6,0x81, - 0x00,0xBD,0xDB,0x97,0xE5,0x55,0xA5,0x0A,0x90,0x8E, /* b */ - 0x43,0xB0,0x1C,0x79,0x8E,0xA5,0xDA,0xA6,0x78,0x8F, - 0x1E,0xA2,0x79,0x4E,0xFC,0xF5,0x71,0x66,0xB8,0xC1, - 0x40,0x39,0x60,0x1E,0x55,0x82,0x73,0x40,0xBE, - 0x00,0x19,0x7B,0x07,0x84,0x5E,0x9B,0xE2,0xD9,0x6A, /* x */ - 0xDB,0x0F,0x5F,0x3C,0x7F,0x2C,0xFF,0xBD,0x7A,0x3E, - 0xB8,0xB6,0xFE,0xC3,0x5C,0x7F,0xD6,0x7F,0x26,0xDD, - 0xF6,0x28,0x5A,0x64,0x4F,0x74,0x0A,0x26,0x14, - 0x00,0xE1,0x9F,0xBE,0xB7,0x6E,0x0D,0xA1,0x71,0x51, /* y */ - 0x7E,0xCF,0x40,0x1B,0x50,0x28,0x9B,0xF0,0x14,0x10, - 0x32,0x88,0x52,0x7A,0x9B,0x41,0x6A,0x10,0x5E,0x80, - 0x26,0x0B,0x54,0x9F,0xDC,0x1B,0x92,0xC0,0x3B, - 0x00,0x00,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC, /* order */ - 0x80,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC,0x80, - 0x01,0x02,0x2D,0x5C,0x91,0xDD,0x17,0x3F,0x8F,0xB5, - 0x61,0xDA,0x68,0x99,0x16,0x44,0x43,0x05,0x1D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+45*6]; } - _EC_X9_62_CHAR2_359V1 = { - { NID_X9_62_characteristic_two_field,20,45,0x4C }, - { 0x2B,0x35,0x49,0x20,0xB7,0x24,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0x5B,0xA1,0x33,0x2D,0xC6, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x01, - 0x56,0x67,0x67,0x6A,0x65,0x4B,0x20,0x75,0x4F,0x35, /* a */ - 0x6E,0xA9,0x20,0x17,0xD9,0x46,0x56,0x7C,0x46,0x67, - 0x55,0x56,0xF1,0x95,0x56,0xA0,0x46,0x16,0xB5,0x67, - 0xD2,0x23,0xA5,0xE0,0x56,0x56,0xFB,0x54,0x90,0x16, - 0xA9,0x66,0x56,0xA5,0x57, - 0x24,0x72,0xE2,0xD0,0x19,0x7C,0x49,0x36,0x3F,0x1F, /* b */ - 0xE7,0xF5,0xB6,0xDB,0x07,0x5D,0x52,0xB6,0x94,0x7D, - 0x13,0x5D,0x8C,0xA4,0x45,0x80,0x5D,0x39,0xBC,0x34, - 0x56,0x26,0x08,0x96,0x87,0x74,0x2B,0x63,0x29,0xE7, - 0x06,0x80,0x23,0x19,0x88, - 0x3C,0x25,0x8E,0xF3,0x04,0x77,0x67,0xE7,0xED,0xE0, /* x */ - 0xF1,0xFD,0xAA,0x79,0xDA,0xEE,0x38,0x41,0x36,0x6A, - 0x13,0x2E,0x16,0x3A,0xCE,0xD4,0xED,0x24,0x01,0xDF, - 0x9C,0x6B,0xDC,0xDE,0x98,0xE8,0xE7,0x07,0xC0,0x7A, - 0x22,0x39,0xB1,0xB0,0x97, - 0x53,0xD7,0xE0,0x85,0x29,0x54,0x70,0x48,0x12,0x1E, /* y */ - 0x9C,0x95,0xF3,0x79,0x1D,0xD8,0x04,0x96,0x39,0x48, - 0xF3,0x4F,0xAE,0x7B,0xF4,0x4E,0xA8,0x23,0x65,0xDC, - 0x78,0x68,0xFE,0x57,0xE4,0xAE,0x2D,0xE2,0x11,0x30, - 0x5A,0x40,0x71,0x04,0xBD, - 0x01,0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1, /* order */ - 0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1,0xAF, - 0x28,0x6B,0xC9,0xFB,0x8F,0x6B,0x85,0xC5,0x56,0x89, - 0x2C,0x20,0xA7,0xEB,0x96,0x4F,0xE7,0x71,0x9E,0x74, - 0xF4,0x90,0x75,0x8D,0x3B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+47*6]; } - _EC_X9_62_CHAR2_368W1 = { - { NID_X9_62_characteristic_two_field,0,47,0xFF70 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x07, - 0x00,0xE0,0xD2,0xEE,0x25,0x09,0x52,0x06,0xF5,0xE2, /* a */ - 0xA4,0xF9,0xED,0x22,0x9F,0x1F,0x25,0x6E,0x79,0xA0, - 0xE2,0xB4,0x55,0x97,0x0D,0x8D,0x0D,0x86,0x5B,0xD9, - 0x47,0x78,0xC5,0x76,0xD6,0x2F,0x0A,0xB7,0x51,0x9C, - 0xCD,0x2A,0x1A,0x90,0x6A,0xE3,0x0D, - 0x00,0xFC,0x12,0x17,0xD4,0x32,0x0A,0x90,0x45,0x2C, /* b */ - 0x76,0x0A,0x58,0xED,0xCD,0x30,0xC8,0xDD,0x06,0x9B, - 0x3C,0x34,0x45,0x38,0x37,0xA3,0x4E,0xD5,0x0C,0xB5, - 0x49,0x17,0xE1,0xC2,0x11,0x2D,0x84,0xD1,0x64,0xF4, - 0x44,0xF8,0xF7,0x47,0x86,0x04,0x6A, - 0x00,0x10,0x85,0xE2,0x75,0x53,0x81,0xDC,0xCC,0xE3, /* x */ - 0xC1,0x55,0x7A,0xFA,0x10,0xC2,0xF0,0xC0,0xC2,0x82, - 0x56,0x46,0xC5,0xB3,0x4A,0x39,0x4C,0xBC,0xFA,0x8B, - 0xC1,0x6B,0x22,0xE7,0xE7,0x89,0xE9,0x27,0xBE,0x21, - 0x6F,0x02,0xE1,0xFB,0x13,0x6A,0x5F, - 0x00,0x7B,0x3E,0xB1,0xBD,0xDC,0xBA,0x62,0xD5,0xD8, /* y */ - 0xB2,0x05,0x9B,0x52,0x57,0x97,0xFC,0x73,0x82,0x2C, - 0x59,0x05,0x9C,0x62,0x3A,0x45,0xFF,0x38,0x43,0xCE, - 0xE8,0xF8,0x7C,0xD1,0x85,0x5A,0xDA,0xA8,0x1E,0x2A, - 0x07,0x50,0xB8,0x0F,0xDA,0x23,0x10, - 0x00,0x00,0x01,0x00,0x90,0x51,0x2D,0xA9,0xAF,0x72, /* order */ - 0xB0,0x83,0x49,0xD9,0x8A,0x5D,0xD4,0xC7,0xB0,0x53, - 0x2E,0xCA,0x51,0xCE,0x03,0xE2,0xD1,0x0F,0x3B,0x7A, - 0xC5,0x79,0xBD,0x87,0xE9,0x09,0xAE,0x40,0xA6,0xF1, - 0x31,0xE9,0xCF,0xCE,0x5B,0xD9,0x67 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+54*6]; } - _EC_X9_62_CHAR2_431R1 = { - { NID_X9_62_characteristic_two_field,0,54,0x2760 }, - { /* no seed */ - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x01, - 0x1A,0x82,0x7E,0xF0,0x0D,0xD6,0xFC,0x0E,0x23,0x4C, /* a */ - 0xAF,0x04,0x6C,0x6A,0x5D,0x8A,0x85,0x39,0x5B,0x23, - 0x6C,0xC4,0xAD,0x2C,0xF3,0x2A,0x0C,0xAD,0xBD,0xC9, - 0xDD,0xF6,0x20,0xB0,0xEB,0x99,0x06,0xD0,0x95,0x7F, - 0x6C,0x6F,0xEA,0xCD,0x61,0x54,0x68,0xDF,0x10,0x4D, - 0xE2,0x96,0xCD,0x8F, - 0x10,0xD9,0xB4,0xA3,0xD9,0x04,0x7D,0x8B,0x15,0x43, /* b */ - 0x59,0xAB,0xFB,0x1B,0x7F,0x54,0x85,0xB0,0x4C,0xEB, - 0x86,0x82,0x37,0xDD,0xC9,0xDE,0xDA,0x98,0x2A,0x67, - 0x9A,0x5A,0x91,0x9B,0x62,0x6D,0x4E,0x50,0xA8,0xDD, - 0x73,0x1B,0x10,0x7A,0x99,0x62,0x38,0x1F,0xB5,0xD8, - 0x07,0xBF,0x26,0x18, - 0x12,0x0F,0xC0,0x5D,0x3C,0x67,0xA9,0x9D,0xE1,0x61, /* x */ - 0xD2,0xF4,0x09,0x26,0x22,0xFE,0xCA,0x70,0x1B,0xE4, - 0xF5,0x0F,0x47,0x58,0x71,0x4E,0x8A,0x87,0xBB,0xF2, - 0xA6,0x58,0xEF,0x8C,0x21,0xE7,0xC5,0xEF,0xE9,0x65, - 0x36,0x1F,0x6C,0x29,0x99,0xC0,0xC2,0x47,0xB0,0xDB, - 0xD7,0x0C,0xE6,0xB7, - 0x20,0xD0,0xAF,0x89,0x03,0xA9,0x6F,0x8D,0x5F,0xA2, /* y */ - 0xC2,0x55,0x74,0x5D,0x3C,0x45,0x1B,0x30,0x2C,0x93, - 0x46,0xD9,0xB7,0xE4,0x85,0xE7,0xBC,0xE4,0x1F,0x6B, - 0x59,0x1F,0x3E,0x8F,0x6A,0xDD,0xCB,0xB0,0xBC,0x4C, - 0x2F,0x94,0x7A,0x7D,0xE1,0xA8,0x9B,0x62,0x5D,0x6A, - 0x59,0x8B,0x37,0x60, - 0x00,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34, /* order */ - 0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03, - 0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x23, - 0xC3,0x13,0xFA,0xB5,0x05,0x89,0x70,0x3B,0x5E,0xC6, - 0x8D,0x35,0x87,0xFE,0xC6,0x0D,0x16,0x1C,0xC1,0x49, - 0xC1,0xAD,0x4A,0x91 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } - _EC_WTLS_1 = { - { NID_X9_62_characteristic_two_field,0,15,2 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x01, - 0x01,0x66,0x79,0x79,0xA4,0x0B,0xA4,0x97,0xE5,0xD5, /* x */ - 0xC2,0x70,0x78,0x06,0x17, - 0x00,0xF4,0x4B,0x4A,0xF1,0xEC,0xC2,0x63,0x0E,0x08, /* y */ - 0x78,0x5C,0xEB,0xCC,0x15, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFD,0xBF, /* order */ - 0x91,0xAF,0x6D,0xEA,0x73 } - }; + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x02, 0x0A, 0x60, 0x19, 0x07, 0xB8, 0xC9, 0x53, 0xCA, 0x14, /* b */ + 0x81, 0xEB, 0x10, 0x51, 0x2F, 0x78, 0x74, 0x4A, 0x32, 0x05, + 0xFD, + 0x03, 0xF0, 0xEB, 0xA1, 0x62, 0x86, 0xA2, 0xD5, 0x7E, 0xA0, /* x */ + 0x99, 0x11, 0x68, 0xD4, 0x99, 0x46, 0x37, 0xE8, 0x34, 0x3E, + 0x36, + 0x00, 0xD5, 0x1F, 0xBC, 0x6C, 0x71, 0xA0, 0x09, 0x4F, 0xA2, /* y */ + 0xCD, 0xD5, 0x45, 0xB1, 0x1C, 0x5C, 0x0C, 0x79, 0x73, 0x24, + 0xF1, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x02, 0x92, 0xFE, 0x77, 0xE7, 0x0C, 0x12, 0xA4, 0x23, 0x4C, + 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} + _EC_SECG_CHAR2_193R1 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + 0x10, 0x3F, 0xAE, 0xC7, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, /* seed */ + 0x61, 0x51, 0x75, 0x77, 0x7F, 0xC5, 0xB1, 0x91, 0xEF, 0x30, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x80, 0x01, + 0x00, 0x17, 0x85, 0x8F, 0xEB, 0x7A, 0x98, 0x97, 0x51, 0x69, /* a */ + 0xE1, 0x71, 0xF7, 0x7B, 0x40, 0x87, 0xDE, 0x09, 0x8A, 0xC8, + 0xA9, 0x11, 0xDF, 0x7B, 0x01, + 0x00, 0xFD, 0xFB, 0x49, 0xBF, 0xE6, 0xC3, 0xA8, 0x9F, 0xAC, /* b */ + 0xAD, 0xAA, 0x7A, 0x1E, 0x5B, 0xBC, 0x7C, 0xC1, 0xC2, 0xE5, + 0xD8, 0x31, 0x47, 0x88, 0x14, + 0x01, 0xF4, 0x81, 0xBC, 0x5F, 0x0F, 0xF8, 0x4A, 0x74, 0xAD, /* x */ + 0x6C, 0xDF, 0x6F, 0xDE, 0xF4, 0xBF, 0x61, 0x79, 0x62, 0x53, + 0x72, 0xD8, 0xC0, 0xC5, 0xE1, + 0x00, 0x25, 0xE3, 0x99, 0xF2, 0x90, 0x37, 0x12, 0xCC, 0xF3, /* y */ + 0xEA, 0x9E, 0x3A, 0x1A, 0xD1, 0x7F, 0xB0, 0xB3, 0x20, 0x1B, + 0x6A, 0xF7, 0xCE, 0x1B, 0x05, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0xC7, 0xF3, 0x4A, 0x77, 0x8F, 0x44, 0x3A, + 0xCC, 0x92, 0x0E, 0xBA, 0x49 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} + _EC_SECG_CHAR2_193R2 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + 0x10, 0xB7, 0xB4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, /* seed */ + 0x17, 0x51, 0x37, 0xC8, 0xA1, 0x6F, 0xD0, 0xDA, 0x22, 0x11, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x80, 0x01, + 0x01, 0x63, 0xF3, 0x5A, 0x51, 0x37, 0xC2, 0xCE, 0x3E, 0xA6, /* a */ + 0xED, 0x86, 0x67, 0x19, 0x0B, 0x0B, 0xC4, 0x3E, 0xCD, 0x69, + 0x97, 0x77, 0x02, 0x70, 0x9B, + 0x00, 0xC9, 0xBB, 0x9E, 0x89, 0x27, 0xD4, 0xD6, 0x4C, 0x37, /* b */ + 0x7E, 0x2A, 0xB2, 0x85, 0x6A, 0x5B, 0x16, 0xE3, 0xEF, 0xB7, + 0xF6, 0x1D, 0x43, 0x16, 0xAE, + 0x00, 0xD9, 0xB6, 0x7D, 0x19, 0x2E, 0x03, 0x67, 0xC8, 0x03, /* x */ + 0xF3, 0x9E, 0x1A, 0x7E, 0x82, 0xCA, 0x14, 0xA6, 0x51, 0x35, + 0x0A, 0xAE, 0x61, 0x7E, 0x8F, + 0x01, 0xCE, 0x94, 0x33, 0x56, 0x07, 0xC3, 0x04, 0xAC, 0x29, /* y */ + 0xE7, 0xDE, 0xFB, 0xD9, 0xCA, 0x01, 0xF5, 0x96, 0xF9, 0x27, + 0x22, 0x4C, 0xDE, 0xCF, 0x6C, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x01, 0x5A, 0xAB, 0x56, 0x1B, 0x00, 0x54, 0x13, + 0xCC, 0xD4, 0xEE, 0x99, 0xD5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} + _EC_NIST_CHAR2_233K = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x01, 0x72, 0x32, 0xBA, 0x85, 0x3A, 0x7E, 0x73, 0x1A, 0xF1, /* x */ + 0x29, 0xF2, 0x2F, 0xF4, 0x14, 0x95, 0x63, 0xA4, 0x19, 0xC2, + 0x6B, 0xF5, 0x0A, 0x4C, 0x9D, 0x6E, 0xEF, 0xAD, 0x61, 0x26, + + 0x01, 0xDB, 0x53, 0x7D, 0xEC, 0xE8, 0x19, 0xB7, 0xF7, 0x0F, /* y */ + 0x55, 0x5A, 0x67, 0xC4, 0x27, 0xA8, 0xCD, 0x9B, 0xF1, 0x8A, + 0xEB, 0x9B, 0x56, 0xE0, 0xC1, 0x10, 0x56, 0xFA, 0xE6, 0xA3, + + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x9D, 0x5B, 0xB9, 0x15, + 0xBC, 0xD4, 0x6E, 0xFB, 0x1A, 0xD5, 0xF1, 0x73, 0xAB, 0xDF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_NIST_CHAR2_233B = { + { + NID_X9_62_characteristic_two_field, 20, 30, 2 + }, + { + 0x74, 0xD5, 0x9F, 0xF0, 0x7F, 0x6B, 0x41, 0x3D, 0x0E, 0xA1, /* seed */ + 0x4B, 0x34, 0x4B, 0x20, 0xA2, 0xDB, 0x04, 0x9B, 0x50, 0xC3, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x66, 0x64, 0x7E, 0xDE, 0x6C, 0x33, 0x2C, 0x7F, 0x8C, /* b */ + 0x09, 0x23, 0xBB, 0x58, 0x21, 0x3B, 0x33, 0x3B, 0x20, 0xE9, + 0xCE, 0x42, 0x81, 0xFE, 0x11, 0x5F, 0x7D, 0x8F, 0x90, 0xAD, + + 0x00, 0xFA, 0xC9, 0xDF, 0xCB, 0xAC, 0x83, 0x13, 0xBB, 0x21, /* x */ + 0x39, 0xF1, 0xBB, 0x75, 0x5F, 0xEF, 0x65, 0xBC, 0x39, 0x1F, + 0x8B, 0x36, 0xF8, 0xF8, 0xEB, 0x73, 0x71, 0xFD, 0x55, 0x8B, + + 0x01, 0x00, 0x6A, 0x08, 0xA4, 0x19, 0x03, 0x35, 0x06, 0x78, /* y */ + 0xE5, 0x85, 0x28, 0xBE, 0xBF, 0x8A, 0x0B, 0xEF, 0xF8, 0x67, + 0xA7, 0xCA, 0x36, 0x71, 0x6F, 0x7E, 0x01, 0xF8, 0x10, 0x52, + + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x13, 0xE9, 0x74, 0xE7, 0x2F, + 0x8A, 0x69, 0x22, 0x03, 0x1D, 0x26, 0x03, 0xCF, 0xE0, 0xD7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} + _EC_SECG_CHAR2_239K1 = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { /* no seed */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x29, 0xA0, 0xB6, 0xA8, 0x87, 0xA9, 0x83, 0xE9, 0x73, 0x09, /* x */ + 0x88, 0xA6, 0x87, 0x27, 0xA8, 0xB2, 0xD1, 0x26, 0xC4, 0x4C, + 0xC2, 0xCC, 0x7B, 0x2A, 0x65, 0x55, 0x19, 0x30, 0x35, 0xDC, + + 0x76, 0x31, 0x08, 0x04, 0xF1, 0x2E, 0x54, 0x9B, 0xDB, 0x01, /* y */ + 0x1C, 0x10, 0x30, 0x89, 0xE7, 0x35, 0x10, 0xAC, 0xB2, 0x75, + 0xFC, 0x31, 0x2A, 0x5D, 0xC6, 0xB7, 0x65, 0x53, 0xF0, 0xCA, + + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x5A, 0x79, 0xFE, 0xC6, 0x7C, + 0xB6, 0xE9, 0x1F, 0x1C, 0x1D, 0xA8, 0x00, 0xE4, 0x78, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 36 * 6]; +} + _EC_NIST_CHAR2_283K = { + { + NID_X9_62_characteristic_two_field, 0, 36, 4 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x05, 0x03, 0x21, 0x3F, 0x78, 0xCA, 0x44, 0x88, 0x3F, 0x1A, /* x */ + 0x3B, 0x81, 0x62, 0xF1, 0x88, 0xE5, 0x53, 0xCD, 0x26, 0x5F, + 0x23, 0xC1, 0x56, 0x7A, 0x16, 0x87, 0x69, 0x13, 0xB0, 0xC2, + 0xAC, 0x24, 0x58, 0x49, 0x28, 0x36, + 0x01, 0xCC, 0xDA, 0x38, 0x0F, 0x1C, 0x9E, 0x31, 0x8D, 0x90, /* y */ + 0xF9, 0x5D, 0x07, 0xE5, 0x42, 0x6F, 0xE8, 0x7E, 0x45, 0xC0, + 0xE8, 0x18, 0x46, 0x98, 0xE4, 0x59, 0x62, 0x36, 0x4E, 0x34, + 0x11, 0x61, 0x77, 0xDD, 0x22, 0x59, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xE9, 0xAE, + 0x2E, 0xD0, 0x75, 0x77, 0x26, 0x5D, 0xFF, 0x7F, 0x94, 0x45, + 0x1E, 0x06, 0x1E, 0x16, 0x3C, 0x61 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 36 * 6]; +} + _EC_NIST_CHAR2_283B = { + { + NID_X9_62_characteristic_two_field, 20, 36, 2 + }, + { + 0x77, 0xE2, 0xB0, 0x73, 0x70, 0xEB, 0x0F, 0x83, 0x2A, 0x6D, /* no seed */ + 0xD5, 0xB6, 0x2D, 0xFC, 0x88, 0xCD, 0x06, 0xBB, 0x84, 0xBE, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x02, 0x7B, 0x68, 0x0A, 0xC8, 0xB8, 0x59, 0x6D, 0xA5, 0xA4, /* b */ + 0xAF, 0x8A, 0x19, 0xA0, 0x30, 0x3F, 0xCA, 0x97, 0xFD, 0x76, + 0x45, 0x30, 0x9F, 0xA2, 0xA5, 0x81, 0x48, 0x5A, 0xF6, 0x26, + 0x3E, 0x31, 0x3B, 0x79, 0xA2, 0xF5, + 0x05, 0xF9, 0x39, 0x25, 0x8D, 0xB7, 0xDD, 0x90, 0xE1, 0x93, /* x */ + 0x4F, 0x8C, 0x70, 0xB0, 0xDF, 0xEC, 0x2E, 0xED, 0x25, 0xB8, + 0x55, 0x7E, 0xAC, 0x9C, 0x80, 0xE2, 0xE1, 0x98, 0xF8, 0xCD, + 0xBE, 0xCD, 0x86, 0xB1, 0x20, 0x53, + 0x03, 0x67, 0x68, 0x54, 0xFE, 0x24, 0x14, 0x1C, 0xB9, 0x8F, /* y */ + 0xE6, 0xD4, 0xB2, 0x0D, 0x02, 0xB4, 0x51, 0x6F, 0xF7, 0x02, + 0x35, 0x0E, 0xDD, 0xB0, 0x82, 0x67, 0x79, 0xC8, 0x13, 0xF0, + 0xDF, 0x45, 0xBE, 0x81, 0x12, 0xF4, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xEF, 0x90, + 0x39, 0x96, 0x60, 0xFC, 0x93, 0x8A, 0x90, 0x16, 0x5B, 0x04, + 0x2A, 0x7C, 0xEF, 0xAD, 0xB3, 0x07 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 52 * 6]; +} + _EC_NIST_CHAR2_409K = { + { + NID_X9_62_characteristic_two_field, 0, 52, 4 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x60, 0xF0, 0x5F, 0x65, 0x8F, 0x49, 0xC1, 0xAD, 0x3A, /* x */ + 0xB1, 0x89, 0x0F, 0x71, 0x84, 0x21, 0x0E, 0xFD, 0x09, 0x87, + 0xE3, 0x07, 0xC8, 0x4C, 0x27, 0xAC, 0xCF, 0xB8, 0xF9, 0xF6, + 0x7C, 0xC2, 0xC4, 0x60, 0x18, 0x9E, 0xB5, 0xAA, 0xAA, 0x62, + 0xEE, 0x22, 0x2E, 0xB1, 0xB3, 0x55, 0x40, 0xCF, 0xE9, 0x02, + 0x37, 0x46, + 0x01, 0xE3, 0x69, 0x05, 0x0B, 0x7C, 0x4E, 0x42, 0xAC, 0xBA, /* y */ + 0x1D, 0xAC, 0xBF, 0x04, 0x29, 0x9C, 0x34, 0x60, 0x78, 0x2F, + 0x91, 0x8E, 0xA4, 0x27, 0xE6, 0x32, 0x51, 0x65, 0xE9, 0xEA, + 0x10, 0xE3, 0xDA, 0x5F, 0x6C, 0x42, 0xE9, 0xC5, 0x52, 0x15, + 0xAA, 0x9C, 0xA2, 0x7A, 0x58, 0x63, 0xEC, 0x48, 0xD8, 0xE0, + 0x28, 0x6B, + 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0x5F, 0x83, 0xB2, + 0xD4, 0xEA, 0x20, 0x40, 0x0E, 0xC4, 0x55, 0x7D, 0x5E, 0xD3, + 0xE3, 0xE7, 0xCA, 0x5B, 0x4B, 0x5C, 0x83, 0xB8, 0xE0, 0x1E, + 0x5F, 0xCF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 52 * 6]; +} + _EC_NIST_CHAR2_409B = { + { + NID_X9_62_characteristic_two_field, 20, 52, 2 + }, + { + 0x40, 0x99, 0xB5, 0xA4, 0x57, 0xF9, 0xD6, 0x9F, 0x79, 0x21, /* seed */ + 0x3D, 0x09, 0x4C, 0x4B, 0xCD, 0x4D, 0x42, 0x62, 0x21, 0x0B, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x21, 0xA5, 0xC2, 0xC8, 0xEE, 0x9F, 0xEB, 0x5C, 0x4B, /* b */ + 0x9A, 0x75, 0x3B, 0x7B, 0x47, 0x6B, 0x7F, 0xD6, 0x42, 0x2E, + 0xF1, 0xF3, 0xDD, 0x67, 0x47, 0x61, 0xFA, 0x99, 0xD6, 0xAC, + 0x27, 0xC8, 0xA9, 0xA1, 0x97, 0xB2, 0x72, 0x82, 0x2F, 0x6C, + 0xD5, 0x7A, 0x55, 0xAA, 0x4F, 0x50, 0xAE, 0x31, 0x7B, 0x13, + 0x54, 0x5F, + 0x01, 0x5D, 0x48, 0x60, 0xD0, 0x88, 0xDD, 0xB3, 0x49, 0x6B, /* x */ + 0x0C, 0x60, 0x64, 0x75, 0x62, 0x60, 0x44, 0x1C, 0xDE, 0x4A, + 0xF1, 0x77, 0x1D, 0x4D, 0xB0, 0x1F, 0xFE, 0x5B, 0x34, 0xE5, + 0x97, 0x03, 0xDC, 0x25, 0x5A, 0x86, 0x8A, 0x11, 0x80, 0x51, + 0x56, 0x03, 0xAE, 0xAB, 0x60, 0x79, 0x4E, 0x54, 0xBB, 0x79, + 0x96, 0xA7, + 0x00, 0x61, 0xB1, 0xCF, 0xAB, 0x6B, 0xE5, 0xF3, 0x2B, 0xBF, /* y */ + 0xA7, 0x83, 0x24, 0xED, 0x10, 0x6A, 0x76, 0x36, 0xB9, 0xC5, + 0xA7, 0xBD, 0x19, 0x8D, 0x01, 0x58, 0xAA, 0x4F, 0x54, 0x88, + 0xD0, 0x8F, 0x38, 0x51, 0x4F, 0x1F, 0xDF, 0x4B, 0x4F, 0x40, + 0xD2, 0x18, 0x1B, 0x36, 0x81, 0xC3, 0x64, 0xBA, 0x02, 0x73, + 0xC7, 0x06, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xE2, 0xAA, 0xD6, + 0xA6, 0x12, 0xF3, 0x33, 0x07, 0xBE, 0x5F, 0xA4, 0x7C, 0x3C, + 0x9E, 0x05, 0x2F, 0x83, 0x81, 0x64, 0xCD, 0x37, 0xD9, 0xA2, + 0x11, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 72 * 6]; +} + _EC_NIST_CHAR2_571K = { + { + NID_X9_62_characteristic_two_field, 0, 72, 4 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x25, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x02, 0x6E, 0xB7, 0xA8, 0x59, 0x92, 0x3F, 0xBC, 0x82, 0x18, /* x */ + 0x96, 0x31, 0xF8, 0x10, 0x3F, 0xE4, 0xAC, 0x9C, 0xA2, 0x97, + 0x00, 0x12, 0xD5, 0xD4, 0x60, 0x24, 0x80, 0x48, 0x01, 0x84, + 0x1C, 0xA4, 0x43, 0x70, 0x95, 0x84, 0x93, 0xB2, 0x05, 0xE6, + 0x47, 0xDA, 0x30, 0x4D, 0xB4, 0xCE, 0xB0, 0x8C, 0xBB, 0xD1, + 0xBA, 0x39, 0x49, 0x47, 0x76, 0xFB, 0x98, 0x8B, 0x47, 0x17, + 0x4D, 0xCA, 0x88, 0xC7, 0xE2, 0x94, 0x52, 0x83, 0xA0, 0x1C, + 0x89, 0x72, + 0x03, 0x49, 0xDC, 0x80, 0x7F, 0x4F, 0xBF, 0x37, 0x4F, 0x4A, /* y */ + 0xEA, 0xDE, 0x3B, 0xCA, 0x95, 0x31, 0x4D, 0xD5, 0x8C, 0xEC, + 0x9F, 0x30, 0x7A, 0x54, 0xFF, 0xC6, 0x1E, 0xFC, 0x00, 0x6D, + 0x8A, 0x2C, 0x9D, 0x49, 0x79, 0xC0, 0xAC, 0x44, 0xAE, 0xA7, + 0x4F, 0xBE, 0xBB, 0xB9, 0xF7, 0x72, 0xAE, 0xDC, 0xB6, 0x20, + 0xB0, 0x1A, 0x7B, 0xA7, 0xAF, 0x1B, 0x32, 0x04, 0x30, 0xC8, + 0x59, 0x19, 0x84, 0xF6, 0x01, 0xCD, 0x4C, 0x14, 0x3E, 0xF1, + 0xC7, 0xA3, + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x13, 0x18, 0x50, 0xE1, + 0xF1, 0x9A, 0x63, 0xE4, 0xB3, 0x91, 0xA8, 0xDB, 0x91, 0x7F, + 0x41, 0x38, 0xB6, 0x30, 0xD8, 0x4B, 0xE5, 0xD6, 0x39, 0x38, + 0x1E, 0x91, 0xDE, 0xB4, 0x5C, 0xFE, 0x77, 0x8F, 0x63, 0x7C, + 0x10, 0x01 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 72 * 6]; +} + _EC_NIST_CHAR2_571B = { + { + NID_X9_62_characteristic_two_field, 20, 72, 2 + }, + { + 0x2A, 0xA0, 0x58, 0xF7, 0x3A, 0x0E, 0x33, 0xAB, 0x48, 0x6B, /* seed */ + 0x0F, 0x61, 0x04, 0x10, 0xC5, 0x3A, 0x7F, 0x13, 0x23, 0x10, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x25, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x02, 0xF4, 0x0E, 0x7E, 0x22, 0x21, 0xF2, 0x95, 0xDE, 0x29, /* b */ + 0x71, 0x17, 0xB7, 0xF3, 0xD6, 0x2F, 0x5C, 0x6A, 0x97, 0xFF, + 0xCB, 0x8C, 0xEF, 0xF1, 0xCD, 0x6B, 0xA8, 0xCE, 0x4A, 0x9A, + 0x18, 0xAD, 0x84, 0xFF, 0xAB, 0xBD, 0x8E, 0xFA, 0x59, 0x33, + 0x2B, 0xE7, 0xAD, 0x67, 0x56, 0xA6, 0x6E, 0x29, 0x4A, 0xFD, + 0x18, 0x5A, 0x78, 0xFF, 0x12, 0xAA, 0x52, 0x0E, 0x4D, 0xE7, + 0x39, 0xBA, 0xCA, 0x0C, 0x7F, 0xFE, 0xFF, 0x7F, 0x29, 0x55, + 0x72, 0x7A, + 0x03, 0x03, 0x00, 0x1D, 0x34, 0xB8, 0x56, 0x29, 0x6C, 0x16, /* x */ + 0xC0, 0xD4, 0x0D, 0x3C, 0xD7, 0x75, 0x0A, 0x93, 0xD1, 0xD2, + 0x95, 0x5F, 0xA8, 0x0A, 0xA5, 0xF4, 0x0F, 0xC8, 0xDB, 0x7B, + 0x2A, 0xBD, 0xBD, 0xE5, 0x39, 0x50, 0xF4, 0xC0, 0xD2, 0x93, + 0xCD, 0xD7, 0x11, 0xA3, 0x5B, 0x67, 0xFB, 0x14, 0x99, 0xAE, + 0x60, 0x03, 0x86, 0x14, 0xF1, 0x39, 0x4A, 0xBF, 0xA3, 0xB4, + 0xC8, 0x50, 0xD9, 0x27, 0xE1, 0xE7, 0x76, 0x9C, 0x8E, 0xEC, + 0x2D, 0x19, + 0x03, 0x7B, 0xF2, 0x73, 0x42, 0xDA, 0x63, 0x9B, 0x6D, 0xCC, /* y */ + 0xFF, 0xFE, 0xB7, 0x3D, 0x69, 0xD7, 0x8C, 0x6C, 0x27, 0xA6, + 0x00, 0x9C, 0xBB, 0xCA, 0x19, 0x80, 0xF8, 0x53, 0x39, 0x21, + 0xE8, 0xA6, 0x84, 0x42, 0x3E, 0x43, 0xBA, 0xB0, 0x8A, 0x57, + 0x62, 0x91, 0xAF, 0x8F, 0x46, 0x1B, 0xB2, 0xA8, 0xB3, 0x53, + 0x1D, 0x2F, 0x04, 0x85, 0xC1, 0x9B, 0x16, 0xE2, 0xF1, 0x51, + 0x6E, 0x23, 0xDD, 0x3C, 0x1A, 0x48, 0x27, 0xAF, 0x1B, 0x8A, + 0xC1, 0x5B, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xE6, 0x61, 0xCE, 0x18, + 0xFF, 0x55, 0x98, 0x73, 0x08, 0x05, 0x9B, 0x18, 0x68, 0x23, + 0x85, 0x1E, 0xC7, 0xDD, 0x9C, 0xA1, 0x16, 0x1D, 0xE9, 0x3D, + 0x51, 0x74, 0xD6, 0x6E, 0x83, 0x82, 0xE9, 0xBB, 0x2F, 0xE8, + 0x4E, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V1 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0xD2, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, + 0xF4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x54, /* seed */ + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x07, 0x25, 0x46, 0xB5, 0x43, 0x52, 0x34, 0xA4, 0x22, 0xE0, /* a */ + 0x78, 0x96, 0x75, 0xF4, 0x32, 0xC8, 0x94, 0x35, 0xDE, 0x52, + 0x42, + 0x00, 0xC9, 0x51, 0x7D, 0x06, 0xD5, 0x24, 0x0D, 0x3C, 0xFF, /* b */ + 0x38, 0xC7, 0x4B, 0x20, 0xB6, 0xCD, 0x4D, 0x6F, 0x9D, 0xD4, + 0xD9, + 0x07, 0xAF, 0x69, 0x98, 0x95, 0x46, 0x10, 0x3D, 0x79, 0x32, /* x */ + 0x9F, 0xCC, 0x3D, 0x74, 0x88, 0x0F, 0x33, 0xBB, 0xE8, 0x03, + 0xCB, + 0x01, 0xEC, 0x23, 0x21, 0x1B, 0x59, 0x66, 0xAD, 0xEA, 0x1D, /* y */ + 0x3F, 0x87, 0xF7, 0xEA, 0x58, 0x48, 0xAE, 0xF0, 0xB7, 0xCA, + 0x9F, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xE6, 0x0F, 0xC8, 0x82, 0x1C, 0xC7, 0x4D, 0xAE, 0xAF, + 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V2 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0x53, 0x81, 0x4C, 0x05, 0x0D, 0x44, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0x0C, 0xA4, 0xE2, 0x9F, 0xFD, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x01, 0x08, 0xB3, 0x9E, 0x77, 0xC4, 0xB1, 0x08, 0xBE, 0xD9, /* a */ + 0x81, 0xED, 0x0E, 0x89, 0x0E, 0x11, 0x7C, 0x51, 0x1C, 0xF0, + 0x72, + 0x06, 0x67, 0xAC, 0xEB, 0x38, 0xAF, 0x4E, 0x48, 0x8C, 0x40, /* b */ + 0x74, 0x33, 0xFF, 0xAE, 0x4F, 0x1C, 0x81, 0x16, 0x38, 0xDF, + 0x20, + 0x00, 0x24, 0x26, 0x6E, 0x4E, 0xB5, 0x10, 0x6D, 0x0A, 0x96, /* x */ + 0x4D, 0x92, 0xC4, 0x86, 0x0E, 0x26, 0x71, 0xDB, 0x9B, 0x6C, + 0xC5, + 0x07, 0x9F, 0x68, 0x4D, 0xDF, 0x66, 0x84, 0xC5, 0xCD, 0x25, /* y */ + 0x8B, 0x38, 0x90, 0x02, 0x1B, 0x23, 0x86, 0xDF, 0xD1, 0x9F, + 0xC5, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFD, 0xF6, 0x4D, 0xE1, 0x15, 0x1A, 0xDB, 0xB7, 0x8F, 0x10, + 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V3 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0x50, 0xCB, 0xF1, 0xD9, 0x5C, 0xA9, 0x4D, 0x69, 0x6E, 0x67, /* seed */ + 0x68, 0x75, 0x61, 0x51, 0x75, 0xF1, 0x6A, 0x36, 0xA3, 0xB8, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x07, 0xA5, 0x26, 0xC6, 0x3D, 0x3E, 0x25, 0xA2, 0x56, 0xA0, /* a */ + 0x07, 0x69, 0x9F, 0x54, 0x47, 0xE3, 0x2A, 0xE4, 0x56, 0xB5, + 0x0E, + 0x03, 0xF7, 0x06, 0x17, 0x98, 0xEB, 0x99, 0xE2, 0x38, 0xFD, /* b */ + 0x6F, 0x1B, 0xF9, 0x5B, 0x48, 0xFE, 0xEB, 0x48, 0x54, 0x25, + 0x2B, + 0x02, 0xF9, 0xF8, 0x7B, 0x7C, 0x57, 0x4D, 0x0B, 0xDE, 0xCF, /* x */ + 0x8A, 0x22, 0xE6, 0x52, 0x47, 0x75, 0xF9, 0x8C, 0xDE, 0xBD, + 0xCB, + 0x05, 0xB9, 0x35, 0x59, 0x0C, 0x15, 0x5E, 0x17, 0xEA, 0x48, /* y */ + 0xEB, 0x3F, 0xF3, 0x71, 0x8B, 0x89, 0x3D, 0xF5, 0x9A, 0x05, + 0xD0, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFE, 0x1A, 0xEE, 0x14, 0x0F, 0x11, 0x0A, 0xFF, 0x96, 0x13, + 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 23 * 6]; +} + _EC_X9_62_CHAR2_176V1 = { + { + NID_X9_62_characteristic_two_field, 0, 23, 0xFF6E + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, + 0x00, 0x00, 0x07, + 0x00, 0xE4, 0xE6, 0xDB, 0x29, 0x95, 0x06, 0x5C, 0x40, 0x7D, /* a */ + 0x9D, 0x39, 0xB8, 0xD0, 0x96, 0x7B, 0x96, 0x70, 0x4B, 0xA8, + 0xE9, 0xC9, 0x0B, + 0x00, 0x5D, 0xDA, 0x47, 0x0A, 0xBE, 0x64, 0x14, 0xDE, 0x8E, /* b */ + 0xC1, 0x33, 0xAE, 0x28, 0xE9, 0xBB, 0xD7, 0xFC, 0xEC, 0x0A, + 0xE0, 0xFF, 0xF2, + 0x00, 0x8D, 0x16, 0xC2, 0x86, 0x67, 0x98, 0xB6, 0x00, 0xF9, /* x */ + 0xF0, 0x8B, 0xB4, 0xA8, 0xE8, 0x60, 0xF3, 0x29, 0x8C, 0xE0, + 0x4A, 0x57, 0x98, + 0x00, 0x6F, 0xA4, 0x53, 0x9C, 0x2D, 0xAD, 0xDD, 0xD6, 0xBA, /* y */ + 0xB5, 0x16, 0x7D, 0x61, 0xB4, 0x36, 0xE1, 0xD9, 0x2B, 0xB1, + 0x6A, 0x56, 0x2C, + 0x00, 0x00, 0x01, 0x00, 0x92, 0x53, 0x73, 0x97, 0xEC, 0xA4, /* order */ + 0xF6, 0x14, 0x57, 0x99, 0xD6, 0x2B, 0x0A, 0x19, 0xCE, 0x06, + 0xFE, 0x26, 0xAD + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V1 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 2 + }, + { + 0x4E, 0x13, 0xCA, 0x54, 0x27, 0x44, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x55, 0x2F, 0x27, 0x9A, 0x8C, 0x84, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x28, 0x66, 0x53, 0x7B, 0x67, 0x67, 0x52, 0x63, 0x6A, 0x68, /* a */ + 0xF5, 0x65, 0x54, 0xE1, 0x26, 0x40, 0x27, 0x6B, 0x64, 0x9E, + 0xF7, 0x52, 0x62, 0x67, + 0x2E, 0x45, 0xEF, 0x57, 0x1F, 0x00, 0x78, 0x6F, 0x67, 0xB0, /* b */ + 0x08, 0x1B, 0x94, 0x95, 0xA3, 0xD9, 0x54, 0x62, 0xF5, 0xDE, + 0x0A, 0xA1, 0x85, 0xEC, + 0x36, 0xB3, 0xDA, 0xF8, 0xA2, 0x32, 0x06, 0xF9, 0xC4, 0xF2, /* x */ + 0x99, 0xD7, 0xB2, 0x1A, 0x9C, 0x36, 0x91, 0x37, 0xF2, 0xC8, + 0x4A, 0xE1, 0xAA, 0x0D, + 0x76, 0x5B, 0xE7, 0x34, 0x33, 0xB3, 0xF9, 0x5E, 0x33, 0x29, /* y */ + 0x32, 0xE7, 0x0E, 0xA2, 0x45, 0xCA, 0x24, 0x18, 0xEA, 0x0E, + 0xF9, 0x80, 0x18, 0xFB, + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x04, 0xA2, 0x0E, 0x90, 0xC3, 0x90, 0x67, 0xC8, + 0x93, 0xBB, 0xB9, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V2 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 4 + }, + { + 0x08, 0x71, 0xEF, 0x2F, 0xEF, 0x24, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0xBE, 0xE0, 0xD9, 0x5C, 0x15, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x40, 0x10, 0x28, 0x77, 0x4D, 0x77, 0x77, 0xC7, 0xB7, 0x66, /* a */ + 0x6D, 0x13, 0x66, 0xEA, 0x43, 0x20, 0x71, 0x27, 0x4F, 0x89, + 0xFF, 0x01, 0xE7, 0x18, + 0x06, 0x20, 0x04, 0x8D, 0x28, 0xBC, 0xBD, 0x03, 0xB6, 0x24, /* b */ + 0x9C, 0x99, 0x18, 0x2B, 0x7C, 0x8C, 0xD1, 0x97, 0x00, 0xC3, + 0x62, 0xC4, 0x6A, 0x01, + 0x38, 0x09, 0xB2, 0xB7, 0xCC, 0x1B, 0x28, 0xCC, 0x5A, 0x87, /* x */ + 0x92, 0x6A, 0xAD, 0x83, 0xFD, 0x28, 0x78, 0x9E, 0x81, 0xE2, + 0xC9, 0xE3, 0xBF, 0x10, + 0x17, 0x43, 0x43, 0x86, 0x62, 0x6D, 0x14, 0xF3, 0xDB, 0xF0, /* y */ + 0x17, 0x60, 0xD9, 0x21, 0x3A, 0x3E, 0x1C, 0xF3, 0x7A, 0xEC, + 0x43, 0x7D, 0x66, 0x8A, + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x50, 0x50, 0x8C, 0xB8, 0x9F, 0x65, 0x28, 0x24, + 0xE0, 0x6B, 0x81, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V3 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 6 + }, + { + 0xE0, 0x53, 0x51, 0x2D, 0xC6, 0x84, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x50, 0x67, 0xAE, 0x78, 0x6D, 0x1F, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x6C, 0x01, 0x07, 0x47, 0x56, 0x09, 0x91, 0x22, 0x22, 0x10, /* a */ + 0x56, 0x91, 0x1C, 0x77, 0xD7, 0x7E, 0x77, 0xA7, 0x77, 0xE7, + 0xE7, 0xE7, 0x7F, 0xCB, + 0x71, 0xFE, 0x1A, 0xF9, 0x26, 0xCF, 0x84, 0x79, 0x89, 0xEF, /* b */ + 0xEF, 0x8D, 0xB4, 0x59, 0xF6, 0x63, 0x94, 0xD9, 0x0F, 0x32, + 0xAD, 0x3F, 0x15, 0xE8, + 0x37, 0x5D, 0x4C, 0xE2, 0x4F, 0xDE, 0x43, 0x44, 0x89, 0xDE, /* x */ + 0x87, 0x46, 0xE7, 0x17, 0x86, 0x01, 0x50, 0x09, 0xE6, 0x6E, + 0x38, 0xA9, 0x26, 0xDD, + 0x54, 0x5A, 0x39, 0x17, 0x61, 0x96, 0x57, 0x5D, 0x98, 0x59, /* y */ + 0x99, 0x36, 0x6E, 0x6A, 0xD3, 0x4C, 0xE0, 0xA7, 0x7C, 0xD7, + 0x12, 0x7B, 0x06, 0xBE, + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, /* order */ + 0x55, 0x55, 0x61, 0x0C, 0x0B, 0x19, 0x68, 0x12, 0xBF, 0xB6, + 0x28, 0x8A, 0x3E, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 27 * 6]; +} + _EC_X9_62_CHAR2_208W1 = { + { + NID_X9_62_characteristic_two_field, 0, 27, 0xFE48 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0xC8, 0x61, 0x9E, 0xD4, 0x5A, 0x62, 0xE6, 0x21, 0x2E, /* b */ + 0x11, 0x60, 0x34, 0x9E, 0x2B, 0xFA, 0x84, 0x44, 0x39, 0xFA, + 0xFC, 0x2A, 0x3F, 0xD1, 0x63, 0x8F, 0x9E, + 0x00, 0x89, 0xFD, 0xFB, 0xE4, 0xAB, 0xE1, 0x93, 0xDF, 0x95, /* x */ + 0x59, 0xEC, 0xF0, 0x7A, 0xC0, 0xCE, 0x78, 0x55, 0x4E, 0x27, + 0x84, 0xEB, 0x8C, 0x1E, 0xD1, 0xA5, 0x7A, + 0x00, 0x0F, 0x55, 0xB5, 0x1A, 0x06, 0xE7, 0x8E, 0x9A, 0xC3, /* y */ + 0x8A, 0x03, 0x5F, 0xF5, 0x20, 0xD8, 0xB0, 0x17, 0x81, 0xBE, + 0xB1, 0xA6, 0xBB, 0x08, 0x61, 0x7D, 0xE3, + 0x00, 0x00, 0x01, 0x01, 0xBA, 0xF9, 0x5C, 0x97, 0x23, 0xC5, /* order */ + 0x7B, 0x6C, 0x21, 0xDA, 0x2E, 0xFF, 0x2D, 0x5E, 0xD5, 0x88, + 0xBD, 0xD5, 0x71, 0x7E, 0x21, 0x2F, 0x9D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V1 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 4 + }, + { + 0xD3, 0x4B, 0x9A, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0xCA, 0x71, 0xB9, 0x20, 0xBF, 0xEF, 0xB0, 0x5D, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x32, 0x01, 0x08, 0x57, 0x07, 0x7C, 0x54, 0x31, 0x12, 0x3A, /* a */ + 0x46, 0xB8, 0x08, 0x90, 0x67, 0x56, 0xF5, 0x43, 0x42, 0x3E, + 0x8D, 0x27, 0x87, 0x75, 0x78, 0x12, 0x57, 0x78, 0xAC, 0x76, + + 0x79, 0x04, 0x08, 0xF2, 0xEE, 0xDA, 0xF3, 0x92, 0xB0, 0x12, /* b */ + 0xED, 0xEF, 0xB3, 0x39, 0x2F, 0x30, 0xF4, 0x32, 0x7C, 0x0C, + 0xA3, 0xF3, 0x1F, 0xC3, 0x83, 0xC4, 0x22, 0xAA, 0x8C, 0x16, + + 0x57, 0x92, 0x70, 0x98, 0xFA, 0x93, 0x2E, 0x7C, 0x0A, 0x96, /* x */ + 0xD3, 0xFD, 0x5B, 0x70, 0x6E, 0xF7, 0xE5, 0xF5, 0xC1, 0x56, + 0xE1, 0x6B, 0x7E, 0x7C, 0x86, 0x03, 0x85, 0x52, 0xE9, 0x1D, + + 0x61, 0xD8, 0xEE, 0x50, 0x77, 0xC3, 0x3F, 0xEC, 0xF6, 0xF1, /* y */ + 0xA1, 0x6B, 0x26, 0x8D, 0xE4, 0x69, 0xC3, 0xC7, 0x74, 0x4E, + 0xA9, 0xA9, 0x71, 0x64, 0x9F, 0xC7, 0xA9, 0x61, 0x63, 0x05, + + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x0F, 0x4D, 0x42, 0xFF, 0xE1, + 0x49, 0x2A, 0x49, 0x93, 0xF1, 0xCA, 0xD6, 0x66, 0xE4, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V2 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 6 + }, + { + 0x2A, 0xA6, 0x98, 0x2F, 0xDF, 0xA4, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x5D, 0x26, 0x67, 0x27, 0x27, 0x7D, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x42, 0x30, 0x01, 0x77, 0x57, 0xA7, 0x67, 0xFA, 0xE4, 0x23, /* a */ + 0x98, 0x56, 0x9B, 0x74, 0x63, 0x25, 0xD4, 0x53, 0x13, 0xAF, + 0x07, 0x66, 0x26, 0x64, 0x79, 0xB7, 0x56, 0x54, 0xE6, 0x5F, + + 0x50, 0x37, 0xEA, 0x65, 0x41, 0x96, 0xCF, 0xF0, 0xCD, 0x82, /* b */ + 0xB2, 0xC1, 0x4A, 0x2F, 0xCF, 0x2E, 0x3F, 0xF8, 0x77, 0x52, + 0x85, 0xB5, 0x45, 0x72, 0x2F, 0x03, 0xEA, 0xCD, 0xB7, 0x4B, + + 0x28, 0xF9, 0xD0, 0x4E, 0x90, 0x00, 0x69, 0xC8, 0xDC, 0x47, /* x */ + 0xA0, 0x85, 0x34, 0xFE, 0x76, 0xD2, 0xB9, 0x00, 0xB7, 0xD7, + 0xEF, 0x31, 0xF5, 0x70, 0x9F, 0x20, 0x0C, 0x4C, 0xA2, 0x05, + + 0x56, 0x67, 0x33, 0x4C, 0x45, 0xAF, 0xF3, 0xB5, 0xA0, 0x3B, /* y */ + 0xAD, 0x9D, 0xD7, 0x5E, 0x2C, 0x71, 0xA9, 0x93, 0x62, 0x56, + 0x7D, 0x54, 0x53, 0xF7, 0xFA, 0x6E, 0x22, 0x7E, 0xC8, 0x33, + + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, /* order */ + 0x55, 0x55, 0x55, 0x55, 0x55, 0x3C, 0x6F, 0x28, 0x85, 0x25, + 0x9C, 0x31, 0xE3, 0xFC, 0xDF, 0x15, 0x46, 0x24, 0x52, 0x2D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V3 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 0xA + }, + { + 0x9E, 0x07, 0x6F, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0xE1, 0x1E, 0x9F, 0xDD, 0x77, 0xF9, 0x20, 0x41, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x01, 0x23, 0x87, 0x74, 0x66, 0x6A, 0x67, 0x76, 0x6D, 0x66, /* a */ + 0x76, 0xF7, 0x78, 0xE6, 0x76, 0xB6, 0x69, 0x99, 0x17, 0x66, + 0x66, 0xE6, 0x87, 0x66, 0x6D, 0x87, 0x66, 0xC6, 0x6A, 0x9F, + + 0x6A, 0x94, 0x19, 0x77, 0xBA, 0x9F, 0x6A, 0x43, 0x51, 0x99, /* b */ + 0xAC, 0xFC, 0x51, 0x06, 0x7E, 0xD5, 0x87, 0xF5, 0x19, 0xC5, + 0xEC, 0xB5, 0x41, 0xB8, 0xE4, 0x41, 0x11, 0xDE, 0x1D, 0x40, + + 0x70, 0xF6, 0xE9, 0xD0, 0x4D, 0x28, 0x9C, 0x4E, 0x89, 0x91, /* x */ + 0x3C, 0xE3, 0x53, 0x0B, 0xFD, 0xE9, 0x03, 0x97, 0x7D, 0x42, + 0xB1, 0x46, 0xD5, 0x39, 0xBF, 0x1B, 0xDE, 0x4E, 0x9C, 0x92, + + 0x2E, 0x5A, 0x0E, 0xAF, 0x6E, 0x5E, 0x13, 0x05, 0xB9, 0x00, /* y */ + 0x4D, 0xCE, 0x5C, 0x0E, 0xD7, 0xFE, 0x59, 0xA3, 0x56, 0x08, + 0xF3, 0x38, 0x37, 0xC8, 0x16, 0xD8, 0x0B, 0x79, 0xF4, 0x61, + + 0x0C, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, /* order */ + 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xAC, 0x49, 0x12, 0xD2, 0xD9, + 0xDF, 0x90, 0x3E, 0xF9, 0x88, 0x8B, 0x8A, 0x0E, 0x4C, 0xFF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 35 * 6]; +} + _EC_X9_62_CHAR2_272W1 = { + { + NID_X9_62_characteristic_two_field, 0, 35, 0xFF06 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x0B, + 0x00, 0x91, 0xA0, 0x91, 0xF0, 0x3B, 0x5F, 0xBA, 0x4A, 0xB2, /* a */ + 0xCC, 0xF4, 0x9C, 0x4E, 0xDD, 0x22, 0x0F, 0xB0, 0x28, 0x71, + 0x2D, 0x42, 0xBE, 0x75, 0x2B, 0x2C, 0x40, 0x09, 0x4D, 0xBA, + 0xCD, 0xB5, 0x86, 0xFB, 0x20, + 0x00, 0x71, 0x67, 0xEF, 0xC9, 0x2B, 0xB2, 0xE3, 0xCE, 0x7C, /* b */ + 0x8A, 0xAA, 0xFF, 0x34, 0xE1, 0x2A, 0x9C, 0x55, 0x70, 0x03, + 0xD7, 0xC7, 0x3A, 0x6F, 0xAF, 0x00, 0x3F, 0x99, 0xF6, 0xCC, + 0x84, 0x82, 0xE5, 0x40, 0xF7, + 0x00, 0x61, 0x08, 0xBA, 0xBB, 0x2C, 0xEE, 0xBC, 0xF7, 0x87, /* x */ + 0x05, 0x8A, 0x05, 0x6C, 0xBE, 0x0C, 0xFE, 0x62, 0x2D, 0x77, + 0x23, 0xA2, 0x89, 0xE0, 0x8A, 0x07, 0xAE, 0x13, 0xEF, 0x0D, + 0x10, 0xD1, 0x71, 0xDD, 0x8D, + 0x00, 0x10, 0xC7, 0x69, 0x57, 0x16, 0x85, 0x1E, 0xEF, 0x6B, /* y */ + 0xA7, 0xF6, 0x87, 0x2E, 0x61, 0x42, 0xFB, 0xD2, 0x41, 0xB8, + 0x30, 0xFF, 0x5E, 0xFC, 0xAC, 0xEC, 0xCA, 0xB0, 0x5E, 0x02, + 0x00, 0x5D, 0xDE, 0x9D, 0x23, + 0x00, 0x00, 0x01, 0x00, 0xFA, 0xF5, 0x13, 0x54, 0xE0, 0xE3, /* order */ + 0x9E, 0x48, 0x92, 0xDF, 0x6E, 0x31, 0x9C, 0x72, 0xC8, 0x16, + 0x16, 0x03, 0xFA, 0x45, 0xAA, 0x7B, 0x99, 0x8A, 0x16, 0x7B, + 0x8F, 0x1E, 0x62, 0x95, 0x21 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 39 * 6]; +} + _EC_X9_62_CHAR2_304W1 = { + { + NID_X9_62_characteristic_two_field, 0, 39, 0xFE2E + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x07, + 0x00, 0xFD, 0x0D, 0x69, 0x31, 0x49, 0xA1, 0x18, 0xF6, 0x51, /* a */ + 0xE6, 0xDC, 0xE6, 0x80, 0x20, 0x85, 0x37, 0x7E, 0x5F, 0x88, + 0x2D, 0x1B, 0x51, 0x0B, 0x44, 0x16, 0x00, 0x74, 0xC1, 0x28, + 0x80, 0x78, 0x36, 0x5A, 0x03, 0x96, 0xC8, 0xE6, 0x81, + 0x00, 0xBD, 0xDB, 0x97, 0xE5, 0x55, 0xA5, 0x0A, 0x90, 0x8E, /* b */ + 0x43, 0xB0, 0x1C, 0x79, 0x8E, 0xA5, 0xDA, 0xA6, 0x78, 0x8F, + 0x1E, 0xA2, 0x79, 0x4E, 0xFC, 0xF5, 0x71, 0x66, 0xB8, 0xC1, + 0x40, 0x39, 0x60, 0x1E, 0x55, 0x82, 0x73, 0x40, 0xBE, + 0x00, 0x19, 0x7B, 0x07, 0x84, 0x5E, 0x9B, 0xE2, 0xD9, 0x6A, /* x */ + 0xDB, 0x0F, 0x5F, 0x3C, 0x7F, 0x2C, 0xFF, 0xBD, 0x7A, 0x3E, + 0xB8, 0xB6, 0xFE, 0xC3, 0x5C, 0x7F, 0xD6, 0x7F, 0x26, 0xDD, + 0xF6, 0x28, 0x5A, 0x64, 0x4F, 0x74, 0x0A, 0x26, 0x14, + 0x00, 0xE1, 0x9F, 0xBE, 0xB7, 0x6E, 0x0D, 0xA1, 0x71, 0x51, /* y */ + 0x7E, 0xCF, 0x40, 0x1B, 0x50, 0x28, 0x9B, 0xF0, 0x14, 0x10, + 0x32, 0x88, 0x52, 0x7A, 0x9B, 0x41, 0x6A, 0x10, 0x5E, 0x80, + 0x26, 0x0B, 0x54, 0x9F, 0xDC, 0x1B, 0x92, 0xC0, 0x3B, + 0x00, 0x00, 0x01, 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, /* order */ + 0x80, 0x01, 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, 0x80, + 0x01, 0x02, 0x2D, 0x5C, 0x91, 0xDD, 0x17, 0x3F, 0x8F, 0xB5, + 0x61, 0xDA, 0x68, 0x99, 0x16, 0x44, 0x43, 0x05, 0x1D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 45 * 6]; +} + _EC_X9_62_CHAR2_359V1 = { + { + NID_X9_62_characteristic_two_field, 20, 45, 0x4C + }, + { + 0x2B, 0x35, 0x49, 0x20, 0xB7, 0x24, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0x5B, 0xA1, 0x33, 0x2D, 0xC6, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x56, 0x67, 0x67, 0x6A, 0x65, 0x4B, 0x20, 0x75, 0x4F, 0x35, /* a */ + 0x6E, 0xA9, 0x20, 0x17, 0xD9, 0x46, 0x56, 0x7C, 0x46, 0x67, + 0x55, 0x56, 0xF1, 0x95, 0x56, 0xA0, 0x46, 0x16, 0xB5, 0x67, + 0xD2, 0x23, 0xA5, 0xE0, 0x56, 0x56, 0xFB, 0x54, 0x90, 0x16, + 0xA9, 0x66, 0x56, 0xA5, 0x57, + 0x24, 0x72, 0xE2, 0xD0, 0x19, 0x7C, 0x49, 0x36, 0x3F, 0x1F, /* b */ + 0xE7, 0xF5, 0xB6, 0xDB, 0x07, 0x5D, 0x52, 0xB6, 0x94, 0x7D, + 0x13, 0x5D, 0x8C, 0xA4, 0x45, 0x80, 0x5D, 0x39, 0xBC, 0x34, + 0x56, 0x26, 0x08, 0x96, 0x87, 0x74, 0x2B, 0x63, 0x29, 0xE7, + 0x06, 0x80, 0x23, 0x19, 0x88, + 0x3C, 0x25, 0x8E, 0xF3, 0x04, 0x77, 0x67, 0xE7, 0xED, 0xE0, /* x */ + 0xF1, 0xFD, 0xAA, 0x79, 0xDA, 0xEE, 0x38, 0x41, 0x36, 0x6A, + 0x13, 0x2E, 0x16, 0x3A, 0xCE, 0xD4, 0xED, 0x24, 0x01, 0xDF, + 0x9C, 0x6B, 0xDC, 0xDE, 0x98, 0xE8, 0xE7, 0x07, 0xC0, 0x7A, + 0x22, 0x39, 0xB1, 0xB0, 0x97, + 0x53, 0xD7, 0xE0, 0x85, 0x29, 0x54, 0x70, 0x48, 0x12, 0x1E, /* y */ + 0x9C, 0x95, 0xF3, 0x79, 0x1D, 0xD8, 0x04, 0x96, 0x39, 0x48, + 0xF3, 0x4F, 0xAE, 0x7B, 0xF4, 0x4E, 0xA8, 0x23, 0x65, 0xDC, + 0x78, 0x68, 0xFE, 0x57, 0xE4, 0xAE, 0x2D, 0xE2, 0x11, 0x30, + 0x5A, 0x40, 0x71, 0x04, 0xBD, + 0x01, 0xAF, 0x28, 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, /* order */ + 0xAF, 0x28, 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, 0xAF, + 0x28, 0x6B, 0xC9, 0xFB, 0x8F, 0x6B, 0x85, 0xC5, 0x56, 0x89, + 0x2C, 0x20, 0xA7, 0xEB, 0x96, 0x4F, 0xE7, 0x71, 0x9E, 0x74, + 0xF4, 0x90, 0x75, 0x8D, 0x3B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 47 * 6]; +} + _EC_X9_62_CHAR2_368W1 = { + { + NID_X9_62_characteristic_two_field, 0, 47, 0xFF70 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x20, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + 0x00, 0xE0, 0xD2, 0xEE, 0x25, 0x09, 0x52, 0x06, 0xF5, 0xE2, /* a */ + 0xA4, 0xF9, 0xED, 0x22, 0x9F, 0x1F, 0x25, 0x6E, 0x79, 0xA0, + 0xE2, 0xB4, 0x55, 0x97, 0x0D, 0x8D, 0x0D, 0x86, 0x5B, 0xD9, + 0x47, 0x78, 0xC5, 0x76, 0xD6, 0x2F, 0x0A, 0xB7, 0x51, 0x9C, + 0xCD, 0x2A, 0x1A, 0x90, 0x6A, 0xE3, 0x0D, + 0x00, 0xFC, 0x12, 0x17, 0xD4, 0x32, 0x0A, 0x90, 0x45, 0x2C, /* b */ + 0x76, 0x0A, 0x58, 0xED, 0xCD, 0x30, 0xC8, 0xDD, 0x06, 0x9B, + 0x3C, 0x34, 0x45, 0x38, 0x37, 0xA3, 0x4E, 0xD5, 0x0C, 0xB5, + 0x49, 0x17, 0xE1, 0xC2, 0x11, 0x2D, 0x84, 0xD1, 0x64, 0xF4, + 0x44, 0xF8, 0xF7, 0x47, 0x86, 0x04, 0x6A, + 0x00, 0x10, 0x85, 0xE2, 0x75, 0x53, 0x81, 0xDC, 0xCC, 0xE3, /* x */ + 0xC1, 0x55, 0x7A, 0xFA, 0x10, 0xC2, 0xF0, 0xC0, 0xC2, 0x82, + 0x56, 0x46, 0xC5, 0xB3, 0x4A, 0x39, 0x4C, 0xBC, 0xFA, 0x8B, + 0xC1, 0x6B, 0x22, 0xE7, 0xE7, 0x89, 0xE9, 0x27, 0xBE, 0x21, + 0x6F, 0x02, 0xE1, 0xFB, 0x13, 0x6A, 0x5F, + 0x00, 0x7B, 0x3E, 0xB1, 0xBD, 0xDC, 0xBA, 0x62, 0xD5, 0xD8, /* y */ + 0xB2, 0x05, 0x9B, 0x52, 0x57, 0x97, 0xFC, 0x73, 0x82, 0x2C, + 0x59, 0x05, 0x9C, 0x62, 0x3A, 0x45, 0xFF, 0x38, 0x43, 0xCE, + 0xE8, 0xF8, 0x7C, 0xD1, 0x85, 0x5A, 0xDA, 0xA8, 0x1E, 0x2A, + 0x07, 0x50, 0xB8, 0x0F, 0xDA, 0x23, 0x10, + 0x00, 0x00, 0x01, 0x00, 0x90, 0x51, 0x2D, 0xA9, 0xAF, 0x72, /* order */ + 0xB0, 0x83, 0x49, 0xD9, 0x8A, 0x5D, 0xD4, 0xC7, 0xB0, 0x53, + 0x2E, 0xCA, 0x51, 0xCE, 0x03, 0xE2, 0xD1, 0x0F, 0x3B, 0x7A, + 0xC5, 0x79, 0xBD, 0x87, 0xE9, 0x09, 0xAE, 0x40, 0xA6, 0xF1, + 0x31, 0xE9, 0xCF, 0xCE, 0x5B, 0xD9, 0x67 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 54 * 6]; +} + _EC_X9_62_CHAR2_431R1 = { + { + NID_X9_62_characteristic_two_field, 0, 54, 0x2760 + }, + { /* no seed */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + 0x1A, 0x82, 0x7E, 0xF0, 0x0D, 0xD6, 0xFC, 0x0E, 0x23, 0x4C, /* a */ + 0xAF, 0x04, 0x6C, 0x6A, 0x5D, 0x8A, 0x85, 0x39, 0x5B, 0x23, + 0x6C, 0xC4, 0xAD, 0x2C, 0xF3, 0x2A, 0x0C, 0xAD, 0xBD, 0xC9, + 0xDD, 0xF6, 0x20, 0xB0, 0xEB, 0x99, 0x06, 0xD0, 0x95, 0x7F, + 0x6C, 0x6F, 0xEA, 0xCD, 0x61, 0x54, 0x68, 0xDF, 0x10, 0x4D, + 0xE2, 0x96, 0xCD, 0x8F, + 0x10, 0xD9, 0xB4, 0xA3, 0xD9, 0x04, 0x7D, 0x8B, 0x15, 0x43, /* b */ + 0x59, 0xAB, 0xFB, 0x1B, 0x7F, 0x54, 0x85, 0xB0, 0x4C, 0xEB, + 0x86, 0x82, 0x37, 0xDD, 0xC9, 0xDE, 0xDA, 0x98, 0x2A, 0x67, + 0x9A, 0x5A, 0x91, 0x9B, 0x62, 0x6D, 0x4E, 0x50, 0xA8, 0xDD, + 0x73, 0x1B, 0x10, 0x7A, 0x99, 0x62, 0x38, 0x1F, 0xB5, 0xD8, + 0x07, 0xBF, 0x26, 0x18, + 0x12, 0x0F, 0xC0, 0x5D, 0x3C, 0x67, 0xA9, 0x9D, 0xE1, 0x61, /* x */ + 0xD2, 0xF4, 0x09, 0x26, 0x22, 0xFE, 0xCA, 0x70, 0x1B, 0xE4, + 0xF5, 0x0F, 0x47, 0x58, 0x71, 0x4E, 0x8A, 0x87, 0xBB, 0xF2, + 0xA6, 0x58, 0xEF, 0x8C, 0x21, 0xE7, 0xC5, 0xEF, 0xE9, 0x65, + 0x36, 0x1F, 0x6C, 0x29, 0x99, 0xC0, 0xC2, 0x47, 0xB0, 0xDB, + 0xD7, 0x0C, 0xE6, 0xB7, + 0x20, 0xD0, 0xAF, 0x89, 0x03, 0xA9, 0x6F, 0x8D, 0x5F, 0xA2, /* y */ + 0xC2, 0x55, 0x74, 0x5D, 0x3C, 0x45, 0x1B, 0x30, 0x2C, 0x93, + 0x46, 0xD9, 0xB7, 0xE4, 0x85, 0xE7, 0xBC, 0xE4, 0x1F, 0x6B, + 0x59, 0x1F, 0x3E, 0x8F, 0x6A, 0xDD, 0xCB, 0xB0, 0xBC, 0x4C, + 0x2F, 0x94, 0x7A, 0x7D, 0xE1, 0xA8, 0x9B, 0x62, 0x5D, 0x6A, + 0x59, 0x8B, 0x37, 0x60, + 0x00, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, /* order */ + 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, + 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x23, + 0xC3, 0x13, 0xFA, 0xB5, 0x05, 0x89, 0x70, 0x3B, 0x5E, 0xC6, + 0x8D, 0x35, 0x87, 0xFE, 0xC6, 0x0D, 0x16, 0x1C, 0xC1, 0x49, + 0xC1, 0xAD, 0x4A, 0x91 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} + _EC_WTLS_1 = { + { + NID_X9_62_characteristic_two_field, 0, 15, 2 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x01, 0x66, 0x79, 0x79, 0xA4, 0x0B, 0xA4, 0x97, 0xE5, 0xD5, /* x */ + 0xC2, 0x70, 0x78, 0x06, 0x17, + 0x00, 0xF4, 0x4B, 0x4A, 0xF1, 0xEC, 0xC2, 0x63, 0x0E, 0x08, /* y */ + 0x78, 0x5C, 0xEB, 0xCC, 0x15, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFD, 0xBF, /* order */ + 0x91, 0xAF, 0x6D, 0xEA, 0x73 + } +}; /* IPSec curves */ /* NOTE: The of curves over a extension field of non prime degree @@ -1768,57 +2151,69 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_IPSEC_155_ID3 = { - { NID_X9_62_characteristic_two_field,0,20,3 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x01, +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_IPSEC_155_ID3 = { + { + NID_X9_62_characteristic_two_field, 0, 20, 3 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x07,0x33,0x8f, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, 0x33, 0x8f, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x7b, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7b, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xc8, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xc8, - 0x02,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA, /* order */ - 0xC7,0xF3,0xC7,0x88,0x1B,0xD0,0x86,0x8F,0xA8,0x6C } - }; + 0x02, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, /* order */ + 0xC7, 0xF3, 0xC7, 0x88, 0x1B, 0xD0, 0x86, 0x8F, 0xA8, 0x6C + } +}; /* NOTE: The of curves over a extension field of non prime degree * is not recommended (Weil-descent). * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_IPSEC_185_ID4 = { - { NID_X9_62_characteristic_two_field,0,24,2 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x1e,0xe9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x18, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x0d, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xED,0xF9,0x7C,0x44,0xDB,0x9F,0x24,0x20, - 0xBA,0xFC,0xA7,0x5E } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_IPSEC_185_ID4 = { + { + NID_X9_62_characteristic_two_field, 0, 24, 2 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x20, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x1e, 0xe9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x18, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x0d, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xED, 0xF9, 0x7C, 0x44, 0xDB, 0x9F, 0x24, 0x20, + 0xBA, 0xFC, 0xA7, 0x5E + } +}; #endif @@ -1830,687 +2225,761 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } * those defined in ANSI X9.62. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_brainpoolP160r1 = { - { NID_X9_62_prime_field, 0,20,1 }, - { /* no seed */ - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* p */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0F, - 0x34,0x0E,0x7B,0xE2,0xA2,0x80,0xEB,0x74,0xE2,0xBE, /* a */ - 0x61,0xBA,0xDA,0x74,0x5D,0x97,0xE8,0xF7,0xC3,0x00, - 0x1E,0x58,0x9A,0x85,0x95,0x42,0x34,0x12,0x13,0x4F, /* b */ - 0xAA,0x2D,0xBD,0xEC,0x95,0xC8,0xD8,0x67,0x5E,0x58, - 0xBE,0xD5,0xAF,0x16,0xEA,0x3F,0x6A,0x4F,0x62,0x93, /* x */ - 0x8C,0x46,0x31,0xEB,0x5A,0xF7,0xBD,0xBC,0xDB,0xC3, - 0x16,0x67,0xCB,0x47,0x7A,0x1A,0x8E,0xC3,0x38,0xF9, /* y */ - 0x47,0x41,0x66,0x9C,0x97,0x63,0x16,0xDA,0x63,0x21, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* order */ - 0x59,0x91,0xD4,0x50,0x29,0x40,0x9E,0x60,0xFC,0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_brainpoolP160t1 = { - { NID_X9_62_prime_field, 0,20,1 }, - { /* no seed */ - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* p */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0F, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* a */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0C, - 0x7A,0x55,0x6B,0x6D,0xAE,0x53,0x5B,0x7B,0x51,0xED, /* b */ - 0x2C,0x4D,0x7D,0xAA,0x7A,0x0B,0x5C,0x55,0xF3,0x80, - 0xB1,0x99,0xB1,0x3B,0x9B,0x34,0xEF,0xC1,0x39,0x7E, /* x */ - 0x64,0xBA,0xEB,0x05,0xAC,0xC2,0x65,0xFF,0x23,0x78, - 0xAD,0xD6,0x71,0x8B,0x7C,0x7C,0x19,0x61,0xF0,0x99, /* y */ - 0x1B,0x84,0x24,0x43,0x77,0x21,0x52,0xC9,0xE0,0xAD, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* order */ - 0x59,0x91,0xD4,0x50,0x29,0x40,0x9E,0x60,0xFC,0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_brainpoolP192r1 = { - { NID_X9_62_prime_field, 0,24,1 }, - { /* no seed */ - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* p */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x97, - 0x6A,0x91,0x17,0x40,0x76,0xB1,0xE0,0xE1,0x9C,0x39, /* a */ - 0xC0,0x31,0xFE,0x86,0x85,0xC1,0xCA,0xE0,0x40,0xE5, - 0xC6,0x9A,0x28,0xEF, - 0x46,0x9A,0x28,0xEF,0x7C,0x28,0xCC,0xA3,0xDC,0x72, /* b */ - 0x1D,0x04,0x4F,0x44,0x96,0xBC,0xCA,0x7E,0xF4,0x14, - 0x6F,0xBF,0x25,0xC9, - 0xC0,0xA0,0x64,0x7E,0xAA,0xB6,0xA4,0x87,0x53,0xB0, /* x */ - 0x33,0xC5,0x6C,0xB0,0xF0,0x90,0x0A,0x2F,0x5C,0x48, - 0x53,0x37,0x5F,0xD6, - 0x14,0xB6,0x90,0x86,0x6A,0xBD,0x5B,0xB8,0x8B,0x5F, /* y */ - 0x48,0x28,0xC1,0x49,0x00,0x02,0xE6,0x77,0x3F,0xA2, - 0xFA,0x29,0x9B,0x8F, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* order */ - 0x46,0x2F,0x9E,0x9E,0x91,0x6B,0x5B,0xE8,0xF1,0x02, - 0x9A,0xC4,0xAC,0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_brainpoolP192t1 = { - { NID_X9_62_prime_field, 0,24,1 }, - { /* no seed */ - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* p */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x97, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* a */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x94, - 0x13,0xD5,0x6F,0xFA,0xEC,0x78,0x68,0x1E,0x68,0xF9, /* b */ - 0xDE,0xB4,0x3B,0x35,0xBE,0xC2,0xFB,0x68,0x54,0x2E, - 0x27,0x89,0x7B,0x79, - 0x3A,0xE9,0xE5,0x8C,0x82,0xF6,0x3C,0x30,0x28,0x2E, /* x */ - 0x1F,0xE7,0xBB,0xF4,0x3F,0xA7,0x2C,0x44,0x6A,0xF6, - 0xF4,0x61,0x81,0x29, - 0x09,0x7E,0x2C,0x56,0x67,0xC2,0x22,0x3A,0x90,0x2A, /* y */ - 0xB5,0xCA,0x44,0x9D,0x00,0x84,0xB7,0xE5,0xB3,0xDE, - 0x7C,0xCC,0x01,0xC9, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* order */ - 0x46,0x2F,0x9E,0x9E,0x91,0x6B,0x5B,0xE8,0xF1,0x02, - 0x9A,0xC4,0xAC,0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_brainpoolP224r1 = { - { NID_X9_62_prime_field, 0,28,1 }, - { /* no seed */ - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* p */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFF, - 0x68,0xA5,0xE6,0x2C,0xA9,0xCE,0x6C,0x1C,0x29,0x98, /* a */ - 0x03,0xA6,0xC1,0x53,0x0B,0x51,0x4E,0x18,0x2A,0xD8, - 0xB0,0x04,0x2A,0x59,0xCA,0xD2,0x9F,0x43, - 0x25,0x80,0xF6,0x3C,0xCF,0xE4,0x41,0x38,0x87,0x07, /* b */ - 0x13,0xB1,0xA9,0x23,0x69,0xE3,0x3E,0x21,0x35,0xD2, - 0x66,0xDB,0xB3,0x72,0x38,0x6C,0x40,0x0B, - 0x0D,0x90,0x29,0xAD,0x2C,0x7E,0x5C,0xF4,0x34,0x08, /* x */ - 0x23,0xB2,0xA8,0x7D,0xC6,0x8C,0x9E,0x4C,0xE3,0x17, - 0x4C,0x1E,0x6E,0xFD,0xEE,0x12,0xC0,0x7D, - 0x58,0xAA,0x56,0xF7,0x72,0xC0,0x72,0x6F,0x24,0xC6, /* y */ - 0xB8,0x9E,0x4E,0xCD,0xAC,0x24,0x35,0x4B,0x9E,0x99, - 0xCA,0xA3,0xF6,0xD3,0x76,0x14,0x02,0xCD, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* order */ - 0x30,0x25,0x75,0xD0,0xFB,0x98,0xD1,0x16,0xBC,0x4B, - 0x6D,0xDE,0xBC,0xA3,0xA5,0xA7,0x93,0x9F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_brainpoolP224t1 = { - { NID_X9_62_prime_field, 0,28,1 }, - { /* no seed */ - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* p */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFF, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* a */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFC, - 0x4B,0x33,0x7D,0x93,0x41,0x04,0xCD,0x7B,0xEF,0x27, /* b */ - 0x1B,0xF6,0x0C,0xED,0x1E,0xD2,0x0D,0xA1,0x4C,0x08, - 0xB3,0xBB,0x64,0xF1,0x8A,0x60,0x88,0x8D, - 0x6A,0xB1,0xE3,0x44,0xCE,0x25,0xFF,0x38,0x96,0x42, /* x */ - 0x4E,0x7F,0xFE,0x14,0x76,0x2E,0xCB,0x49,0xF8,0x92, - 0x8A,0xC0,0xC7,0x60,0x29,0xB4,0xD5,0x80, - 0x03,0x74,0xE9,0xF5,0x14,0x3E,0x56,0x8C,0xD2,0x3F, /* y */ - 0x3F,0x4D,0x7C,0x0D,0x4B,0x1E,0x41,0xC8,0xCC,0x0D, - 0x1C,0x6A,0xBD,0x5F,0x1A,0x46,0xDB,0x4C, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* order */ - 0x30,0x25,0x75,0xD0,0xFB,0x98,0xD1,0x16,0xBC,0x4B, - 0x6D,0xDE,0xBC,0xA3,0xA5,0xA7,0x93,0x9F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_brainpoolP256r1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* p */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x77, - 0x7D,0x5A,0x09,0x75,0xFC,0x2C,0x30,0x57,0xEE,0xF6, /* a */ - 0x75,0x30,0x41,0x7A,0xFF,0xE7,0xFB,0x80,0x55,0xC1, - 0x26,0xDC,0x5C,0x6C,0xE9,0x4A,0x4B,0x44,0xF3,0x30, - 0xB5,0xD9, - 0x26,0xDC,0x5C,0x6C,0xE9,0x4A,0x4B,0x44,0xF3,0x30, /* b */ - 0xB5,0xD9,0xBB,0xD7,0x7C,0xBF,0x95,0x84,0x16,0x29, - 0x5C,0xF7,0xE1,0xCE,0x6B,0xCC,0xDC,0x18,0xFF,0x8C, - 0x07,0xB6, - 0x8B,0xD2,0xAE,0xB9,0xCB,0x7E,0x57,0xCB,0x2C,0x4B, /* x */ - 0x48,0x2F,0xFC,0x81,0xB7,0xAF,0xB9,0xDE,0x27,0xE1, - 0xE3,0xBD,0x23,0xC2,0x3A,0x44,0x53,0xBD,0x9A,0xCE, - 0x32,0x62, - 0x54,0x7E,0xF8,0x35,0xC3,0xDA,0xC4,0xFD,0x97,0xF8, /* y */ - 0x46,0x1A,0x14,0x61,0x1D,0xC9,0xC2,0x77,0x45,0x13, - 0x2D,0xED,0x8E,0x54,0x5C,0x1D,0x54,0xC7,0x2F,0x04, - 0x69,0x97, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* order */ - 0x0A,0x90,0x9D,0x83,0x8D,0x71,0x8C,0x39,0x7A,0xA3, - 0xB5,0x61,0xA6,0xF7,0x90,0x1E,0x0E,0x82,0x97,0x48, - 0x56,0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_brainpoolP256t1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* p */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x77, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* a */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x74, - 0x66,0x2C,0x61,0xC4,0x30,0xD8,0x4E,0xA4,0xFE,0x66, /* b */ - 0xA7,0x73,0x3D,0x0B,0x76,0xB7,0xBF,0x93,0xEB,0xC4, - 0xAF,0x2F,0x49,0x25,0x6A,0xE5,0x81,0x01,0xFE,0xE9, - 0x2B,0x04, - 0xA3,0xE8,0xEB,0x3C,0xC1,0xCF,0xE7,0xB7,0x73,0x22, /* x */ - 0x13,0xB2,0x3A,0x65,0x61,0x49,0xAF,0xA1,0x42,0xC4, - 0x7A,0xAF,0xBC,0x2B,0x79,0xA1,0x91,0x56,0x2E,0x13, - 0x05,0xF4, - 0x2D,0x99,0x6C,0x82,0x34,0x39,0xC5,0x6D,0x7F,0x7B, /* y */ - 0x22,0xE1,0x46,0x44,0x41,0x7E,0x69,0xBC,0xB6,0xDE, - 0x39,0xD0,0x27,0x00,0x1D,0xAB,0xE8,0xF3,0x5B,0x25, - 0xC9,0xBE, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* order */ - 0x0A,0x90,0x9D,0x83,0x8D,0x71,0x8C,0x39,0x7A,0xA3, - 0xB5,0x61,0xA6,0xF7,0x90,0x1E,0x0E,0x82,0x97,0x48, - 0x56,0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+40*6]; } - _EC_brainpoolP320r1 = { - { NID_X9_62_prime_field, 0,40,1 }, - { /* no seed */ - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* p */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x27, - 0x3E,0xE3,0x0B,0x56,0x8F,0xBA,0xB0,0xF8,0x83,0xCC, /* a */ - 0xEB,0xD4,0x6D,0x3F,0x3B,0xB8,0xA2,0xA7,0x35,0x13, - 0xF5,0xEB,0x79,0xDA,0x66,0x19,0x0E,0xB0,0x85,0xFF, - 0xA9,0xF4,0x92,0xF3,0x75,0xA9,0x7D,0x86,0x0E,0xB4, - 0x52,0x08,0x83,0x94,0x9D,0xFD,0xBC,0x42,0xD3,0xAD, /* b */ - 0x19,0x86,0x40,0x68,0x8A,0x6F,0xE1,0x3F,0x41,0x34, - 0x95,0x54,0xB4,0x9A,0xCC,0x31,0xDC,0xCD,0x88,0x45, - 0x39,0x81,0x6F,0x5E,0xB4,0xAC,0x8F,0xB1,0xF1,0xA6, - 0x43,0xBD,0x7E,0x9A,0xFB,0x53,0xD8,0xB8,0x52,0x89, /* x */ - 0xBC,0xC4,0x8E,0xE5,0xBF,0xE6,0xF2,0x01,0x37,0xD1, - 0x0A,0x08,0x7E,0xB6,0xE7,0x87,0x1E,0x2A,0x10,0xA5, - 0x99,0xC7,0x10,0xAF,0x8D,0x0D,0x39,0xE2,0x06,0x11, - 0x14,0xFD,0xD0,0x55,0x45,0xEC,0x1C,0xC8,0xAB,0x40, /* y */ - 0x93,0x24,0x7F,0x77,0x27,0x5E,0x07,0x43,0xFF,0xED, - 0x11,0x71,0x82,0xEA,0xA9,0xC7,0x78,0x77,0xAA,0xAC, - 0x6A,0xC7,0xD3,0x52,0x45,0xD1,0x69,0x2E,0x8E,0xE1, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* order */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA5, - 0xB6,0x8F,0x12,0xA3,0x2D,0x48,0x2E,0xC7,0xEE,0x86, - 0x58,0xE9,0x86,0x91,0x55,0x5B,0x44,0xC5,0x93,0x11 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+40*6]; } - _EC_brainpoolP320t1 = { - { NID_X9_62_prime_field, 0,40,1 }, - { /* no seed */ - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* p */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x27, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* a */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x24, - 0xA7,0xF5,0x61,0xE0,0x38,0xEB,0x1E,0xD5,0x60,0xB3, /* b */ - 0xD1,0x47,0xDB,0x78,0x20,0x13,0x06,0x4C,0x19,0xF2, - 0x7E,0xD2,0x7C,0x67,0x80,0xAA,0xF7,0x7F,0xB8,0xA5, - 0x47,0xCE,0xB5,0xB4,0xFE,0xF4,0x22,0x34,0x03,0x53, - 0x92,0x5B,0xE9,0xFB,0x01,0xAF,0xC6,0xFB,0x4D,0x3E, /* x */ - 0x7D,0x49,0x90,0x01,0x0F,0x81,0x34,0x08,0xAB,0x10, - 0x6C,0x4F,0x09,0xCB,0x7E,0xE0,0x78,0x68,0xCC,0x13, - 0x6F,0xFF,0x33,0x57,0xF6,0x24,0xA2,0x1B,0xED,0x52, - 0x63,0xBA,0x3A,0x7A,0x27,0x48,0x3E,0xBF,0x66,0x71, /* y */ - 0xDB,0xEF,0x7A,0xBB,0x30,0xEB,0xEE,0x08,0x4E,0x58, - 0xA0,0xB0,0x77,0xAD,0x42,0xA5,0xA0,0x98,0x9D,0x1E, - 0xE7,0x1B,0x1B,0x9B,0xC0,0x45,0x5F,0xB0,0xD2,0xC3, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* order */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA5, - 0xB6,0x8F,0x12,0xA3,0x2D,0x48,0x2E,0xC7,0xEE,0x86, - 0x58,0xE9,0x86,0x91,0x55,0x5B,0x44,0xC5,0x93,0x11 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+48*6]; } - _EC_brainpoolP384r1 = { - { NID_X9_62_prime_field, 0,48,1 }, - { /* no seed */ - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* p */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x53, - 0x7B,0xC3,0x82,0xC6,0x3D,0x8C,0x15,0x0C,0x3C,0x72, /* a */ - 0x08,0x0A,0xCE,0x05,0xAF,0xA0,0xC2,0xBE,0xA2,0x8E, - 0x4F,0xB2,0x27,0x87,0x13,0x91,0x65,0xEF,0xBA,0x91, - 0xF9,0x0F,0x8A,0xA5,0x81,0x4A,0x50,0x3A,0xD4,0xEB, - 0x04,0xA8,0xC7,0xDD,0x22,0xCE,0x28,0x26, - 0x04,0xA8,0xC7,0xDD,0x22,0xCE,0x28,0x26,0x8B,0x39, /* b */ - 0xB5,0x54,0x16,0xF0,0x44,0x7C,0x2F,0xB7,0x7D,0xE1, - 0x07,0xDC,0xD2,0xA6,0x2E,0x88,0x0E,0xA5,0x3E,0xEB, - 0x62,0xD5,0x7C,0xB4,0x39,0x02,0x95,0xDB,0xC9,0x94, - 0x3A,0xB7,0x86,0x96,0xFA,0x50,0x4C,0x11, - 0x1D,0x1C,0x64,0xF0,0x68,0xCF,0x45,0xFF,0xA2,0xA6, /* x */ - 0x3A,0x81,0xB7,0xC1,0x3F,0x6B,0x88,0x47,0xA3,0xE7, - 0x7E,0xF1,0x4F,0xE3,0xDB,0x7F,0xCA,0xFE,0x0C,0xBD, - 0x10,0xE8,0xE8,0x26,0xE0,0x34,0x36,0xD6,0x46,0xAA, - 0xEF,0x87,0xB2,0xE2,0x47,0xD4,0xAF,0x1E, - 0x8A,0xBE,0x1D,0x75,0x20,0xF9,0xC2,0xA4,0x5C,0xB1, /* y */ - 0xEB,0x8E,0x95,0xCF,0xD5,0x52,0x62,0xB7,0x0B,0x29, - 0xFE,0xEC,0x58,0x64,0xE1,0x9C,0x05,0x4F,0xF9,0x91, - 0x29,0x28,0x0E,0x46,0x46,0x21,0x77,0x91,0x81,0x11, - 0x42,0x82,0x03,0x41,0x26,0x3C,0x53,0x15, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* order */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB3,0x1F,0x16,0x6E,0x6C,0xAC,0x04, - 0x25,0xA7,0xCF,0x3A,0xB6,0xAF,0x6B,0x7F,0xC3,0x10, - 0x3B,0x88,0x32,0x02,0xE9,0x04,0x65,0x65 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+48*6]; } - _EC_brainpoolP384t1 = { - { NID_X9_62_prime_field, 0,48,1 }, - { /* no seed */ - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* p */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x53, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* a */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x50, - 0x7F,0x51,0x9E,0xAD,0xA7,0xBD,0xA8,0x1B,0xD8,0x26, /* b */ - 0xDB,0xA6,0x47,0x91,0x0F,0x8C,0x4B,0x93,0x46,0xED, - 0x8C,0xCD,0xC6,0x4E,0x4B,0x1A,0xBD,0x11,0x75,0x6D, - 0xCE,0x1D,0x20,0x74,0xAA,0x26,0x3B,0x88,0x80,0x5C, - 0xED,0x70,0x35,0x5A,0x33,0xB4,0x71,0xEE, - 0x18,0xDE,0x98,0xB0,0x2D,0xB9,0xA3,0x06,0xF2,0xAF, /* x */ - 0xCD,0x72,0x35,0xF7,0x2A,0x81,0x9B,0x80,0xAB,0x12, - 0xEB,0xD6,0x53,0x17,0x24,0x76,0xFE,0xCD,0x46,0x2A, - 0xAB,0xFF,0xC4,0xFF,0x19,0x1B,0x94,0x6A,0x5F,0x54, - 0xD8,0xD0,0xAA,0x2F,0x41,0x88,0x08,0xCC, - 0x25,0xAB,0x05,0x69,0x62,0xD3,0x06,0x51,0xA1,0x14, /* y */ - 0xAF,0xD2,0x75,0x5A,0xD3,0x36,0x74,0x7F,0x93,0x47, - 0x5B,0x7A,0x1F,0xCA,0x3B,0x88,0xF2,0xB6,0xA2,0x08, - 0xCC,0xFE,0x46,0x94,0x08,0x58,0x4D,0xC2,0xB2,0x91, - 0x26,0x75,0xBF,0x5B,0x9E,0x58,0x29,0x28, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* order */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB3,0x1F,0x16,0x6E,0x6C,0xAC,0x04, - 0x25,0xA7,0xCF,0x3A,0xB6,0xAF,0x6B,0x7F,0xC3,0x10, - 0x3B,0x88,0x32,0x02,0xE9,0x04,0x65,0x65 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+64*6]; } - _EC_brainpoolP512r1 = { - { NID_X9_62_prime_field, 0,64,1 }, - { /* no seed */ - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* p */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF3, - 0x78,0x30,0xA3,0x31,0x8B,0x60,0x3B,0x89,0xE2,0x32, /* a */ - 0x71,0x45,0xAC,0x23,0x4C,0xC5,0x94,0xCB,0xDD,0x8D, - 0x3D,0xF9,0x16,0x10,0xA8,0x34,0x41,0xCA,0xEA,0x98, - 0x63,0xBC,0x2D,0xED,0x5D,0x5A,0xA8,0x25,0x3A,0xA1, - 0x0A,0x2E,0xF1,0xC9,0x8B,0x9A,0xC8,0xB5,0x7F,0x11, - 0x17,0xA7,0x2B,0xF2,0xC7,0xB9,0xE7,0xC1,0xAC,0x4D, - 0x77,0xFC,0x94,0xCA, - 0x3D,0xF9,0x16,0x10,0xA8,0x34,0x41,0xCA,0xEA,0x98, /* b */ - 0x63,0xBC,0x2D,0xED,0x5D,0x5A,0xA8,0x25,0x3A,0xA1, - 0x0A,0x2E,0xF1,0xC9,0x8B,0x9A,0xC8,0xB5,0x7F,0x11, - 0x17,0xA7,0x2B,0xF2,0xC7,0xB9,0xE7,0xC1,0xAC,0x4D, - 0x77,0xFC,0x94,0xCA,0xDC,0x08,0x3E,0x67,0x98,0x40, - 0x50,0xB7,0x5E,0xBA,0xE5,0xDD,0x28,0x09,0xBD,0x63, - 0x80,0x16,0xF7,0x23, - 0x81,0xAE,0xE4,0xBD,0xD8,0x2E,0xD9,0x64,0x5A,0x21, /* x */ - 0x32,0x2E,0x9C,0x4C,0x6A,0x93,0x85,0xED,0x9F,0x70, - 0xB5,0xD9,0x16,0xC1,0xB4,0x3B,0x62,0xEE,0xF4,0xD0, - 0x09,0x8E,0xFF,0x3B,0x1F,0x78,0xE2,0xD0,0xD4,0x8D, - 0x50,0xD1,0x68,0x7B,0x93,0xB9,0x7D,0x5F,0x7C,0x6D, - 0x50,0x47,0x40,0x6A,0x5E,0x68,0x8B,0x35,0x22,0x09, - 0xBC,0xB9,0xF8,0x22, - 0x7D,0xDE,0x38,0x5D,0x56,0x63,0x32,0xEC,0xC0,0xEA, /* y */ - 0xBF,0xA9,0xCF,0x78,0x22,0xFD,0xF2,0x09,0xF7,0x00, - 0x24,0xA5,0x7B,0x1A,0xA0,0x00,0xC5,0x5B,0x88,0x1F, - 0x81,0x11,0xB2,0xDC,0xDE,0x49,0x4A,0x5F,0x48,0x5E, - 0x5B,0xCA,0x4B,0xD8,0x8A,0x27,0x63,0xAE,0xD1,0xCA, - 0x2B,0x2F,0xA8,0xF0,0x54,0x06,0x78,0xCD,0x1E,0x0F, - 0x3A,0xD8,0x08,0x92, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* order */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x70,0x55,0x3E,0x5C,0x41,0x4C,0xA9,0x26,0x19, - 0x41,0x86,0x61,0x19,0x7F,0xAC,0x10,0x47,0x1D,0xB1, - 0xD3,0x81,0x08,0x5D,0xDA,0xDD,0xB5,0x87,0x96,0x82, - 0x9C,0xA9,0x00,0x69 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+64*6]; } - _EC_brainpoolP512t1 = { - { NID_X9_62_prime_field, 0,64,1 }, - { /* no seed */ - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* p */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF3, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* a */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF0, - 0x7C,0xBB,0xBC,0xF9,0x44,0x1C,0xFA,0xB7,0x6E,0x18, /* b */ - 0x90,0xE4,0x68,0x84,0xEA,0xE3,0x21,0xF7,0x0C,0x0B, - 0xCB,0x49,0x81,0x52,0x78,0x97,0x50,0x4B,0xEC,0x3E, - 0x36,0xA6,0x2B,0xCD,0xFA,0x23,0x04,0x97,0x65,0x40, - 0xF6,0x45,0x00,0x85,0xF2,0xDA,0xE1,0x45,0xC2,0x25, - 0x53,0xB4,0x65,0x76,0x36,0x89,0x18,0x0E,0xA2,0x57, - 0x18,0x67,0x42,0x3E, - 0x64,0x0E,0xCE,0x5C,0x12,0x78,0x87,0x17,0xB9,0xC1, /* x */ - 0xBA,0x06,0xCB,0xC2,0xA6,0xFE,0xBA,0x85,0x84,0x24, - 0x58,0xC5,0x6D,0xDE,0x9D,0xB1,0x75,0x8D,0x39,0xC0, - 0x31,0x3D,0x82,0xBA,0x51,0x73,0x5C,0xDB,0x3E,0xA4, - 0x99,0xAA,0x77,0xA7,0xD6,0x94,0x3A,0x64,0xF7,0xA3, - 0xF2,0x5F,0xE2,0x6F,0x06,0xB5,0x1B,0xAA,0x26,0x96, - 0xFA,0x90,0x35,0xDA, - 0x5B,0x53,0x4B,0xD5,0x95,0xF5,0xAF,0x0F,0xA2,0xC8, /* y */ - 0x92,0x37,0x6C,0x84,0xAC,0xE1,0xBB,0x4E,0x30,0x19, - 0xB7,0x16,0x34,0xC0,0x11,0x31,0x15,0x9C,0xAE,0x03, - 0xCE,0xE9,0xD9,0x93,0x21,0x84,0xBE,0xEF,0x21,0x6B, - 0xD7,0x1D,0xF2,0xDA,0xDF,0x86,0xA6,0x27,0x30,0x6E, - 0xCF,0xF9,0x6D,0xBB,0x8B,0xAC,0xE1,0x98,0xB6,0x1E, - 0x00,0xF8,0xB3,0x32, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* order */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x70,0x55,0x3E,0x5C,0x41,0x4C,0xA9,0x26,0x19, - 0x41,0x86,0x61,0x19,0x7F,0xAC,0x10,0x47,0x1D,0xB1, - 0xD3,0x81,0x08,0x5D,0xDA,0xDD,0xB5,0x87,0x96,0x82, - 0x9C,0xA9,0x00,0x69 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_FRP256v1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* p */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x39,0x61,0xAD,0xBC, - 0xAB,0xC8,0xCA,0x6D,0xE8,0xFC,0xF3,0x53,0xD8,0x6E, - 0x9C,0x03, - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* a */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x39,0x61,0xAD,0xBC, - 0xAB,0xC8,0xCA,0x6D,0xE8,0xFC,0xF3,0x53,0xD8,0x6E, - 0x9C,0x00, - 0xEE,0x35,0x3F,0xCA,0x54,0x28,0xA9,0x30,0x0D,0x4A, /* b */ - 0xBA,0x75,0x4A,0x44,0xC0,0x0F,0xDF,0xEC,0x0C,0x9A, - 0xE4,0xB1,0xA1,0x80,0x30,0x75,0xED,0x96,0x7B,0x7B, - 0xB7,0x3F, - 0xB6,0xB3,0xD4,0xC3,0x56,0xC1,0x39,0xEB,0x31,0x18, /* x */ - 0x3D,0x47,0x49,0xD4,0x23,0x95,0x8C,0x27,0xD2,0xDC, - 0xAF,0x98,0xB7,0x01,0x64,0xC9,0x7A,0x2D,0xD9,0x8F, - 0x5C,0xFF, - 0x61,0x42,0xE0,0xF7,0xC8,0xB2,0x04,0x91,0x1F,0x92, /* y */ - 0x71,0xF0,0xF3,0xEC,0xEF,0x8C,0x27,0x01,0xC3,0x07, - 0xE8,0xE4,0xC9,0xE1,0x83,0x11,0x5A,0x15,0x54,0x06, - 0x2C,0xFB, - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* order */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x53,0xDC,0x67,0xE1, - 0x40,0xD2,0xBF,0x94,0x1F,0xFD,0xD4,0x59,0xC6,0xD6, - 0x55,0xE1 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_brainpoolP160r1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { /* no seed */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* p */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + 0x34, 0x0E, 0x7B, 0xE2, 0xA2, 0x80, 0xEB, 0x74, 0xE2, 0xBE, /* a */ + 0x61, 0xBA, 0xDA, 0x74, 0x5D, 0x97, 0xE8, 0xF7, 0xC3, 0x00, + 0x1E, 0x58, 0x9A, 0x85, 0x95, 0x42, 0x34, 0x12, 0x13, 0x4F, /* b */ + 0xAA, 0x2D, 0xBD, 0xEC, 0x95, 0xC8, 0xD8, 0x67, 0x5E, 0x58, + 0xBE, 0xD5, 0xAF, 0x16, 0xEA, 0x3F, 0x6A, 0x4F, 0x62, 0x93, /* x */ + 0x8C, 0x46, 0x31, 0xEB, 0x5A, 0xF7, 0xBD, 0xBC, 0xDB, 0xC3, + 0x16, 0x67, 0xCB, 0x47, 0x7A, 0x1A, 0x8E, 0xC3, 0x38, 0xF9, /* y */ + 0x47, 0x41, 0x66, 0x9C, 0x97, 0x63, 0x16, 0xDA, 0x63, 0x21, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* order */ + 0x59, 0x91, 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_brainpoolP160t1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { /* no seed */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* p */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* a */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0C, + 0x7A, 0x55, 0x6B, 0x6D, 0xAE, 0x53, 0x5B, 0x7B, 0x51, 0xED, /* b */ + 0x2C, 0x4D, 0x7D, 0xAA, 0x7A, 0x0B, 0x5C, 0x55, 0xF3, 0x80, + 0xB1, 0x99, 0xB1, 0x3B, 0x9B, 0x34, 0xEF, 0xC1, 0x39, 0x7E, /* x */ + 0x64, 0xBA, 0xEB, 0x05, 0xAC, 0xC2, 0x65, 0xFF, 0x23, 0x78, + 0xAD, 0xD6, 0x71, 0x8B, 0x7C, 0x7C, 0x19, 0x61, 0xF0, 0x99, /* y */ + 0x1B, 0x84, 0x24, 0x43, 0x77, 0x21, 0x52, 0xC9, 0xE0, 0xAD, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* order */ + 0x59, 0x91, 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_brainpoolP192r1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* p */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x97, + 0x6A, 0x91, 0x17, 0x40, 0x76, 0xB1, 0xE0, 0xE1, 0x9C, 0x39, /* a */ + 0xC0, 0x31, 0xFE, 0x86, 0x85, 0xC1, 0xCA, 0xE0, 0x40, 0xE5, + 0xC6, 0x9A, 0x28, 0xEF, + 0x46, 0x9A, 0x28, 0xEF, 0x7C, 0x28, 0xCC, 0xA3, 0xDC, 0x72, /* b */ + 0x1D, 0x04, 0x4F, 0x44, 0x96, 0xBC, 0xCA, 0x7E, 0xF4, 0x14, + 0x6F, 0xBF, 0x25, 0xC9, + 0xC0, 0xA0, 0x64, 0x7E, 0xAA, 0xB6, 0xA4, 0x87, 0x53, 0xB0, /* x */ + 0x33, 0xC5, 0x6C, 0xB0, 0xF0, 0x90, 0x0A, 0x2F, 0x5C, 0x48, + 0x53, 0x37, 0x5F, 0xD6, + 0x14, 0xB6, 0x90, 0x86, 0x6A, 0xBD, 0x5B, 0xB8, 0x8B, 0x5F, /* y */ + 0x48, 0x28, 0xC1, 0x49, 0x00, 0x02, 0xE6, 0x77, 0x3F, 0xA2, + 0xFA, 0x29, 0x9B, 0x8F, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* order */ + 0x46, 0x2F, 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, + 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_brainpoolP192t1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* p */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x97, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* a */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x94, + 0x13, 0xD5, 0x6F, 0xFA, 0xEC, 0x78, 0x68, 0x1E, 0x68, 0xF9, /* b */ + 0xDE, 0xB4, 0x3B, 0x35, 0xBE, 0xC2, 0xFB, 0x68, 0x54, 0x2E, + 0x27, 0x89, 0x7B, 0x79, + 0x3A, 0xE9, 0xE5, 0x8C, 0x82, 0xF6, 0x3C, 0x30, 0x28, 0x2E, /* x */ + 0x1F, 0xE7, 0xBB, 0xF4, 0x3F, 0xA7, 0x2C, 0x44, 0x6A, 0xF6, + 0xF4, 0x61, 0x81, 0x29, + 0x09, 0x7E, 0x2C, 0x56, 0x67, 0xC2, 0x22, 0x3A, 0x90, 0x2A, /* y */ + 0xB5, 0xCA, 0x44, 0x9D, 0x00, 0x84, 0xB7, 0xE5, 0xB3, 0xDE, + 0x7C, 0xCC, 0x01, 0xC9, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* order */ + 0x46, 0x2F, 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, + 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_brainpoolP224r1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* p */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFF, + 0x68, 0xA5, 0xE6, 0x2C, 0xA9, 0xCE, 0x6C, 0x1C, 0x29, 0x98, /* a */ + 0x03, 0xA6, 0xC1, 0x53, 0x0B, 0x51, 0x4E, 0x18, 0x2A, 0xD8, + 0xB0, 0x04, 0x2A, 0x59, 0xCA, 0xD2, 0x9F, 0x43, + 0x25, 0x80, 0xF6, 0x3C, 0xCF, 0xE4, 0x41, 0x38, 0x87, 0x07, /* b */ + 0x13, 0xB1, 0xA9, 0x23, 0x69, 0xE3, 0x3E, 0x21, 0x35, 0xD2, + 0x66, 0xDB, 0xB3, 0x72, 0x38, 0x6C, 0x40, 0x0B, + 0x0D, 0x90, 0x29, 0xAD, 0x2C, 0x7E, 0x5C, 0xF4, 0x34, 0x08, /* x */ + 0x23, 0xB2, 0xA8, 0x7D, 0xC6, 0x8C, 0x9E, 0x4C, 0xE3, 0x17, + 0x4C, 0x1E, 0x6E, 0xFD, 0xEE, 0x12, 0xC0, 0x7D, + 0x58, 0xAA, 0x56, 0xF7, 0x72, 0xC0, 0x72, 0x6F, 0x24, 0xC6, /* y */ + 0xB8, 0x9E, 0x4E, 0xCD, 0xAC, 0x24, 0x35, 0x4B, 0x9E, 0x99, + 0xCA, 0xA3, 0xF6, 0xD3, 0x76, 0x14, 0x02, 0xCD, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* order */ + 0x30, 0x25, 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, + 0x6D, 0xDE, 0xBC, 0xA3, 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_brainpoolP224t1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* p */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFF, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* a */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFC, + 0x4B, 0x33, 0x7D, 0x93, 0x41, 0x04, 0xCD, 0x7B, 0xEF, 0x27, /* b */ + 0x1B, 0xF6, 0x0C, 0xED, 0x1E, 0xD2, 0x0D, 0xA1, 0x4C, 0x08, + 0xB3, 0xBB, 0x64, 0xF1, 0x8A, 0x60, 0x88, 0x8D, + 0x6A, 0xB1, 0xE3, 0x44, 0xCE, 0x25, 0xFF, 0x38, 0x96, 0x42, /* x */ + 0x4E, 0x7F, 0xFE, 0x14, 0x76, 0x2E, 0xCB, 0x49, 0xF8, 0x92, + 0x8A, 0xC0, 0xC7, 0x60, 0x29, 0xB4, 0xD5, 0x80, + 0x03, 0x74, 0xE9, 0xF5, 0x14, 0x3E, 0x56, 0x8C, 0xD2, 0x3F, /* y */ + 0x3F, 0x4D, 0x7C, 0x0D, 0x4B, 0x1E, 0x41, 0xC8, 0xCC, 0x0D, + 0x1C, 0x6A, 0xBD, 0x5F, 0x1A, 0x46, 0xDB, 0x4C, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* order */ + 0x30, 0x25, 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, + 0x6D, 0xDE, 0xBC, 0xA3, 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_brainpoolP256r1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* p */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x77, + 0x7D, 0x5A, 0x09, 0x75, 0xFC, 0x2C, 0x30, 0x57, 0xEE, 0xF6, /* a */ + 0x75, 0x30, 0x41, 0x7A, 0xFF, 0xE7, 0xFB, 0x80, 0x55, 0xC1, + 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, + 0xB5, 0xD9, + 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, /* b */ + 0xB5, 0xD9, 0xBB, 0xD7, 0x7C, 0xBF, 0x95, 0x84, 0x16, 0x29, + 0x5C, 0xF7, 0xE1, 0xCE, 0x6B, 0xCC, 0xDC, 0x18, 0xFF, 0x8C, + 0x07, 0xB6, + 0x8B, 0xD2, 0xAE, 0xB9, 0xCB, 0x7E, 0x57, 0xCB, 0x2C, 0x4B, /* x */ + 0x48, 0x2F, 0xFC, 0x81, 0xB7, 0xAF, 0xB9, 0xDE, 0x27, 0xE1, + 0xE3, 0xBD, 0x23, 0xC2, 0x3A, 0x44, 0x53, 0xBD, 0x9A, 0xCE, + 0x32, 0x62, + 0x54, 0x7E, 0xF8, 0x35, 0xC3, 0xDA, 0xC4, 0xFD, 0x97, 0xF8, /* y */ + 0x46, 0x1A, 0x14, 0x61, 0x1D, 0xC9, 0xC2, 0x77, 0x45, 0x13, + 0x2D, 0xED, 0x8E, 0x54, 0x5C, 0x1D, 0x54, 0xC7, 0x2F, 0x04, + 0x69, 0x97, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* order */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, + 0xB5, 0x61, 0xA6, 0xF7, 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, + 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_brainpoolP256t1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* p */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x77, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* a */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x74, + 0x66, 0x2C, 0x61, 0xC4, 0x30, 0xD8, 0x4E, 0xA4, 0xFE, 0x66, /* b */ + 0xA7, 0x73, 0x3D, 0x0B, 0x76, 0xB7, 0xBF, 0x93, 0xEB, 0xC4, + 0xAF, 0x2F, 0x49, 0x25, 0x6A, 0xE5, 0x81, 0x01, 0xFE, 0xE9, + 0x2B, 0x04, + 0xA3, 0xE8, 0xEB, 0x3C, 0xC1, 0xCF, 0xE7, 0xB7, 0x73, 0x22, /* x */ + 0x13, 0xB2, 0x3A, 0x65, 0x61, 0x49, 0xAF, 0xA1, 0x42, 0xC4, + 0x7A, 0xAF, 0xBC, 0x2B, 0x79, 0xA1, 0x91, 0x56, 0x2E, 0x13, + 0x05, 0xF4, + 0x2D, 0x99, 0x6C, 0x82, 0x34, 0x39, 0xC5, 0x6D, 0x7F, 0x7B, /* y */ + 0x22, 0xE1, 0x46, 0x44, 0x41, 0x7E, 0x69, 0xBC, 0xB6, 0xDE, + 0x39, 0xD0, 0x27, 0x00, 0x1D, 0xAB, 0xE8, 0xF3, 0x5B, 0x25, + 0xC9, 0xBE, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* order */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, + 0xB5, 0x61, 0xA6, 0xF7, 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, + 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} + _EC_brainpoolP320r1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { /* no seed */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* p */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x27, + 0x3E, 0xE3, 0x0B, 0x56, 0x8F, 0xBA, 0xB0, 0xF8, 0x83, 0xCC, /* a */ + 0xEB, 0xD4, 0x6D, 0x3F, 0x3B, 0xB8, 0xA2, 0xA7, 0x35, 0x13, + 0xF5, 0xEB, 0x79, 0xDA, 0x66, 0x19, 0x0E, 0xB0, 0x85, 0xFF, + 0xA9, 0xF4, 0x92, 0xF3, 0x75, 0xA9, 0x7D, 0x86, 0x0E, 0xB4, + 0x52, 0x08, 0x83, 0x94, 0x9D, 0xFD, 0xBC, 0x42, 0xD3, 0xAD, /* b */ + 0x19, 0x86, 0x40, 0x68, 0x8A, 0x6F, 0xE1, 0x3F, 0x41, 0x34, + 0x95, 0x54, 0xB4, 0x9A, 0xCC, 0x31, 0xDC, 0xCD, 0x88, 0x45, + 0x39, 0x81, 0x6F, 0x5E, 0xB4, 0xAC, 0x8F, 0xB1, 0xF1, 0xA6, + 0x43, 0xBD, 0x7E, 0x9A, 0xFB, 0x53, 0xD8, 0xB8, 0x52, 0x89, /* x */ + 0xBC, 0xC4, 0x8E, 0xE5, 0xBF, 0xE6, 0xF2, 0x01, 0x37, 0xD1, + 0x0A, 0x08, 0x7E, 0xB6, 0xE7, 0x87, 0x1E, 0x2A, 0x10, 0xA5, + 0x99, 0xC7, 0x10, 0xAF, 0x8D, 0x0D, 0x39, 0xE2, 0x06, 0x11, + 0x14, 0xFD, 0xD0, 0x55, 0x45, 0xEC, 0x1C, 0xC8, 0xAB, 0x40, /* y */ + 0x93, 0x24, 0x7F, 0x77, 0x27, 0x5E, 0x07, 0x43, 0xFF, 0xED, + 0x11, 0x71, 0x82, 0xEA, 0xA9, 0xC7, 0x78, 0x77, 0xAA, 0xAC, + 0x6A, 0xC7, 0xD3, 0x52, 0x45, 0xD1, 0x69, 0x2E, 0x8E, 0xE1, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* order */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, + 0xB6, 0x8F, 0x12, 0xA3, 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, + 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} + _EC_brainpoolP320t1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { /* no seed */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* p */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x27, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* a */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x24, + 0xA7, 0xF5, 0x61, 0xE0, 0x38, 0xEB, 0x1E, 0xD5, 0x60, 0xB3, /* b */ + 0xD1, 0x47, 0xDB, 0x78, 0x20, 0x13, 0x06, 0x4C, 0x19, 0xF2, + 0x7E, 0xD2, 0x7C, 0x67, 0x80, 0xAA, 0xF7, 0x7F, 0xB8, 0xA5, + 0x47, 0xCE, 0xB5, 0xB4, 0xFE, 0xF4, 0x22, 0x34, 0x03, 0x53, + 0x92, 0x5B, 0xE9, 0xFB, 0x01, 0xAF, 0xC6, 0xFB, 0x4D, 0x3E, /* x */ + 0x7D, 0x49, 0x90, 0x01, 0x0F, 0x81, 0x34, 0x08, 0xAB, 0x10, + 0x6C, 0x4F, 0x09, 0xCB, 0x7E, 0xE0, 0x78, 0x68, 0xCC, 0x13, + 0x6F, 0xFF, 0x33, 0x57, 0xF6, 0x24, 0xA2, 0x1B, 0xED, 0x52, + 0x63, 0xBA, 0x3A, 0x7A, 0x27, 0x48, 0x3E, 0xBF, 0x66, 0x71, /* y */ + 0xDB, 0xEF, 0x7A, 0xBB, 0x30, 0xEB, 0xEE, 0x08, 0x4E, 0x58, + 0xA0, 0xB0, 0x77, 0xAD, 0x42, 0xA5, 0xA0, 0x98, 0x9D, 0x1E, + 0xE7, 0x1B, 0x1B, 0x9B, 0xC0, 0x45, 0x5F, 0xB0, 0xD2, 0xC3, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* order */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, + 0xB6, 0x8F, 0x12, 0xA3, 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, + 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} + _EC_brainpoolP384r1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { /* no seed */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* p */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + 0x7B, 0xC3, 0x82, 0xC6, 0x3D, 0x8C, 0x15, 0x0C, 0x3C, 0x72, /* a */ + 0x08, 0x0A, 0xCE, 0x05, 0xAF, 0xA0, 0xC2, 0xBE, 0xA2, 0x8E, + 0x4F, 0xB2, 0x27, 0x87, 0x13, 0x91, 0x65, 0xEF, 0xBA, 0x91, + 0xF9, 0x0F, 0x8A, 0xA5, 0x81, 0x4A, 0x50, 0x3A, 0xD4, 0xEB, + 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, + 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, 0x8B, 0x39, /* b */ + 0xB5, 0x54, 0x16, 0xF0, 0x44, 0x7C, 0x2F, 0xB7, 0x7D, 0xE1, + 0x07, 0xDC, 0xD2, 0xA6, 0x2E, 0x88, 0x0E, 0xA5, 0x3E, 0xEB, + 0x62, 0xD5, 0x7C, 0xB4, 0x39, 0x02, 0x95, 0xDB, 0xC9, 0x94, + 0x3A, 0xB7, 0x86, 0x96, 0xFA, 0x50, 0x4C, 0x11, + 0x1D, 0x1C, 0x64, 0xF0, 0x68, 0xCF, 0x45, 0xFF, 0xA2, 0xA6, /* x */ + 0x3A, 0x81, 0xB7, 0xC1, 0x3F, 0x6B, 0x88, 0x47, 0xA3, 0xE7, + 0x7E, 0xF1, 0x4F, 0xE3, 0xDB, 0x7F, 0xCA, 0xFE, 0x0C, 0xBD, + 0x10, 0xE8, 0xE8, 0x26, 0xE0, 0x34, 0x36, 0xD6, 0x46, 0xAA, + 0xEF, 0x87, 0xB2, 0xE2, 0x47, 0xD4, 0xAF, 0x1E, + 0x8A, 0xBE, 0x1D, 0x75, 0x20, 0xF9, 0xC2, 0xA4, 0x5C, 0xB1, /* y */ + 0xEB, 0x8E, 0x95, 0xCF, 0xD5, 0x52, 0x62, 0xB7, 0x0B, 0x29, + 0xFE, 0xEC, 0x58, 0x64, 0xE1, 0x9C, 0x05, 0x4F, 0xF9, 0x91, + 0x29, 0x28, 0x0E, 0x46, 0x46, 0x21, 0x77, 0x91, 0x81, 0x11, + 0x42, 0x82, 0x03, 0x41, 0x26, 0x3C, 0x53, 0x15, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* order */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB3, 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, + 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, 0x6B, 0x7F, 0xC3, 0x10, + 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} + _EC_brainpoolP384t1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { /* no seed */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* p */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* a */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x50, + 0x7F, 0x51, 0x9E, 0xAD, 0xA7, 0xBD, 0xA8, 0x1B, 0xD8, 0x26, /* b */ + 0xDB, 0xA6, 0x47, 0x91, 0x0F, 0x8C, 0x4B, 0x93, 0x46, 0xED, + 0x8C, 0xCD, 0xC6, 0x4E, 0x4B, 0x1A, 0xBD, 0x11, 0x75, 0x6D, + 0xCE, 0x1D, 0x20, 0x74, 0xAA, 0x26, 0x3B, 0x88, 0x80, 0x5C, + 0xED, 0x70, 0x35, 0x5A, 0x33, 0xB4, 0x71, 0xEE, + 0x18, 0xDE, 0x98, 0xB0, 0x2D, 0xB9, 0xA3, 0x06, 0xF2, 0xAF, /* x */ + 0xCD, 0x72, 0x35, 0xF7, 0x2A, 0x81, 0x9B, 0x80, 0xAB, 0x12, + 0xEB, 0xD6, 0x53, 0x17, 0x24, 0x76, 0xFE, 0xCD, 0x46, 0x2A, + 0xAB, 0xFF, 0xC4, 0xFF, 0x19, 0x1B, 0x94, 0x6A, 0x5F, 0x54, + 0xD8, 0xD0, 0xAA, 0x2F, 0x41, 0x88, 0x08, 0xCC, + 0x25, 0xAB, 0x05, 0x69, 0x62, 0xD3, 0x06, 0x51, 0xA1, 0x14, /* y */ + 0xAF, 0xD2, 0x75, 0x5A, 0xD3, 0x36, 0x74, 0x7F, 0x93, 0x47, + 0x5B, 0x7A, 0x1F, 0xCA, 0x3B, 0x88, 0xF2, 0xB6, 0xA2, 0x08, + 0xCC, 0xFE, 0x46, 0x94, 0x08, 0x58, 0x4D, 0xC2, 0xB2, 0x91, + 0x26, 0x75, 0xBF, 0x5B, 0x9E, 0x58, 0x29, 0x28, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* order */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB3, 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, + 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, 0x6B, 0x7F, 0xC3, 0x10, + 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} + _EC_brainpoolP512r1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { /* no seed */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* p */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + 0x78, 0x30, 0xA3, 0x31, 0x8B, 0x60, 0x3B, 0x89, 0xE2, 0x32, /* a */ + 0x71, 0x45, 0xAC, 0x23, 0x4C, 0xC5, 0x94, 0xCB, 0xDD, 0x8D, + 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, + 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, + 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, + 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, + 0x77, 0xFC, 0x94, 0xCA, + 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, /* b */ + 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, + 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, + 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, + 0x77, 0xFC, 0x94, 0xCA, 0xDC, 0x08, 0x3E, 0x67, 0x98, 0x40, + 0x50, 0xB7, 0x5E, 0xBA, 0xE5, 0xDD, 0x28, 0x09, 0xBD, 0x63, + 0x80, 0x16, 0xF7, 0x23, + 0x81, 0xAE, 0xE4, 0xBD, 0xD8, 0x2E, 0xD9, 0x64, 0x5A, 0x21, /* x */ + 0x32, 0x2E, 0x9C, 0x4C, 0x6A, 0x93, 0x85, 0xED, 0x9F, 0x70, + 0xB5, 0xD9, 0x16, 0xC1, 0xB4, 0x3B, 0x62, 0xEE, 0xF4, 0xD0, + 0x09, 0x8E, 0xFF, 0x3B, 0x1F, 0x78, 0xE2, 0xD0, 0xD4, 0x8D, + 0x50, 0xD1, 0x68, 0x7B, 0x93, 0xB9, 0x7D, 0x5F, 0x7C, 0x6D, + 0x50, 0x47, 0x40, 0x6A, 0x5E, 0x68, 0x8B, 0x35, 0x22, 0x09, + 0xBC, 0xB9, 0xF8, 0x22, + 0x7D, 0xDE, 0x38, 0x5D, 0x56, 0x63, 0x32, 0xEC, 0xC0, 0xEA, /* y */ + 0xBF, 0xA9, 0xCF, 0x78, 0x22, 0xFD, 0xF2, 0x09, 0xF7, 0x00, + 0x24, 0xA5, 0x7B, 0x1A, 0xA0, 0x00, 0xC5, 0x5B, 0x88, 0x1F, + 0x81, 0x11, 0xB2, 0xDC, 0xDE, 0x49, 0x4A, 0x5F, 0x48, 0x5E, + 0x5B, 0xCA, 0x4B, 0xD8, 0x8A, 0x27, 0x63, 0xAE, 0xD1, 0xCA, + 0x2B, 0x2F, 0xA8, 0xF0, 0x54, 0x06, 0x78, 0xCD, 0x1E, 0x0F, + 0x3A, 0xD8, 0x08, 0x92, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* order */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, 0x4C, 0xA9, 0x26, 0x19, + 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, 0x1D, 0xB1, + 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} + _EC_brainpoolP512t1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { /* no seed */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* p */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* a */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF0, + 0x7C, 0xBB, 0xBC, 0xF9, 0x44, 0x1C, 0xFA, 0xB7, 0x6E, 0x18, /* b */ + 0x90, 0xE4, 0x68, 0x84, 0xEA, 0xE3, 0x21, 0xF7, 0x0C, 0x0B, + 0xCB, 0x49, 0x81, 0x52, 0x78, 0x97, 0x50, 0x4B, 0xEC, 0x3E, + 0x36, 0xA6, 0x2B, 0xCD, 0xFA, 0x23, 0x04, 0x97, 0x65, 0x40, + 0xF6, 0x45, 0x00, 0x85, 0xF2, 0xDA, 0xE1, 0x45, 0xC2, 0x25, + 0x53, 0xB4, 0x65, 0x76, 0x36, 0x89, 0x18, 0x0E, 0xA2, 0x57, + 0x18, 0x67, 0x42, 0x3E, + 0x64, 0x0E, 0xCE, 0x5C, 0x12, 0x78, 0x87, 0x17, 0xB9, 0xC1, /* x */ + 0xBA, 0x06, 0xCB, 0xC2, 0xA6, 0xFE, 0xBA, 0x85, 0x84, 0x24, + 0x58, 0xC5, 0x6D, 0xDE, 0x9D, 0xB1, 0x75, 0x8D, 0x39, 0xC0, + 0x31, 0x3D, 0x82, 0xBA, 0x51, 0x73, 0x5C, 0xDB, 0x3E, 0xA4, + 0x99, 0xAA, 0x77, 0xA7, 0xD6, 0x94, 0x3A, 0x64, 0xF7, 0xA3, + 0xF2, 0x5F, 0xE2, 0x6F, 0x06, 0xB5, 0x1B, 0xAA, 0x26, 0x96, + 0xFA, 0x90, 0x35, 0xDA, + 0x5B, 0x53, 0x4B, 0xD5, 0x95, 0xF5, 0xAF, 0x0F, 0xA2, 0xC8, /* y */ + 0x92, 0x37, 0x6C, 0x84, 0xAC, 0xE1, 0xBB, 0x4E, 0x30, 0x19, + 0xB7, 0x16, 0x34, 0xC0, 0x11, 0x31, 0x15, 0x9C, 0xAE, 0x03, + 0xCE, 0xE9, 0xD9, 0x93, 0x21, 0x84, 0xBE, 0xEF, 0x21, 0x6B, + 0xD7, 0x1D, 0xF2, 0xDA, 0xDF, 0x86, 0xA6, 0x27, 0x30, 0x6E, + 0xCF, 0xF9, 0x6D, 0xBB, 0x8B, 0xAC, 0xE1, 0x98, 0xB6, 0x1E, + 0x00, 0xF8, 0xB3, 0x32, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* order */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, 0x4C, 0xA9, 0x26, 0x19, + 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, 0x1D, 0xB1, + 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_FRP256v1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* p */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x39, 0x61, 0xAD, 0xBC, + 0xAB, 0xC8, 0xCA, 0x6D, 0xE8, 0xFC, 0xF3, 0x53, 0xD8, 0x6E, + 0x9C, 0x03, + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* a */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x39, 0x61, 0xAD, 0xBC, + 0xAB, 0xC8, 0xCA, 0x6D, 0xE8, 0xFC, 0xF3, 0x53, 0xD8, 0x6E, + 0x9C, 0x00, + 0xEE, 0x35, 0x3F, 0xCA, 0x54, 0x28, 0xA9, 0x30, 0x0D, 0x4A, /* b */ + 0xBA, 0x75, 0x4A, 0x44, 0xC0, 0x0F, 0xDF, 0xEC, 0x0C, 0x9A, + 0xE4, 0xB1, 0xA1, 0x80, 0x30, 0x75, 0xED, 0x96, 0x7B, 0x7B, + 0xB7, 0x3F, + 0xB6, 0xB3, 0xD4, 0xC3, 0x56, 0xC1, 0x39, 0xEB, 0x31, 0x18, /* x */ + 0x3D, 0x47, 0x49, 0xD4, 0x23, 0x95, 0x8C, 0x27, 0xD2, 0xDC, + 0xAF, 0x98, 0xB7, 0x01, 0x64, 0xC9, 0x7A, 0x2D, 0xD9, 0x8F, + 0x5C, 0xFF, + 0x61, 0x42, 0xE0, 0xF7, 0xC8, 0xB2, 0x04, 0x91, 0x1F, 0x92, /* y */ + 0x71, 0xF0, 0xF3, 0xEC, 0xEF, 0x8C, 0x27, 0x01, 0xC3, 0x07, + 0xE8, 0xE4, 0xC9, 0xE1, 0x83, 0x11, 0x5A, 0x15, 0x54, 0x06, + 0x2C, 0xFB, + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* order */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x53, 0xDC, 0x67, 0xE1, + 0x40, 0xD2, 0xBF, 0x94, 0x1F, 0xFD, 0xD4, 0x59, 0xC6, 0xD6, + 0x55, 0xE1 + } +}; typedef struct _ec_list_element_st { - int nid; + int nid; const EC_CURVE_DATA *data; - const EC_METHOD *(*meth)(void); + const EC_METHOD *(*meth) (void); const char *comment; - } ec_list_element; +} ec_list_element; static const ec_list_element curve_list[] = { /* prime field curves */ /* secg curves */ - { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, - { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field" }, - { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field" }, - { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field" }, - { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field" }, - { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field" }, - { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, + {NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field"}, + {NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field"}, + {NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field"}, + {NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field"}, + {NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field"}, + {NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field"}, + {NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field"}, /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ - { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, - { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, + {NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field"}, + {NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" }, + {NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field"}, #else - { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, + {NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field"}, #endif - { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, + {NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field"}, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ - { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, + {NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" }, + {NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field"}, #else - { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, + {NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field"}, #endif /* X9.62 curves */ - { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, - { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, - { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field" }, - { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, - { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, - { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, + {NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field"}, + {NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" }, + {NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field"}, #else - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, + {NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field"}, #endif #ifndef OPENSSL_NO_EC2M /* characteristic two field curves */ /* NIST/SECG curves */ - { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field" }, - { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field" }, - { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field" }, - { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field" }, - { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field" }, - { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field" }, - { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field" }, - { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field" }, - { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field" }, + {NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field"}, + {NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field"}, + {NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field"}, + {NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field"}, + {NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field"}, + {NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field"}, + {NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field"}, + {NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field"}, + {NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field"}, /* X9.62 curves */ - { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field" }, - { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field" }, - { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field" }, - { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field" }, - { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field" }, - { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field" }, - { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field" }, - /* the WAP/WTLS curves - * [unlike SECG, spec has its own OIDs for curves from X9.62] */ - { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + {NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field"}, + {NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field"}, + {NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field"}, + {NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field"}, + {NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field"}, + {NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field"}, + {NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field"}, + /* + * the WAP/WTLS curves [unlike SECG, spec has its own OIDs for curves + * from X9.62] + */ + {NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field"}, #endif - { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field" }, + {NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field"}, #ifndef OPENSSL_NO_EC2M - { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + {NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, #endif - { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curve over a 224 bit prime field" }, + {NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curve over a 224 bit prime field"}, #ifndef OPENSSL_NO_EC2M /* IPSec curves */ - { NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, - { NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, + {NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, + {NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, #endif /* RFC 5639 curves */ - { NID_brainpoolP160r1, &_EC_brainpoolP160r1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, - { NID_brainpoolP160t1, &_EC_brainpoolP160t1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, - { NID_brainpoolP192r1, &_EC_brainpoolP192r1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, - { NID_brainpoolP192t1, &_EC_brainpoolP192t1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, - { NID_brainpoolP224r1, &_EC_brainpoolP224r1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, - { NID_brainpoolP224t1, &_EC_brainpoolP224t1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, - { NID_brainpoolP256r1, &_EC_brainpoolP256r1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, - { NID_brainpoolP256t1, &_EC_brainpoolP256t1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, - { NID_brainpoolP320r1, &_EC_brainpoolP320r1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, - { NID_brainpoolP320t1, &_EC_brainpoolP320t1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, - { NID_brainpoolP384r1, &_EC_brainpoolP384r1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, - { NID_brainpoolP384t1, &_EC_brainpoolP384t1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, - { NID_brainpoolP512r1, &_EC_brainpoolP512r1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, - { NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, + {NID_brainpoolP160r1, &_EC_brainpoolP160r1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP160t1, &_EC_brainpoolP160t1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP192r1, &_EC_brainpoolP192r1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP192t1, &_EC_brainpoolP192t1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP224r1, &_EC_brainpoolP224r1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP224t1, &_EC_brainpoolP224t1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP256r1, &_EC_brainpoolP256r1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP256t1, &_EC_brainpoolP256t1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP320r1, &_EC_brainpoolP320r1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP320t1, &_EC_brainpoolP320t1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP384r1, &_EC_brainpoolP384r1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP384t1, &_EC_brainpoolP384t1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP512r1, &_EC_brainpoolP512r1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, + {NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, /* ANSSI */ - { NID_FRP256v1, &_EC_FRP256v1.h, 0, "FRP256v1"} + {NID_FRP256v1, &_EC_FRP256v1.h, 0, "FRP256v1"} }; #define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element)) -static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) - { - EC_GROUP *group=NULL; - EC_POINT *P=NULL; - BN_CTX *ctx=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; - int ok=0; - int seed_len,param_len; +static EC_GROUP * +ec_group_new_from_data(const ec_list_element curve) +{ + EC_GROUP *group = NULL; + EC_POINT *P = NULL; + BN_CTX *ctx = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *order = NULL; + int ok = 0; + int seed_len, param_len; const EC_METHOD *meth; const EC_CURVE_DATA *data; const unsigned char *params; - if ((ctx = BN_CTX_new()) == NULL) - { + if ((ctx = BN_CTX_new()) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE); goto err; - } - + } data = curve.data; - seed_len = data->seed_len; + seed_len = data->seed_len; param_len = data->param_len; - params = (const unsigned char *)(data+1); /* skip header */ - params += seed_len; /* skip seed */ + params = (const unsigned char *) (data + 1); /* skip header */ + params += seed_len; /* skip seed */ - if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL)) - || !(a = BN_bin2bn(params+1*param_len, param_len, NULL)) - || !(b = BN_bin2bn(params+2*param_len, param_len, NULL))) - { + if (!(p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) || + !(a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) || + !(b = BN_bin2bn(params + 2 * param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - - if (curve.meth != 0) - { + } + if (curve.meth != 0) { meth = curve.meth(); if (((group = EC_GROUP_new(meth)) == NULL) || - (!(group->meth->group_set_curve(group, p, a, b, ctx)))) - { + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } - else if (data->field_type == NID_X9_62_prime_field) - { - if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) - { + } else if (data->field_type == NID_X9_62_prime_field) { + if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } + } #ifndef OPENSSL_NO_EC2M - else /* field_type == NID_X9_62_characteristic_two_field */ - { - if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) - { + else { /* field_type == + * NID_X9_62_characteristic_two_field */ + if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } + } #endif - if ((P = EC_POINT_new(group)) == NULL) - { + if ((P = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - - if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL)) - || !(y = BN_bin2bn(params+4*param_len, param_len, NULL))) - { + } + if (!(x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) + || !(y = BN_bin2bn(params + 4 * param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) - { + } + if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - if (!(order = BN_bin2bn(params+5*param_len, param_len, NULL)) - || !BN_set_word(x, (BN_ULONG)data->cofactor)) - { + } + if (!(order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) + || !BN_set_word(x, (BN_ULONG) data->cofactor)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - if (!EC_GROUP_set_generator(group, P, order, x)) - { + } + if (!EC_GROUP_set_generator(group, P, order, x)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - if (seed_len) - { - if (!EC_GROUP_set_seed(group, params-seed_len, seed_len)) - { + } + if (seed_len) { + if (!EC_GROUP_set_seed(group, params - seed_len, seed_len)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } - ok=1; + } + ok = 1; err: - if (!ok) - { + if (!ok) { EC_GROUP_free(group); group = NULL; - } + } if (P) EC_POINT_free(P); if (ctx) @@ -2528,48 +2997,45 @@ err: if (y) BN_free(y); return group; - } +} -EC_GROUP *EC_GROUP_new_by_curve_name(int nid) - { +EC_GROUP * +EC_GROUP_new_by_curve_name(int nid) +{ size_t i; EC_GROUP *ret = NULL; if (nid <= 0) return NULL; - for (i=0; i -EC_KEY *EC_KEY_new(void) - { +EC_KEY * +EC_KEY_new(void) +{ EC_KEY *ret; - ret=(EC_KEY *)malloc(sizeof(EC_KEY)); - if (ret == NULL) - { + ret = (EC_KEY *) malloc(sizeof(EC_KEY)); + if (ret == NULL) { ECerr(EC_F_EC_KEY_NEW, ERR_R_MALLOC_FAILURE); - return(NULL); - } - - ret->version = 1; + return (NULL); + } + ret->version = 1; ret->flags = 0; - ret->group = NULL; + ret->group = NULL; ret->pub_key = NULL; - ret->priv_key= NULL; - ret->enc_flag= 0; + ret->priv_key = NULL; + ret->enc_flag = 0; ret->conv_form = POINT_CONVERSION_UNCOMPRESSED; - ret->references= 1; + ret->references = 1; ret->method_data = NULL; - return(ret); - } + return (ret); +} -EC_KEY *EC_KEY_new_by_curve_name(int nid) - { +EC_KEY * +EC_KEY_new_by_curve_name(int nid) +{ EC_KEY *ret = EC_KEY_new(); if (ret == NULL) return NULL; ret->group = EC_GROUP_new_by_curve_name(nid); - if (ret->group == NULL) - { + if (ret->group == NULL) { EC_KEY_free(ret); return NULL; - } - return ret; } + return ret; +} -void EC_KEY_free(EC_KEY *r) - { +void +EC_KEY_free(EC_KEY * r) +{ int i; - if (r == NULL) return; + if (r == NULL) + return; - i=CRYPTO_add(&r->references,-1,CRYPTO_LOCK_EC); - if (i > 0) return; + i = CRYPTO_add(&r->references, -1, CRYPTO_LOCK_EC); + if (i > 0) + return; - if (r->group != NULL) + if (r->group != NULL) EC_GROUP_free(r->group); - if (r->pub_key != NULL) + if (r->pub_key != NULL) EC_POINT_free(r->pub_key); if (r->priv_key != NULL) BN_clear_free(r->priv_key); EC_EX_DATA_free_all_data(&r->method_data); - OPENSSL_cleanse((void *)r, sizeof(EC_KEY)); + OPENSSL_cleanse((void *) r, sizeof(EC_KEY)); free(r); - } +} -EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) - { +EC_KEY * +EC_KEY_copy(EC_KEY * dest, const EC_KEY * src) +{ EC_EXTRA_DATA *d; - if (dest == NULL || src == NULL) - { + if (dest == NULL || src == NULL) { ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } + } /* copy the parameters */ - if (src->group) - { + if (src->group) { const EC_METHOD *meth = EC_GROUP_method_of(src->group); /* clear the old group */ if (dest->group) @@ -146,10 +147,9 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) return NULL; if (!EC_GROUP_copy(dest->group, src->group)) return NULL; - } - /* copy the public key */ - if (src->pub_key && src->group) - { + } + /* copy the public key */ + if (src->pub_key && src->group) { if (dest->pub_key) EC_POINT_free(dest->pub_key); dest->pub_key = EC_POINT_new(src->group); @@ -157,83 +157,81 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) return NULL; if (!EC_POINT_copy(dest->pub_key, src->pub_key)) return NULL; - } + } /* copy the private key */ - if (src->priv_key) - { - if (dest->priv_key == NULL) - { + if (src->priv_key) { + if (dest->priv_key == NULL) { dest->priv_key = BN_new(); if (dest->priv_key == NULL) return NULL; - } + } if (!BN_copy(dest->priv_key, src->priv_key)) return NULL; - } + } /* copy method/extra data */ EC_EX_DATA_free_all_data(&dest->method_data); - for (d = src->method_data; d != NULL; d = d->next) - { + for (d = src->method_data; d != NULL; d = d->next) { void *t = d->dup_func(d->data); - + if (t == NULL) return 0; - if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, d->free_func, d->clear_free_func)) + if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, + d->free_func, d->clear_free_func)) return 0; - } + } /* copy the rest */ - dest->enc_flag = src->enc_flag; + dest->enc_flag = src->enc_flag; dest->conv_form = src->conv_form; - dest->version = src->version; + dest->version = src->version; dest->flags = src->flags; return dest; - } +} -EC_KEY *EC_KEY_dup(const EC_KEY *ec_key) - { +EC_KEY * +EC_KEY_dup(const EC_KEY * ec_key) +{ EC_KEY *ret = EC_KEY_new(); if (ret == NULL) return NULL; - if (EC_KEY_copy(ret, ec_key) == NULL) - { + if (EC_KEY_copy(ret, ec_key) == NULL) { EC_KEY_free(ret); return NULL; - } - return ret; } + return ret; +} -int EC_KEY_up_ref(EC_KEY *r) - { +int +EC_KEY_up_ref(EC_KEY * r) +{ int i = CRYPTO_add(&r->references, 1, CRYPTO_LOCK_EC); return ((i > 1) ? 1 : 0); - } +} -int EC_KEY_generate_key(EC_KEY *eckey) - { - int ok = 0; - BN_CTX *ctx = NULL; - BIGNUM *priv_key = NULL, *order = NULL; +int +EC_KEY_generate_key(EC_KEY * eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + BIGNUM *priv_key = NULL, *order = NULL; EC_POINT *pub_key = NULL; - if (!eckey || !eckey->group) - { + if (!eckey || !eckey->group) { ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if ((order = BN_new()) == NULL) goto err; - if ((ctx = BN_CTX_new()) == NULL) goto err; + } + if ((order = BN_new()) == NULL) + goto err; + if ((ctx = BN_CTX_new()) == NULL) + goto err; - if (eckey->priv_key == NULL) - { + if (eckey->priv_key == NULL) { priv_key = BN_new(); if (priv_key == NULL) goto err; - } - else + } else priv_key = eckey->priv_key; if (!EC_GROUP_get_order(eckey->group, order, ctx)) @@ -244,127 +242,115 @@ int EC_KEY_generate_key(EC_KEY *eckey) goto err; while (BN_is_zero(priv_key)); - if (eckey->pub_key == NULL) - { + if (eckey->pub_key == NULL) { pub_key = EC_POINT_new(eckey->group); if (pub_key == NULL) goto err; - } - else + } else pub_key = eckey->pub_key; if (!EC_POINT_mul(eckey->group, pub_key, priv_key, NULL, NULL, ctx)) goto err; eckey->priv_key = priv_key; - eckey->pub_key = pub_key; + eckey->pub_key = pub_key; - ok=1; + ok = 1; -err: +err: if (order) BN_free(order); - if (pub_key != NULL && eckey->pub_key == NULL) + if (pub_key != NULL && eckey->pub_key == NULL) EC_POINT_free(pub_key); if (priv_key != NULL && eckey->priv_key == NULL) BN_free(priv_key); if (ctx != NULL) BN_CTX_free(ctx); - return(ok); - } + return (ok); +} -int EC_KEY_check_key(const EC_KEY *eckey) - { - int ok = 0; - BN_CTX *ctx = NULL; - const BIGNUM *order = NULL; +int +EC_KEY_check_key(const EC_KEY * eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + const BIGNUM *order = NULL; EC_POINT *point = NULL; - if (!eckey || !eckey->group || !eckey->pub_key) - { + if (!eckey || !eckey->group || !eckey->pub_key) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) - { + } + if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_AT_INFINITY); goto err; - } - + } if ((ctx = BN_CTX_new()) == NULL) goto err; if ((point = EC_POINT_new(eckey->group)) == NULL) goto err; /* testing whether the pub_key is on the elliptic curve */ - if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx)) - { + if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } + } /* testing whether pub_key * order is the point at infinity */ order = &eckey->group->order; - if (BN_is_zero(order)) - { + if (BN_is_zero(order)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER); goto err; - } - if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) - { + } + if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB); goto err; - } - if (!EC_POINT_is_at_infinity(eckey->group, point)) - { + } + if (!EC_POINT_is_at_infinity(eckey->group, point)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER); goto err; - } - /* in case the priv_key is present : - * check if generator * priv_key == pub_key + } + /* + * in case the priv_key is present : check if generator * priv_key == + * pub_key */ - if (eckey->priv_key) - { - if (BN_cmp(eckey->priv_key, order) >= 0) - { + if (eckey->priv_key) { + if (BN_cmp(eckey->priv_key, order) >= 0) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER); goto err; - } + } if (!EC_POINT_mul(eckey->group, point, eckey->priv_key, - NULL, NULL, ctx)) - { + NULL, NULL, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB); goto err; - } - if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, - ctx) != 0) - { + } + if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, + ctx) != 0) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY); goto err; - } } + } ok = 1; err: - if (ctx != NULL) + if (ctx != NULL) BN_CTX_free(ctx); if (point != NULL) EC_POINT_free(point); - return(ok); - } + return (ok); +} -int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) - { +int +EC_KEY_set_public_key_affine_coordinates(EC_KEY * key, BIGNUM * x, BIGNUM * y) +{ BN_CTX *ctx = NULL; BIGNUM *tx, *ty; EC_POINT *point = NULL; int ok = 0, tmp_nid, is_char_two = 0; - if (!key || !key->group || !x || !y) - { + if (!key || !key->group || !x || !y) { ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, - ERR_R_PASSED_NULL_PARAMETER); + ERR_R_PASSED_NULL_PARAMETER); return 0; - } + } ctx = BN_CTX_new(); if (!ctx) goto err; @@ -376,41 +362,38 @@ int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(key->group)); - if (tmp_nid == NID_X9_62_characteristic_two_field) + if (tmp_nid == NID_X9_62_characteristic_two_field) is_char_two = 1; tx = BN_CTX_get(ctx); ty = BN_CTX_get(ctx); #ifndef OPENSSL_NO_EC2M - if (is_char_two) - { + if (is_char_two) { if (!EC_POINT_set_affine_coordinates_GF2m(key->group, point, - x, y, ctx)) + x, y, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(key->group, point, - tx, ty, ctx)) + tx, ty, ctx)) goto err; - } - else + } else #endif - { + { if (!EC_POINT_set_affine_coordinates_GFp(key->group, point, - x, y, ctx)) + x, y, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GFp(key->group, point, - tx, ty, ctx)) + tx, ty, ctx)) goto err; - } - /* Check if retrieved coordinates match originals: if not values - * are out of range. + } + /* + * Check if retrieved coordinates match originals: if not values are + * out of range. */ - if (BN_cmp(x, tx) || BN_cmp(y, ty)) - { + if (BN_cmp(x, tx) || BN_cmp(y, ty)) { ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, - EC_R_COORDINATES_OUT_OF_RANGE); + EC_R_COORDINATES_OUT_OF_RANGE); goto err; - } - + } if (!EC_KEY_set_public_key(key, point)) goto err; @@ -419,79 +402,92 @@ int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) ok = 1; - err: +err: if (ctx) BN_CTX_free(ctx); if (point) EC_POINT_free(point); return ok; - } +} -const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key) - { +const EC_GROUP * +EC_KEY_get0_group(const EC_KEY * key) +{ return key->group; - } +} -int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group) - { +int +EC_KEY_set_group(EC_KEY * key, const EC_GROUP * group) +{ if (key->group != NULL) EC_GROUP_free(key->group); key->group = EC_GROUP_dup(group); return (key->group == NULL) ? 0 : 1; - } +} -const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key) - { +const BIGNUM * +EC_KEY_get0_private_key(const EC_KEY * key) +{ return key->priv_key; - } +} -int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *priv_key) - { +int +EC_KEY_set_private_key(EC_KEY * key, const BIGNUM * priv_key) +{ if (key->priv_key) BN_clear_free(key->priv_key); key->priv_key = BN_dup(priv_key); return (key->priv_key == NULL) ? 0 : 1; - } +} -const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key) - { +const EC_POINT * +EC_KEY_get0_public_key(const EC_KEY * key) +{ return key->pub_key; - } +} -int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub_key) - { +int +EC_KEY_set_public_key(EC_KEY * key, const EC_POINT * pub_key) +{ if (key->pub_key != NULL) EC_POINT_free(key->pub_key); key->pub_key = EC_POINT_dup(pub_key, key->group); return (key->pub_key == NULL) ? 0 : 1; - } +} -unsigned int EC_KEY_get_enc_flags(const EC_KEY *key) - { +unsigned int +EC_KEY_get_enc_flags(const EC_KEY * key) +{ return key->enc_flag; - } +} -void EC_KEY_set_enc_flags(EC_KEY *key, unsigned int flags) - { +void +EC_KEY_set_enc_flags(EC_KEY * key, unsigned int flags) +{ key->enc_flag = flags; - } +} -point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key) - { +point_conversion_form_t +EC_KEY_get_conv_form(const EC_KEY * key) +{ return key->conv_form; - } +} -void EC_KEY_set_conv_form(EC_KEY *key, point_conversion_form_t cform) - { +void +EC_KEY_set_conv_form(EC_KEY * key, point_conversion_form_t cform) +{ key->conv_form = cform; if (key->group != NULL) EC_GROUP_set_point_conversion_form(key->group, cform); - } - -void *EC_KEY_get_key_method_data(EC_KEY *key, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +} + +void * +EC_KEY_get_key_method_data(EC_KEY *key, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ void *ret; CRYPTO_r_lock(CRYPTO_LOCK_EC); @@ -499,11 +495,14 @@ void *EC_KEY_get_key_method_data(EC_KEY *key, CRYPTO_r_unlock(CRYPTO_LOCK_EC); return ret; - } - -void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +} + +void * +EC_KEY_insert_key_method_data(EC_KEY * key, void *data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA *ex_data; CRYPTO_w_lock(CRYPTO_LOCK_EC); @@ -513,32 +512,37 @@ void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data, CRYPTO_w_unlock(CRYPTO_LOCK_EC); return ex_data; - } +} -void EC_KEY_set_asn1_flag(EC_KEY *key, int flag) - { +void +EC_KEY_set_asn1_flag(EC_KEY * key, int flag) +{ if (key->group != NULL) EC_GROUP_set_asn1_flag(key->group, flag); - } +} -int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx) - { +int +EC_KEY_precompute_mult(EC_KEY * key, BN_CTX * ctx) +{ if (key->group == NULL) return 0; return EC_GROUP_precompute_mult(key->group, ctx); - } +} -int EC_KEY_get_flags(const EC_KEY *key) - { +int +EC_KEY_get_flags(const EC_KEY * key) +{ return key->flags; - } +} -void EC_KEY_set_flags(EC_KEY *key, int flags) - { +void +EC_KEY_set_flags(EC_KEY * key, int flags) +{ key->flags |= flags; - } +} -void EC_KEY_clear_flags(EC_KEY *key, int flags) - { +void +EC_KEY_clear_flags(EC_KEY * key, int flags) +{ key->flags &= ~flags; - } +} diff --git a/lib/libcrypto/ec/ec_lib.c b/lib/libcrypto/ec/ec_lib.c index 546fd08e382..b37efac246a 100644 --- a/lib/libcrypto/ec/ec_lib.c +++ b/lib/libcrypto/ec/ec_lib.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Binary polynomial ECC support in OpenSSL originally developed by + * Binary polynomial ECC support in OpenSSL originally developed by * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. */ @@ -73,28 +73,24 @@ static const char EC_version[] = "EC" OPENSSL_VERSION_PTEXT; /* functions for EC_GROUP objects */ -EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) - { +EC_GROUP * +EC_GROUP_new(const EC_METHOD * meth) +{ EC_GROUP *ret; - if (meth == NULL) - { + if (meth == NULL) { ECerr(EC_F_EC_GROUP_NEW, EC_R_SLOT_FULL); return NULL; - } - if (meth->group_init == 0) - { + } + if (meth->group_init == 0) { ECerr(EC_F_EC_GROUP_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return NULL; - } - + } ret = malloc(sizeof *ret); - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_GROUP_NEW, ERR_R_MALLOC_FAILURE); return NULL; - } - + } ret->meth = meth; ret->extra_data = NULL; @@ -103,26 +99,26 @@ EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) BN_init(&ret->order); BN_init(&ret->cofactor); - ret->curve_name = 0; - ret->asn1_flag = 0; - ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED; + ret->curve_name = 0; + ret->asn1_flag = 0; + ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED; ret->seed = NULL; ret->seed_len = 0; - if (!meth->group_init(ret)) - { + if (!meth->group_init(ret)) { free(ret); return NULL; - } - - return ret; } + return ret; +} -void EC_GROUP_free(EC_GROUP *group) - { - if (!group) return; +void +EC_GROUP_free(EC_GROUP * group) +{ + if (!group) + return; if (group->meth->group_finish != 0) group->meth->group_finish(group); @@ -138,12 +134,14 @@ void EC_GROUP_free(EC_GROUP *group) free(group->seed); free(group); - } - +} + -void EC_GROUP_clear_free(EC_GROUP *group) - { - if (!group) return; +void +EC_GROUP_clear_free(EC_GROUP * group) +{ + if (!group) + return; if (group->meth->group_clear_finish != 0) group->meth->group_clear_finish(group); @@ -157,74 +155,69 @@ void EC_GROUP_clear_free(EC_GROUP *group) BN_clear_free(&group->order); BN_clear_free(&group->cofactor); - if (group->seed) - { + if (group->seed) { OPENSSL_cleanse(group->seed, group->seed_len); free(group->seed); - } - + } OPENSSL_cleanse(group, sizeof *group); free(group); - } +} -int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +EC_GROUP_copy(EC_GROUP * dest, const EC_GROUP * src) +{ EC_EXTRA_DATA *d; - if (dest->meth->group_copy == 0) - { + if (dest->meth->group_copy == 0) { ECerr(EC_F_EC_GROUP_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (dest->meth != src->meth) - { + } + if (dest->meth != src->meth) { ECerr(EC_F_EC_GROUP_COPY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } + } if (dest == src) return 1; - + EC_EX_DATA_free_all_data(&dest->extra_data); - for (d = src->extra_data; d != NULL; d = d->next) - { + for (d = src->extra_data; d != NULL; d = d->next) { void *t = d->dup_func(d->data); - + if (t == NULL) return 0; - if (!EC_EX_DATA_set_data(&dest->extra_data, t, d->dup_func, d->free_func, d->clear_free_func)) + if (!EC_EX_DATA_set_data(&dest->extra_data, t, d->dup_func, + d->free_func, d->clear_free_func)) return 0; - } + } - if (src->generator != NULL) - { - if (dest->generator == NULL) - { + if (src->generator != NULL) { + if (dest->generator == NULL) { dest->generator = EC_POINT_new(dest); - if (dest->generator == NULL) return 0; - } - if (!EC_POINT_copy(dest->generator, src->generator)) return 0; + if (dest->generator == NULL) + return 0; } - else - { + if (!EC_POINT_copy(dest->generator, src->generator)) + return 0; + } else { /* src->generator == NULL */ - if (dest->generator != NULL) - { + if (dest->generator != NULL) { EC_POINT_clear_free(dest->generator); dest->generator = NULL; - } } + } - if (!BN_copy(&dest->order, &src->order)) return 0; - if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0; + if (!BN_copy(&dest->order, &src->order)) + return 0; + if (!BN_copy(&dest->cofactor, &src->cofactor)) + return 0; dest->curve_name = src->curve_name; - dest->asn1_flag = src->asn1_flag; - dest->asn1_form = src->asn1_form; + dest->asn1_flag = src->asn1_flag; + dest->asn1_form = src->asn1_form; - if (src->seed) - { + if (src->seed) { if (dest->seed) free(dest->seed); dest->seed = malloc(src->seed_len); @@ -233,153 +226,168 @@ int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src) if (!memcpy(dest->seed, src->seed, src->seed_len)) return 0; dest->seed_len = src->seed_len; - } - else - { + } else { if (dest->seed) free(dest->seed); dest->seed = NULL; dest->seed_len = 0; - } - + } + return dest->meth->group_copy(dest, src); - } +} -EC_GROUP *EC_GROUP_dup(const EC_GROUP *a) - { +EC_GROUP * +EC_GROUP_dup(const EC_GROUP * a) +{ EC_GROUP *t = NULL; int ok = 0; - if (a == NULL) return NULL; + if (a == NULL) + return NULL; - if ((t = EC_GROUP_new(a->meth)) == NULL) return(NULL); - if (!EC_GROUP_copy(t, a)) goto err; + if ((t = EC_GROUP_new(a->meth)) == NULL) + return (NULL); + if (!EC_GROUP_copy(t, a)) + goto err; ok = 1; - err: - if (!ok) - { - if (t) EC_GROUP_free(t); +err: + if (!ok) { + if (t) + EC_GROUP_free(t); return NULL; - } - else return t; - } + } else + return t; +} -const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group) - { +const EC_METHOD * +EC_GROUP_method_of(const EC_GROUP *group) +{ return group->meth; - } +} -int EC_METHOD_get_field_type(const EC_METHOD *meth) - { - return meth->field_type; - } +int +EC_METHOD_get_field_type(const EC_METHOD *meth) +{ + return meth->field_type; +} -int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor) - { - if (generator == NULL) - { +int +EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, + const BIGNUM *order, const BIGNUM *cofactor) +{ + if (generator == NULL) { ECerr(EC_F_EC_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER); - return 0 ; - } - - if (group->generator == NULL) - { + return 0; + } + if (group->generator == NULL) { group->generator = EC_POINT_new(group); - if (group->generator == NULL) return 0; - } - if (!EC_POINT_copy(group->generator, generator)) return 0; + if (group->generator == NULL) + return 0; + } + if (!EC_POINT_copy(group->generator, generator)) + return 0; - if (order != NULL) - { if (!BN_copy(&group->order, order)) return 0; } - else + if (order != NULL) { + if (!BN_copy(&group->order, order)) + return 0; + } else BN_zero(&group->order); - if (cofactor != NULL) - { if (!BN_copy(&group->cofactor, cofactor)) return 0; } - else + if (cofactor != NULL) { + if (!BN_copy(&group->cofactor, cofactor)) + return 0; + } else BN_zero(&group->cofactor); return 1; - } +} -const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group) - { +const EC_POINT * +EC_GROUP_get0_generator(const EC_GROUP *group) +{ return group->generator; - } +} -int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) - { +int +EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) +{ if (!BN_copy(order, &group->order)) return 0; return !BN_is_zero(order); - } +} -int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx) - { +int +EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx) +{ if (!BN_copy(cofactor, &group->cofactor)) return 0; return !BN_is_zero(&group->cofactor); - } +} -void EC_GROUP_set_curve_name(EC_GROUP *group, int nid) - { +void +EC_GROUP_set_curve_name(EC_GROUP * group, int nid) +{ group->curve_name = nid; - } +} -int EC_GROUP_get_curve_name(const EC_GROUP *group) - { +int +EC_GROUP_get_curve_name(const EC_GROUP * group) +{ return group->curve_name; - } +} -void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag) - { +void +EC_GROUP_set_asn1_flag(EC_GROUP * group, int flag) +{ group->asn1_flag = flag; - } +} -int EC_GROUP_get_asn1_flag(const EC_GROUP *group) - { +int +EC_GROUP_get_asn1_flag(const EC_GROUP * group) +{ return group->asn1_flag; - } +} -void EC_GROUP_set_point_conversion_form(EC_GROUP *group, - point_conversion_form_t form) - { +void +EC_GROUP_set_point_conversion_form(EC_GROUP * group, + point_conversion_form_t form) +{ group->asn1_form = form; - } +} -point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group) - { +point_conversion_form_t +EC_GROUP_get_point_conversion_form(const EC_GROUP * group) +{ return group->asn1_form; - } +} -size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len) - { - if (group->seed) - { +size_t +EC_GROUP_set_seed(EC_GROUP * group, const unsigned char *p, size_t len) +{ + if (group->seed) { free(group->seed); group->seed = NULL; group->seed_len = 0; - } - + } if (!len || !p) return 1; @@ -389,94 +397,101 @@ size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len) group->seed_len = len; return len; - } +} -unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group) - { +unsigned char * +EC_GROUP_get0_seed(const EC_GROUP * group) +{ return group->seed; - } +} -size_t EC_GROUP_get_seed_len(const EC_GROUP *group) - { +size_t +EC_GROUP_get_seed_len(const EC_GROUP * group) +{ return group->seed_len; - } +} -int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_set_curve == 0) - { +int +EC_GROUP_set_curve_GFp(EC_GROUP * group, const BIGNUM * p, const BIGNUM * a, + const BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_set_curve == 0) { ECerr(EC_F_EC_GROUP_SET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_set_curve(group, p, a, b, ctx); } + return group->meth->group_set_curve(group, p, a, b, ctx); +} -int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_get_curve == 0) - { +int +EC_GROUP_get_curve_GFp(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, + BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_get_curve == 0) { ECerr(EC_F_EC_GROUP_GET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_curve(group, p, a, b, ctx); } + return group->meth->group_get_curve(group, p, a, b, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_set_curve == 0) - { +int +EC_GROUP_set_curve_GF2m(EC_GROUP * group, const BIGNUM * p, const BIGNUM * a, + const BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_set_curve == 0) { ECerr(EC_F_EC_GROUP_SET_CURVE_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_set_curve(group, p, a, b, ctx); } + return group->meth->group_set_curve(group, p, a, b, ctx); +} -int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_get_curve == 0) - { +int +EC_GROUP_get_curve_GF2m(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, + BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_get_curve == 0) { ECerr(EC_F_EC_GROUP_GET_CURVE_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_curve(group, p, a, b, ctx); } + return group->meth->group_get_curve(group, p, a, b, ctx); +} #endif -int EC_GROUP_get_degree(const EC_GROUP *group) - { - if (group->meth->group_get_degree == 0) - { +int +EC_GROUP_get_degree(const EC_GROUP * group) +{ + if (group->meth->group_get_degree == 0) { ECerr(EC_F_EC_GROUP_GET_DEGREE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_degree(group); } + return group->meth->group_get_degree(group); +} -int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { - if (group->meth->group_check_discriminant == 0) - { +int +EC_GROUP_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ + if (group->meth->group_check_discriminant == 0) { ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_check_discriminant(group, ctx); } + return group->meth->group_check_discriminant(group, ctx); +} -int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) - { - int r = 0; +int +EC_GROUP_cmp(const EC_GROUP * a, const EC_GROUP * b, BN_CTX * ctx) +{ + int r = 0; BIGNUM *a1, *a2, *a3, *b1, *b2, *b3; BN_CTX *ctx_new = NULL; - /* compare the field types*/ + /* compare the field types */ if (EC_METHOD_get_field_type(EC_GROUP_method_of(a)) != EC_METHOD_get_field_type(EC_GROUP_method_of(b))) return 1; @@ -489,7 +504,7 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) ctx_new = ctx = BN_CTX_new(); if (!ctx) return -1; - + BN_CTX_start(ctx); a1 = BN_CTX_get(ctx); a2 = BN_CTX_get(ctx); @@ -497,16 +512,15 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) b1 = BN_CTX_get(ctx); b2 = BN_CTX_get(ctx); b3 = BN_CTX_get(ctx); - if (!b3) - { + if (!b3) { BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return -1; - } - - /* XXX This approach assumes that the external representation - * of curves over the same field type is the same. + } + /* + * XXX This approach assumes that the external representation of + * curves over the same field type is the same. */ if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) || !b->meth->group_get_curve(b, b1, b2, b3, ctx)) @@ -517,51 +531,50 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) /* XXX EC_POINT_cmp() assumes that the methods are equal */ if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a), - EC_GROUP_get0_generator(b), ctx)) + EC_GROUP_get0_generator(b), ctx)) r = 1; - if (!r) - { + if (!r) { /* compare the order and cofactor */ if (!EC_GROUP_get_order(a, a1, ctx) || !EC_GROUP_get_order(b, b1, ctx) || !EC_GROUP_get_cofactor(a, a2, ctx) || - !EC_GROUP_get_cofactor(b, b2, ctx)) - { + !EC_GROUP_get_cofactor(b, b2, ctx)) { BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return -1; - } + } if (BN_cmp(a1, b1) || BN_cmp(a2, b2)) r = 1; - } - + } BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return r; - } +} /* this has 'package' visibility */ -int EC_EX_DATA_set_data(EC_EXTRA_DATA **ex_data, void *data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +int +EC_EX_DATA_set_data(EC_EXTRA_DATA ** ex_data, void *data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return 0; - for (d = *ex_data; d != NULL; d = d->next) - { - if (d->dup_func == dup_func && d->free_func == free_func && d->clear_free_func == clear_free_func) - { + for (d = *ex_data; d != NULL; d = d->next) { + if (d->dup_func == dup_func && d->free_func == free_func && + d->clear_free_func == clear_free_func) { ECerr(EC_F_EC_EX_DATA_SET_DATA, EC_R_SLOT_FULL); return 0; - } } + } if (data == NULL) /* no explicit entry needed */ @@ -580,163 +593,169 @@ int EC_EX_DATA_set_data(EC_EXTRA_DATA **ex_data, void *data, *ex_data = d; return 1; - } +} /* this has 'package' visibility */ -void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void * +EC_EX_DATA_get_data(const EC_EXTRA_DATA * ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ const EC_EXTRA_DATA *d; - for (d = ex_data; d != NULL; d = d->next) - { + for (d = ex_data; d != NULL; d = d->next) { if (d->dup_func == dup_func && d->free_func == free_func && d->clear_free_func == clear_free_func) return d->data; - } - - return NULL; } + return NULL; +} + /* this has 'package' visibility */ -void EC_EX_DATA_free_data(EC_EXTRA_DATA **ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void +EC_EX_DATA_free_data(EC_EXTRA_DATA ** ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA **p; if (ex_data == NULL) return; - for (p = ex_data; *p != NULL; p = &((*p)->next)) - { - if ((*p)->dup_func == dup_func && (*p)->free_func == free_func && (*p)->clear_free_func == clear_free_func) - { + for (p = ex_data; *p != NULL; p = &((*p)->next)) { + if ((*p)->dup_func == dup_func && + (*p)->free_func == free_func && + (*p)->clear_free_func == clear_free_func) { EC_EXTRA_DATA *next = (*p)->next; (*p)->free_func((*p)->data); free(*p); - + *p = next; return; - } } } +} /* this has 'package' visibility */ -void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void +EC_EX_DATA_clear_free_data(EC_EXTRA_DATA ** ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA **p; if (ex_data == NULL) return; - for (p = ex_data; *p != NULL; p = &((*p)->next)) - { - if ((*p)->dup_func == dup_func && (*p)->free_func == free_func && (*p)->clear_free_func == clear_free_func) - { + for (p = ex_data; *p != NULL; p = &((*p)->next)) { + if ((*p)->dup_func == dup_func && + (*p)->free_func == free_func && + (*p)->clear_free_func == clear_free_func) { EC_EXTRA_DATA *next = (*p)->next; (*p)->clear_free_func((*p)->data); free(*p); - + *p = next; return; - } } } +} /* this has 'package' visibility */ -void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **ex_data) - { +void +EC_EX_DATA_free_all_data(EC_EXTRA_DATA ** ex_data) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return; d = *ex_data; - while (d) - { + while (d) { EC_EXTRA_DATA *next = d->next; - + d->free_func(d->data); free(d); - + d = next; - } - *ex_data = NULL; } + *ex_data = NULL; +} /* this has 'package' visibility */ -void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **ex_data) - { +void +EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA ** ex_data) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return; d = *ex_data; - while (d) - { + while (d) { EC_EXTRA_DATA *next = d->next; - + d->clear_free_func(d->data); free(d); - + d = next; - } - *ex_data = NULL; } + *ex_data = NULL; +} /* functions for EC_POINT objects */ -EC_POINT *EC_POINT_new(const EC_GROUP *group) - { +EC_POINT * +EC_POINT_new(const EC_GROUP * group) +{ EC_POINT *ret; - if (group == NULL) - { + if (group == NULL) { ECerr(EC_F_EC_POINT_NEW, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } - if (group->meth->point_init == 0) - { + } + if (group->meth->point_init == 0) { ECerr(EC_F_EC_POINT_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return NULL; - } - + } ret = malloc(sizeof *ret); - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_POINT_NEW, ERR_R_MALLOC_FAILURE); return NULL; - } - + } ret->meth = group->meth; - - if (!ret->meth->point_init(ret)) - { + + if (!ret->meth->point_init(ret)) { free(ret); return NULL; - } - - return ret; } + return ret; +} -void EC_POINT_free(EC_POINT *point) - { - if (!point) return; +void +EC_POINT_free(EC_POINT * point) +{ + if (!point) + return; if (point->meth->point_finish != 0) point->meth->point_finish(point); free(point); - } - +} -void EC_POINT_clear_free(EC_POINT *point) - { - if (!point) return; + +void +EC_POINT_clear_free(EC_POINT * point) +{ + if (!point) + return; if (point->meth->point_clear_finish != 0) point->meth->point_clear_finish(point); @@ -744,301 +763,290 @@ void EC_POINT_clear_free(EC_POINT *point) point->meth->point_finish(point); OPENSSL_cleanse(point, sizeof *point); free(point); - } +} -int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src) - { - if (dest->meth->point_copy == 0) - { +int +EC_POINT_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (dest->meth->point_copy == 0) { ECerr(EC_F_EC_POINT_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (dest->meth != src->meth) - { + } + if (dest->meth != src->meth) { ECerr(EC_F_EC_POINT_COPY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } + } if (dest == src) return 1; return dest->meth->point_copy(dest, src); - } +} -EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group) - { +EC_POINT * +EC_POINT_dup(const EC_POINT * a, const EC_GROUP * group) +{ EC_POINT *t; int r; - if (a == NULL) return NULL; + if (a == NULL) + return NULL; t = EC_POINT_new(group); - if (t == NULL) return(NULL); + if (t == NULL) + return (NULL); r = EC_POINT_copy(t, a); - if (!r) - { + if (!r) { EC_POINT_free(t); return NULL; - } - else return t; - } + } else + return t; +} -const EC_METHOD *EC_POINT_method_of(const EC_POINT *point) - { +const EC_METHOD * +EC_POINT_method_of(const EC_POINT * point) +{ return point->meth; - } +} -int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { - if (group->meth->point_set_to_infinity == 0) - { +int +EC_POINT_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ + if (group->meth->point_set_to_infinity == 0) { ECerr(EC_F_EC_POINT_SET_TO_INFINITY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_TO_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_to_infinity(group, point); } + return group->meth->point_set_to_infinity(group, point); +} -int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) - { - if (group->meth->point_set_Jprojective_coordinates_GFp == 0) - { +int +EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) +{ + if (group->meth->point_set_Jprojective_coordinates_GFp == 0) { ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); } + return group->meth->point_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); +} -int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) - { - if (group->meth->point_get_Jprojective_coordinates_GFp == 0) - { +int +EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) +{ + if (group->meth->point_get_Jprojective_coordinates_GFp == 0) { ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); } + return group->meth->point_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); +} -int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_set_affine_coordinates == 0) - { +int +EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_set_affine_coordinates == 0) - { +int +EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); +} #endif -int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_get_affine_coordinates == 0) - { +int +EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_get_affine_coordinates == 0) - { +int +EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} #endif -int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - if (group->meth->add == 0) - { +int +EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + if (group->meth->add == 0) { ECerr(EC_F_EC_POINT_ADD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if ((group->meth != r->meth) || (r->meth != a->meth) || (a->meth != b->meth)) - { + } + if ((group->meth != r->meth) || (r->meth != a->meth) || (a->meth != b->meth)) { ECerr(EC_F_EC_POINT_ADD, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->add(group, r, a, b, ctx); } + return group->meth->add(group, r, a, b, ctx); +} -int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { - if (group->meth->dbl == 0) - { +int +EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) +{ + if (group->meth->dbl == 0) { ECerr(EC_F_EC_POINT_DBL, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if ((group->meth != r->meth) || (r->meth != a->meth)) - { + } + if ((group->meth != r->meth) || (r->meth != a->meth)) { ECerr(EC_F_EC_POINT_DBL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->dbl(group, r, a, ctx); } + return group->meth->dbl(group, r, a, ctx); +} -int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) - { - if (group->meth->invert == 0) - { +int +EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) +{ + if (group->meth->invert == 0) { ECerr(EC_F_EC_POINT_INVERT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != a->meth) - { + } + if (group->meth != a->meth) { ECerr(EC_F_EC_POINT_INVERT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->invert(group, a, ctx); } + return group->meth->invert(group, a, ctx); +} -int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { - if (group->meth->is_at_infinity == 0) - { +int +EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ + if (group->meth->is_at_infinity == 0) { ECerr(EC_F_EC_POINT_IS_AT_INFINITY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_IS_AT_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->is_at_infinity(group, point); } + return group->meth->is_at_infinity(group, point); +} -int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { - if (group->meth->is_on_curve == 0) - { +int +EC_POINT_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) +{ + if (group->meth->is_on_curve == 0) { ECerr(EC_F_EC_POINT_IS_ON_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_IS_ON_CURVE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->is_on_curve(group, point, ctx); } + return group->meth->is_on_curve(group, point, ctx); +} -int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - if (group->meth->point_cmp == 0) - { +int +EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, + BN_CTX * ctx) +{ + if (group->meth->point_cmp == 0) { ECerr(EC_F_EC_POINT_CMP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; - } - if ((group->meth != a->meth) || (a->meth != b->meth)) - { + } + if ((group->meth != a->meth) || (a->meth != b->meth)) { ECerr(EC_F_EC_POINT_CMP, EC_R_INCOMPATIBLE_OBJECTS); return -1; - } - return group->meth->point_cmp(group, a, b, ctx); } + return group->meth->point_cmp(group, a, b, ctx); +} -int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { - if (group->meth->make_affine == 0) - { +int +EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ + if (group->meth->make_affine == 0) { ECerr(EC_F_EC_POINT_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->make_affine(group, point, ctx); } + return group->meth->make_affine(group, point, ctx); +} -int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], + BN_CTX *ctx) +{ size_t i; - if (group->meth->points_make_affine == 0) - { + if (group->meth->points_make_affine == 0) { ECerr(EC_F_EC_POINTS_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - for (i = 0; i < num; i++) - { - if (group->meth != points[i]->meth) - { + } + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { ECerr(EC_F_EC_POINTS_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } } - return group->meth->points_make_affine(group, num, points, ctx); } + return group->meth->points_make_affine(group, num, points, ctx); +} /* Functions for point multiplication. @@ -1047,19 +1055,21 @@ int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], * otherwise we dispatch through methods. */ -int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); return group->meth->mul(group, r, scalar, num, points, scalars, ctx); - } +} -int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, - const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) - { +int +EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, + const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) +{ /* just a convenient interface to EC_POINTs_mul() */ const EC_POINT *points[1]; @@ -1068,11 +1078,14 @@ int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, points[0] = point; scalars[0] = p_scalar; - return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx); - } + return EC_POINTs_mul(group, r, g_scalar, + (point != NULL && p_scalar != NULL), + points, scalars, ctx); +} -int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +EC_GROUP_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_precompute_mult(group, ctx); @@ -1080,11 +1093,12 @@ int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (group->meth->precompute_mult != 0) return group->meth->precompute_mult(group, ctx); else - return 1; /* nothing to do, so report success */ - } + return 1; /* nothing to do, so report success */ +} -int EC_GROUP_have_precompute_mult(const EC_GROUP *group) - { +int +EC_GROUP_have_precompute_mult(const EC_GROUP * group) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_have_precompute_mult(group); @@ -1092,5 +1106,6 @@ int EC_GROUP_have_precompute_mult(const EC_GROUP *group) if (group->meth->have_precompute_mult != 0) return group->meth->have_precompute_mult(group); else - return 0; /* cannot tell whether precomputation has been performed */ - } + return 0; /* cannot tell whether precomputation has + * been performed */ +} diff --git a/lib/libcrypto/ec/ec_mult.c b/lib/libcrypto/ec/ec_mult.c index b48c888048b..c0525c49406 100644 --- a/lib/libcrypto/ec/ec_mult.c +++ b/lib/libcrypto/ec/ec_mult.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -80,46 +80,49 @@ /* structure for precomputed multiples of the generator */ typedef struct ec_pre_comp_st { - const EC_GROUP *group; /* parent EC_GROUP object */ - size_t blocksize; /* block size for wNAF splitting */ - size_t numblocks; /* max. number of blocks for which we have precomputation */ - size_t w; /* window size */ - EC_POINT **points; /* array with pre-calculated multiples of generator: - * 'num' pointers to EC_POINT objects followed by a NULL */ - size_t num; /* numblocks * 2^(w-1) */ + const EC_GROUP *group; /* parent EC_GROUP object */ + size_t blocksize; /* block size for wNAF splitting */ + size_t numblocks; /* max. number of blocks for which we have + * precomputation */ + size_t w; /* window size */ + EC_POINT **points; /* array with pre-calculated multiples of + * generator: 'num' pointers to EC_POINT + * objects followed by a NULL */ + size_t num; /* numblocks * 2^(w-1) */ int references; } EC_PRE_COMP; - + /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ static void *ec_pre_comp_dup(void *); static void ec_pre_comp_free(void *); static void ec_pre_comp_clear_free(void *); -static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) - { +static EC_PRE_COMP * +ec_pre_comp_new(const EC_GROUP * group) +{ EC_PRE_COMP *ret = NULL; if (!group) return NULL; - ret = (EC_PRE_COMP *)malloc(sizeof(EC_PRE_COMP)); - if (!ret) - { + ret = (EC_PRE_COMP *) malloc(sizeof(EC_PRE_COMP)); + if (!ret) { ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } ret->group = group; - ret->blocksize = 8; /* default */ + ret->blocksize = 8; /* default */ ret->numblocks = 0; - ret->w = 4; /* default */ + ret->w = 4; /* default */ ret->points = NULL; ret->num = 0; ret->references = 1; return ret; - } +} -static void *ec_pre_comp_dup(void *src_) - { +static void * +ec_pre_comp_dup(void *src_) +{ EC_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ @@ -127,10 +130,11 @@ static void *ec_pre_comp_dup(void *src_) CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void ec_pre_comp_free(void *pre_) - { +static void +ec_pre_comp_free(void *pre_) +{ int i; EC_PRE_COMP *pre = pre_; @@ -141,19 +145,19 @@ static void ec_pre_comp_free(void *pre_) if (i > 0) return; - if (pre->points) - { + if (pre->points) { EC_POINT **p; for (p = pre->points; *p != NULL; p++) EC_POINT_free(*p); free(pre->points); - } - free(pre); } + free(pre); +} -static void ec_pre_comp_clear_free(void *pre_) - { +static void +ec_pre_comp_clear_free(void *pre_) +{ int i; EC_PRE_COMP *pre = pre_; @@ -164,20 +168,18 @@ static void ec_pre_comp_clear_free(void *pre_) if (i > 0) return; - if (pre->points) - { + if (pre->points) { EC_POINT **p; - for (p = pre->points; *p != NULL; p++) - { + for (p = pre->points; *p != NULL; p++) { EC_POINT_clear_free(*p); OPENSSL_cleanse(p, sizeof *p); - } - free(pre->points); } + free(pre->points); + } OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} @@ -190,138 +192,125 @@ static void ec_pre_comp_clear_free(void *pre_) * with the exception that the most significant digit may be only * w-1 zeros away from that next non-zero digit. */ -static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) - { +static signed char * +compute_wNAF(const BIGNUM * scalar, int w, size_t * ret_len) +{ int window_val; int ok = 0; signed char *r = NULL; int sign = 1; int bit, next_bit, mask; size_t len = 0, j; - - if (BN_is_zero(scalar)) - { + + if (BN_is_zero(scalar)) { r = malloc(1); - if (!r) - { + if (!r) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); goto err; - } + } r[0] = 0; *ret_len = 1; return r; - } - - if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ - { + } + if (w <= 0 || w > 7) { + /* 'signed char' can represent integers with + * absolute values less than 2^7 */ ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - bit = 1 << w; /* at most 128 */ - next_bit = bit << 1; /* at most 256 */ - mask = next_bit - 1; /* at most 255 */ + } + bit = 1 << w; /* at most 128 */ + next_bit = bit << 1; /* at most 256 */ + mask = next_bit - 1; /* at most 255 */ - if (BN_is_negative(scalar)) - { + if (BN_is_negative(scalar)) { sign = -1; - } - - if (scalar->d == NULL || scalar->top == 0) - { + } + if (scalar->d == NULL || scalar->top == 0) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - + } len = BN_num_bits(scalar); - r = malloc(len + 1); /* modified wNAF may be one digit longer than binary representation - * (*ret_len will be set to the actual length, i.e. at most - * BN_num_bits(scalar) + 1) */ - if (r == NULL) - { + r = malloc(len + 1); /* modified wNAF may be one digit longer than + * binary representation (*ret_len will be + * set to the actual length, i.e. at most + * BN_num_bits(scalar) + 1) */ + if (r == NULL) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); goto err; - } + } window_val = scalar->d[0] & mask; j = 0; - while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ - { + while ((window_val != 0) || (j + w + 1 < len)) { + /* if j+w+1 >= len, window_val will not increase */ int digit = 0; /* 0 <= window_val <= 2^(w+1) */ - - if (window_val & 1) - { + if (window_val & 1) { /* 0 < window_val < 2^(w+1) */ - - if (window_val & bit) - { - digit = window_val - next_bit; /* -2^w < digit < 0 */ - -#if 1 /* modified wNAF */ - if (j + w + 1 >= len) - { - /* special case for generating modified wNAFs: - * no new bits will be added into window_val, - * so using a positive digit here will decrease - * the total length of the representation */ - - digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ - } -#endif - } - else - { - digit = window_val; /* 0 < digit < 2^w */ + if (window_val & bit) { + digit = window_val - next_bit; /* -2^w < digit < 0 */ + +#if 1 /* modified wNAF */ + if (j + w + 1 >= len) { + /* + * special case for generating + * modified wNAFs: no new bits will + * be added into window_val, so using + * a positive digit here will + * decrease the total length of the + * representation + */ + + digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ } - - if (digit <= -bit || digit >= bit || !(digit & 1)) - { +#endif + } else { + digit = window_val; /* 0 < digit < 2^w */ + } + + if (digit <= -bit || digit >= bit || !(digit & 1)) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - + } window_val -= digit; - /* now window_val is 0 or 2^(w+1) in standard wNAF generation; - * for modified window NAFs, it may also be 2^w + /* + * now window_val is 0 or 2^(w+1) in standard wNAF + * generation; for modified window NAFs, it may also + * be 2^w */ - if (window_val != 0 && window_val != next_bit && window_val != bit) - { + if (window_val != 0 && window_val != next_bit && window_val != bit) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } } - + } r[j++] = sign * digit; window_val >>= 1; window_val += bit * BN_is_bit_set(scalar, j + w); - if (window_val > next_bit) - { + if (window_val > next_bit) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } } + } - if (j > len + 1) - { + if (j > len + 1) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } + } len = j; ok = 1; - err: - if (!ok) - { +err: + if (!ok) { free(r); r = NULL; - } + } if (ok) *ret_len = len; return r; - } +} /* TODO: table should be optimised for the wNAF-based implementation, @@ -343,374 +332,353 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) * scalar*generator * in the addition if scalar != NULL */ -int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_wNAF_mul(const EC_GROUP * group, EC_POINT * r, const BIGNUM * scalar, + size_t num, const EC_POINT * points[], const BIGNUM * scalars[], BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; const EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t totalnum; - size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ + size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ size_t pre_points_per_block = 0; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; - size_t *wsize = NULL; /* individual window sizes */ - signed char **wNAF = NULL; /* individual wNAFs */ + size_t *wsize = NULL; /* individual window sizes */ + signed char **wNAF = NULL; /* individual wNAFs */ size_t *wNAF_len = NULL; size_t max_len = 0; size_t num_val; - EC_POINT **val = NULL; /* precomputation */ + EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; - EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */ + EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or + * 'pre_comp->points' */ const EC_PRE_COMP *pre_comp = NULL; - int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars, - * i.e. precomputation is not available */ + int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be + * treated like other scalars, i.e. + * precomputation is not available */ int ret = 0; - - if (group->meth != r->meth) - { + + if (group->meth != r->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - - if ((scalar == NULL) && (num == 0)) - { + } + if ((scalar == NULL) && (num == 0)) { return EC_POINT_set_to_infinity(group, r); - } - - for (i = 0; i < num; i++) - { - if (group->meth != points[i]->meth) - { + } + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } } + } - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; - } - - if (scalar != NULL) - { + } + if (scalar != NULL) { generator = EC_GROUP_get0_generator(group); - if (generator == NULL) - { + if (generator == NULL) { ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); goto err; - } - + } /* look if we can use precomputed multiples of generator */ pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); - if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) - { + if (pre_comp && pre_comp->numblocks && + (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) { blocksize = pre_comp->blocksize; - /* determine maximum number of blocks that wNAF splitting may yield - * (NB: maximum wNAF length is bit length plus one) */ + /* + * determine maximum number of blocks that wNAF + * splitting may yield (NB: maximum wNAF length is + * bit length plus one) + */ numblocks = (BN_num_bits(scalar) / blocksize) + 1; - /* we cannot use more blocks than we have precomputation for */ + /* + * we cannot use more blocks than we have + * precomputation for + */ if (numblocks > pre_comp->numblocks) numblocks = pre_comp->numblocks; - pre_points_per_block = (size_t)1 << (pre_comp->w - 1); + pre_points_per_block = (size_t) 1 << (pre_comp->w - 1); /* check that pre_comp looks sane */ - if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) - { + if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } } - else - { + } else { /* can't use precomputation */ pre_comp = NULL; numblocks = 1; - num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */ - } + num_scalar = 1; /* treat 'scalar' like 'num'-th + * element of 'scalars' */ } - + } totalnum = num + numblocks; - wsize = malloc(totalnum * sizeof wsize[0]); + wsize = malloc(totalnum * sizeof wsize[0]); wNAF_len = malloc(totalnum * sizeof wNAF_len[0]); - wNAF = malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */ - val_sub = malloc(totalnum * sizeof val_sub[0]); - - if (!wsize || !wNAF_len || !wNAF || !val_sub) - { + wNAF = malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for + * pivot */ + val_sub = malloc(totalnum * sizeof val_sub[0]); + + if (!wsize || !wNAF_len || !wNAF || !val_sub) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - wNAF[0] = NULL; /* preliminary pivot */ + } + wNAF[0] = NULL; /* preliminary pivot */ /* num_val will be the total number of temporarily precomputed points */ num_val = 0; - for (i = 0; i < num + num_scalar; i++) - { + for (i = 0; i < num + num_scalar; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); - num_val += (size_t)1 << (wsize[i] - 1); - wNAF[i + 1] = NULL; /* make sure we always have a pivot */ + num_val += (size_t) 1 << (wsize[i] - 1); + wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); if (wNAF[i] == NULL) goto err; if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; - } + } - if (numblocks) - { + if (numblocks) { /* we go here iff scalar != NULL */ - - if (pre_comp == NULL) - { - if (num_scalar != 1) - { + + if (pre_comp == NULL) { + if (num_scalar != 1) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - /* we have already generated a wNAF for 'scalar' */ } - else - { + /* we have already generated a wNAF for 'scalar' */ + } else { signed char *tmp_wNAF = NULL; size_t tmp_len = 0; - - if (num_scalar != 0) - { + + if (num_scalar != 0) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - - /* use the window size for which we have precomputation */ + } + /* + * use the window size for which we have + * precomputation + */ wsize[num] = pre_comp->w; tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); if (!tmp_wNAF) goto err; - if (tmp_len <= max_len) - { - /* One of the other wNAFs is at least as long - * as the wNAF belonging to the generator, - * so wNAF splitting will not buy us anything. */ + if (tmp_len <= max_len) { + /* + * One of the other wNAFs is at least as long + * as the wNAF belonging to the generator, so + * wNAF splitting will not buy us anything. + */ numblocks = 1; - totalnum = num + 1; /* don't use wNAF splitting */ + totalnum = num + 1; /* don't use wNAF + * splitting */ wNAF[num] = tmp_wNAF; wNAF[num + 1] = NULL; wNAF_len[num] = tmp_len; if (tmp_len > max_len) max_len = tmp_len; - /* pre_comp->points starts with the points that we need here: */ + /* + * pre_comp->points starts with the points + * that we need here: + */ val_sub[num] = pre_comp->points; - } - else - { - /* don't include tmp_wNAF directly into wNAF array - * - use wNAF splitting and include the blocks */ + } else { + /* + * don't include tmp_wNAF directly into wNAF + * array - use wNAF splitting and include the + * blocks + */ signed char *pp; EC_POINT **tmp_points; - - if (tmp_len < numblocks * blocksize) - { - /* possibly we can do with fewer blocks than estimated */ + + if (tmp_len < numblocks * blocksize) { + /* + * possibly we can do with fewer + * blocks than estimated + */ numblocks = (tmp_len + blocksize - 1) / blocksize; - if (numblocks > pre_comp->numblocks) - { + if (numblocks > pre_comp->numblocks) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - totalnum = num + numblocks; } - + totalnum = num + numblocks; + } /* split wNAF in 'numblocks' parts */ pp = tmp_wNAF; tmp_points = pre_comp->points; - for (i = num; i < totalnum; i++) - { - if (i < totalnum - 1) - { + for (i = num; i < totalnum; i++) { + if (i < totalnum - 1) { wNAF_len[i] = blocksize; - if (tmp_len < blocksize) - { + if (tmp_len < blocksize) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - tmp_len -= blocksize; } - else - /* last block gets whatever is left - * (this could be more or less than 'blocksize'!) */ + tmp_len -= blocksize; + } else + /* + * last block gets whatever + * is left (this could be + * more or less than + * 'blocksize'!) + */ wNAF_len[i] = tmp_len; - + wNAF[i + 1] = NULL; wNAF[i] = malloc(wNAF_len[i]); - if (wNAF[i] == NULL) - { + if (wNAF[i] == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); free(tmp_wNAF); goto err; - } + } memcpy(wNAF[i], pp, wNAF_len[i]); if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; - if (*tmp_points == NULL) - { + if (*tmp_points == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); free(tmp_wNAF); goto err; - } + } val_sub[i] = tmp_points; tmp_points += pre_points_per_block; pp += blocksize; - } - free(tmp_wNAF); } + free(tmp_wNAF); } } - - /* All points we precompute now go into a single array 'val'. - * 'val_sub[i]' is a pointer to the subarray for the i-th point, - * or to a subarray of 'pre_comp->points' if we already have precomputation. */ + } + /* + * All points we precompute now go into a single array 'val'. + * 'val_sub[i]' is a pointer to the subarray for the i-th point, or + * to a subarray of 'pre_comp->points' if we already have + * precomputation. + */ val = malloc((num_val + 1) * sizeof val[0]); - if (val == NULL) - { + if (val == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - val[num_val] = NULL; /* pivot element */ + } + val[num_val] = NULL; /* pivot element */ /* allocate points for precomputation */ v = val; - for (i = 0; i < num + num_scalar; i++) - { + for (i = 0; i < num + num_scalar; i++) { val_sub[i] = v; - for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) - { + for (j = 0; j < ((size_t) 1 << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); - if (*v == NULL) goto err; + if (*v == NULL) + goto err; v++; - } } - if (!(v == val + num_val)) - { + } + if (!(v == val + num_val)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - + } if (!(tmp = EC_POINT_new(group))) goto err; - /* prepare precomputed values: - * val_sub[i][0] := points[i] - * val_sub[i][1] := 3 * points[i] - * val_sub[i][2] := 5 * points[i] - * ... + /* + * prepare precomputed values: val_sub[i][0] := points[i] + * val_sub[i][1] := 3 * points[i] val_sub[i][2] := 5 * points[i] ... */ - for (i = 0; i < num + num_scalar; i++) - { - if (i < num) - { - if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; - } - else - { - if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; - } + for (i = 0; i < num + num_scalar; i++) { + if (i < num) { + if (!EC_POINT_copy(val_sub[i][0], points[i])) + goto err; + } else { + if (!EC_POINT_copy(val_sub[i][0], generator)) + goto err; + } - if (wsize[i] > 1) - { - if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; - for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) - { - if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; - } + if (wsize[i] > 1) { + if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) + goto err; + for (j = 1; j < ((size_t) 1 << (wsize[i] - 1)); j++) { + if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) + goto err; } } + } -#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ +#if 1 /* optional; EC_window_bits_for_scalar_size + * assumes we do this step */ if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; #endif r_is_at_infinity = 1; - for (k = max_len - 1; k >= 0; k--) - { - if (!r_is_at_infinity) - { - if (!EC_POINT_dbl(group, r, r, ctx)) goto err; - } - - for (i = 0; i < totalnum; i++) - { - if (wNAF_len[i] > (size_t)k) - { + for (k = max_len - 1; k >= 0; k--) { + if (!r_is_at_infinity) { + if (!EC_POINT_dbl(group, r, r, ctx)) + goto err; + } + for (i = 0; i < totalnum; i++) { + if (wNAF_len[i] > (size_t) k) { int digit = wNAF[i][k]; int is_neg; - if (digit) - { + if (digit) { is_neg = digit < 0; if (is_neg) digit = -digit; - if (is_neg != r_is_inverted) - { - if (!r_is_at_infinity) - { - if (!EC_POINT_invert(group, r, ctx)) goto err; - } - r_is_inverted = !r_is_inverted; + if (is_neg != r_is_inverted) { + if (!r_is_at_infinity) { + if (!EC_POINT_invert(group, r, ctx)) + goto err; } - + r_is_inverted = !r_is_inverted; + } /* digit > 0 */ - if (r_is_at_infinity) - { - if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; + if (r_is_at_infinity) { + if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) + goto err; r_is_at_infinity = 0; - } - else - { - if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; - } + } else { + if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) + goto err; } } } } + } - if (r_is_at_infinity) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; - } - else - { + if (r_is_at_infinity) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { if (r_is_inverted) - if (!EC_POINT_invert(group, r, ctx)) goto err; - } - + if (!EC_POINT_invert(group, r, ctx)) + goto err; + } + ret = 1; - err: +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (tmp != NULL) @@ -719,34 +687,31 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, free(wsize); if (wNAF_len != NULL) free(wNAF_len); - if (wNAF != NULL) - { + if (wNAF != NULL) { signed char **w; - + for (w = wNAF; *w != NULL; w++) free(*w); - + free(wNAF); - } - if (val != NULL) - { + } + if (val != NULL) { for (v = val; *v != NULL; v++) EC_POINT_clear_free(*v); free(val); - } - if (val_sub != NULL) - { + } + if (val_sub != NULL) { free(val_sub); - } - return ret; } + return ret; +} /* ec_wNAF_precompute_mult() * creates an EC_PRE_COMP object with preprecomputed multiples of the generator * for use with wNAF splitting as implemented in ec_wNAF_mul(). - * + * * 'pre_comp->points' is an array of multiples of the generator * of the following form: * points[0] = generator; @@ -762,13 +727,15 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator * points[2^(w-1)*numblocks] = NULL */ -int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_wNAF_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ const EC_POINT *generator; EC_POINT *tmp_point = NULL, *base = NULL, **var; BN_CTX *new_ctx = NULL; BIGNUM *order; - size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; + size_t i, bits, w, pre_points_per_block, blocksize, numblocks, + num; EC_POINT **points = NULL; EC_PRE_COMP *pre_comp; int ret = 0; @@ -780,81 +747,72 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) return 0; generator = EC_GROUP_get0_generator(group); - if (generator == NULL) - { + if (generator == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; - } - + } BN_CTX_start(ctx); order = BN_CTX_get(ctx); - if (order == NULL) goto err; - - if (!EC_GROUP_get_order(group, order, ctx)) goto err; - if (BN_is_zero(order)) - { - ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); + if (order == NULL) goto err; - } + if (!EC_GROUP_get_order(group, order, ctx)) + goto err; + if (BN_is_zero(order)) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); + goto err; + } bits = BN_num_bits(order); - /* The following parameters mean we precompute (approximately) - * one point per bit. - * - * TBD: The combination 8, 4 is perfect for 160 bits; for other - * bit lengths, other parameter combinations might provide better + /* + * The following parameters mean we precompute (approximately) one + * point per bit. + * + * TBD: The combination 8, 4 is perfect for 160 bits; for other bit + * lengths, other parameter combinations might provide better * efficiency. */ blocksize = 8; w = 4; - if (EC_window_bits_for_scalar_size(bits) > w) - { + if (EC_window_bits_for_scalar_size(bits) > w) { /* let's not make the window too small ... */ w = EC_window_bits_for_scalar_size(bits); - } + } + numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks + * to use for wNAF + * splitting */ - numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ - - pre_points_per_block = (size_t)1 << (w - 1); - num = pre_points_per_block * numblocks; /* number of points to compute and store */ + pre_points_per_block = (size_t) 1 << (w - 1); + num = pre_points_per_block * numblocks; /* number of points to + * compute and store */ - points = malloc(sizeof (EC_POINT*)*(num + 1)); - if (!points) - { + points = malloc(sizeof(EC_POINT *) * (num + 1)); + if (!points) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } - + } var = points; - var[num] = NULL; /* pivot */ - for (i = 0; i < num; i++) - { - if ((var[i] = EC_POINT_new(group)) == NULL) - { + var[num] = NULL; /* pivot */ + for (i = 0; i < num; i++) { + if ((var[i] = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } } + } - if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) - { + if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } - + } if (!EC_POINT_copy(base, generator)) goto err; - + /* do the precomputation */ - for (i = 0; i < numblocks; i++) - { + for (i = 0; i < numblocks; i++) { size_t j; if (!EC_POINT_dbl(group, tmp_point, base, ctx)) @@ -863,37 +821,35 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (!EC_POINT_copy(*var++, base)) goto err; - for (j = 1; j < pre_points_per_block; j++, var++) - { + for (j = 1; j < pre_points_per_block; j++, var++) { /* calculate odd multiples of the current base point */ if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) goto err; - } + } - if (i < numblocks - 1) - { - /* get the next base (multiply current one by 2^blocksize) */ + if (i < numblocks - 1) { + /* + * get the next base (multiply current one by + * 2^blocksize) + */ size_t k; - if (blocksize <= 2) - { + if (blocksize <= 2) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); goto err; - } - + } if (!EC_POINT_dbl(group, base, tmp_point, ctx)) goto err; - for (k = 2; k < blocksize; k++) - { - if (!EC_POINT_dbl(group,base,base,ctx)) + for (k = 2; k < blocksize; k++) { + if (!EC_POINT_dbl(group, base, base, ctx)) goto err; - } } - } + } + } if (!EC_POINTs_make_affine(group, num, points, ctx)) goto err; - + pre_comp->group = group; pre_comp->blocksize = blocksize; pre_comp->numblocks = numblocks; @@ -908,33 +864,33 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) pre_comp = NULL; ret = 1; - err: +err: if (ctx != NULL) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); if (pre_comp) ec_pre_comp_free(pre_comp); - if (points) - { + if (points) { EC_POINT **p; for (p = points; *p != NULL; p++) EC_POINT_free(*p); free(points); - } + } if (tmp_point) EC_POINT_free(tmp_point); if (base) EC_POINT_free(base); return ret; - } +} -int ec_wNAF_have_precompute_mult(const EC_GROUP *group) - { +int +ec_wNAF_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) return 1; else return 0; - } +} diff --git a/lib/libcrypto/ec/ec_oct.c b/lib/libcrypto/ec/ec_oct.c index fd9db0798d3..e0fb62fee2f 100644 --- a/lib/libcrypto/ec/ec_oct.c +++ b/lib/libcrypto/ec/ec_oct.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Binary polynomial ECC support in OpenSSL originally developed by + * Binary polynomial ECC support in OpenSSL originally developed by * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. */ @@ -68,132 +68,123 @@ #include "ec_lcl.h" -int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { +int +EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, int y_bit, BN_CTX * ctx) +{ if (group->meth->point_set_compressed_coordinates == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); #endif - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { +int +EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, int y_bit, BN_CTX * ctx) +{ if (group->meth->point_set_compressed_coordinates == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); else return ec_GF2m_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); +} #endif -size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) +{ if (group->meth->point2oct == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_point2oct(group, point, - form, buf, len, ctx); + form, buf, len, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_point2oct(group, point, - form, buf, len, ctx); + form, buf, len, ctx); #endif - } - - return group->meth->point2oct(group, point, form, buf, len, ctx); } + return group->meth->point2oct(group, point, form, buf, len, ctx); +} -int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->oct2point == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { +int +EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ + if (group->meth->oct2point == 0 && + !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_oct2point(group, point, - buf, len, ctx); + buf, len, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_oct2point(group, point, - buf, len, ctx); + buf, len, ctx); #endif - } - return group->meth->oct2point(group, point, buf, len, ctx); } - + return group->meth->oct2point(group, point, buf, len, ctx); +} diff --git a/lib/libcrypto/ec/ec_pmeth.c b/lib/libcrypto/ec/ec_pmeth.c index c970d8c9ca2..28f501070c5 100644 --- a/lib/libcrypto/ec/ec_pmeth.c +++ b/lib/libcrypto/ec/ec_pmeth.c @@ -9,7 +9,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -66,16 +66,16 @@ /* EC pkey context structure */ -typedef struct - { +typedef struct { /* Key and paramgen group */ EC_GROUP *gen_group; /* message digest */ const EVP_MD *md; - } EC_PKEY_CTX; +} EC_PKEY_CTX; -static int pkey_ec_init(EVP_PKEY_CTX *ctx) - { +static int +pkey_ec_init(EVP_PKEY_CTX * ctx) +{ EC_PKEY_CTX *dctx; dctx = malloc(sizeof(EC_PKEY_CTX)); if (!dctx) @@ -86,55 +86,52 @@ static int pkey_ec_init(EVP_PKEY_CTX *ctx) ctx->data = dctx; return 1; - } +} -static int pkey_ec_copy(EVP_PKEY_CTX *dst, EVP_PKEY_CTX *src) - { +static int +pkey_ec_copy(EVP_PKEY_CTX * dst, EVP_PKEY_CTX * src) +{ EC_PKEY_CTX *dctx, *sctx; if (!pkey_ec_init(dst)) return 0; - sctx = src->data; + sctx = src->data; dctx = dst->data; - if (sctx->gen_group) - { + if (sctx->gen_group) { dctx->gen_group = EC_GROUP_dup(sctx->gen_group); if (!dctx->gen_group) return 0; - } + } dctx->md = sctx->md; return 1; - } +} -static void pkey_ec_cleanup(EVP_PKEY_CTX *ctx) - { +static void +pkey_ec_cleanup(EVP_PKEY_CTX * ctx) +{ EC_PKEY_CTX *dctx = ctx->data; - if (dctx) - { + if (dctx) { if (dctx->gen_group) EC_GROUP_free(dctx->gen_group); free(dctx); - } } +} -static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, - const unsigned char *tbs, size_t tbslen) - { +static int +pkey_ec_sign(EVP_PKEY_CTX * ctx, unsigned char *sig, size_t * siglen, + const unsigned char *tbs, size_t tbslen) +{ int ret, type; unsigned int sltmp; EC_PKEY_CTX *dctx = ctx->data; EC_KEY *ec = ctx->pkey->pkey.ec; - if (!sig) - { + if (!sig) { *siglen = ECDSA_size(ec); return 1; - } - else if(*siglen < (size_t)ECDSA_size(ec)) - { + } else if (*siglen < (size_t) ECDSA_size(ec)) { ECerr(EC_F_PKEY_EC_SIGN, EC_R_BUFFER_TOO_SMALL); return 0; - } - + } if (dctx->md) type = EVP_MD_type(dctx->md); else @@ -145,14 +142,15 @@ static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, if (ret <= 0) return ret; - *siglen = (size_t)sltmp; + *siglen = (size_t) sltmp; return 1; - } +} -static int pkey_ec_verify(EVP_PKEY_CTX *ctx, - const unsigned char *sig, size_t siglen, - const unsigned char *tbs, size_t tbslen) - { +static int +pkey_ec_verify(EVP_PKEY_CTX * ctx, + const unsigned char *sig, size_t siglen, + const unsigned char *tbs, size_t tbslen) +{ int ret, type; EC_PKEY_CTX *dctx = ctx->data; EC_KEY *ec = ctx->pkey->pkey.ec; @@ -165,116 +163,111 @@ static int pkey_ec_verify(EVP_PKEY_CTX *ctx, ret = ECDSA_verify(type, tbs, tbslen, sig, siglen, ec); return ret; - } +} -static int pkey_ec_derive(EVP_PKEY_CTX *ctx, unsigned char *key, size_t *keylen) - { +static int +pkey_ec_derive(EVP_PKEY_CTX * ctx, unsigned char *key, size_t * keylen) +{ int ret; size_t outlen; const EC_POINT *pubkey = NULL; - if (!ctx->pkey || !ctx->peerkey) - { + if (!ctx->pkey || !ctx->peerkey) { ECerr(EC_F_PKEY_EC_DERIVE, EC_R_KEYS_NOT_SET); return 0; - } - - if (!key) - { + } + if (!key) { const EC_GROUP *group; group = EC_KEY_get0_group(ctx->pkey->pkey.ec); - *keylen = (EC_GROUP_get_degree(group) + 7)/8; + *keylen = (EC_GROUP_get_degree(group) + 7) / 8; return 1; - } - + } pubkey = EC_KEY_get0_public_key(ctx->peerkey->pkey.ec); - /* NB: unlike PKCS#3 DH, if *outlen is less than maximum size this is + /* + * NB: unlike PKCS#3 DH, if *outlen is less than maximum size this is * not an error, the result is truncated. */ outlen = *keylen; - + ret = ECDH_compute_key(key, outlen, pubkey, ctx->pkey->pkey.ec, 0); if (ret < 0) return ret; *keylen = ret; return 1; - } +} -static int pkey_ec_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) - { +static int +pkey_ec_ctrl(EVP_PKEY_CTX * ctx, int type, int p1, void *p2) +{ EC_PKEY_CTX *dctx = ctx->data; EC_GROUP *group; - switch (type) - { - case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: + switch (type) { + case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: group = EC_GROUP_new_by_curve_name(p1); - if (group == NULL) - { + if (group == NULL) { ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_CURVE); return 0; - } + } if (dctx->gen_group) EC_GROUP_free(dctx->gen_group); dctx->gen_group = group; return 1; - case EVP_PKEY_CTRL_MD: - if (EVP_MD_type((const EVP_MD *)p2) != NID_sha1 && - EVP_MD_type((const EVP_MD *)p2) != NID_ecdsa_with_SHA1 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha224 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha256 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha384 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha512) - { + case EVP_PKEY_CTRL_MD: + if (EVP_MD_type((const EVP_MD *) p2) != NID_sha1 && + EVP_MD_type((const EVP_MD *) p2) != NID_ecdsa_with_SHA1 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha224 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha256 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha384 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha512) { ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_DIGEST_TYPE); return 0; - } + } dctx->md = p2; return 1; - case EVP_PKEY_CTRL_PEER_KEY: + case EVP_PKEY_CTRL_PEER_KEY: /* Default behaviour is OK */ - case EVP_PKEY_CTRL_DIGESTINIT: - case EVP_PKEY_CTRL_PKCS7_SIGN: - case EVP_PKEY_CTRL_CMS_SIGN: + case EVP_PKEY_CTRL_DIGESTINIT: + case EVP_PKEY_CTRL_PKCS7_SIGN: + case EVP_PKEY_CTRL_CMS_SIGN: return 1; - default: + default: return -2; - } } - -static int pkey_ec_ctrl_str(EVP_PKEY_CTX *ctx, - const char *type, const char *value) - { - if (!strcmp(type, "ec_paramgen_curve")) - { +} + +static int +pkey_ec_ctrl_str(EVP_PKEY_CTX * ctx, + const char *type, const char *value) +{ + if (!strcmp(type, "ec_paramgen_curve")) { int nid; nid = OBJ_sn2nid(value); if (nid == NID_undef) nid = OBJ_ln2nid(value); - if (nid == NID_undef) - { + if (nid == NID_undef) { ECerr(EC_F_PKEY_EC_CTRL_STR, EC_R_INVALID_CURVE); return 0; - } - return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); } - return -2; + return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); } + return -2; +} -static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) - { +static int +pkey_ec_paramgen(EVP_PKEY_CTX * ctx, EVP_PKEY * pkey) +{ EC_KEY *ec = NULL; EC_PKEY_CTX *dctx = ctx->data; int ret = 0; - if (dctx->gen_group == NULL) - { + if (dctx->gen_group == NULL) { ECerr(EC_F_PKEY_EC_PARAMGEN, EC_R_NO_PARAMETERS_SET); return 0; - } + } ec = EC_KEY_new(); if (!ec) return 0; @@ -284,16 +277,16 @@ static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) else EC_KEY_free(ec); return ret; - } +} -static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) - { +static int +pkey_ec_keygen(EVP_PKEY_CTX * ctx, EVP_PKEY * pkey) +{ EC_KEY *ec = NULL; - if (ctx->pkey == NULL) - { + if (ctx->pkey == NULL) { ECerr(EC_F_PKEY_EC_KEYGEN, EC_R_NO_PARAMETERS_SET); return 0; - } + } ec = EC_KEY_new(); if (!ec) return 0; @@ -302,7 +295,7 @@ static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) if (!EVP_PKEY_copy_parameters(pkey, ctx->pkey)) return 0; return EC_KEY_generate_key(pkey->pkey.ec); - } +} const EVP_PKEY_METHOD ec_pkey_meth = { .pkey_id = EVP_PKEY_EC, diff --git a/lib/libcrypto/ec/ec_print.c b/lib/libcrypto/ec/ec_print.c index 1655332c3c5..84a78903b38 100644 --- a/lib/libcrypto/ec/ec_print.c +++ b/lib/libcrypto/ec/ec_print.c @@ -7,7 +7,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -56,29 +56,25 @@ #include #include "ec_lcl.h" -BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, - const EC_POINT *point, - point_conversion_form_t form, - BIGNUM *ret, - BN_CTX *ctx) - { - size_t buf_len=0; +BIGNUM * +EC_POINT_point2bn(const EC_GROUP * group, const EC_POINT * point, + point_conversion_form_t form, BIGNUM * ret, BN_CTX * ctx) +{ + size_t buf_len = 0; unsigned char *buf; buf_len = EC_POINT_point2oct(group, point, form, - NULL, 0, ctx); + NULL, 0, ctx); if (buf_len == 0) return NULL; if ((buf = malloc(buf_len)) == NULL) return NULL; - if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) - { + if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) { free(buf); return NULL; - } - + } ret = BN_bin2bn(buf, buf_len, ret); free(buf); @@ -86,103 +82,90 @@ BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, return ret; } -EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, - const BIGNUM *bn, - EC_POINT *point, - BN_CTX *ctx) - { - size_t buf_len=0; +EC_POINT * +EC_POINT_bn2point(const EC_GROUP * group, + const BIGNUM * bn, EC_POINT * point, BN_CTX * ctx) +{ + size_t buf_len = 0; unsigned char *buf; - EC_POINT *ret; + EC_POINT *ret; - if ((buf_len = BN_num_bytes(bn)) == 0) return NULL; + if ((buf_len = BN_num_bytes(bn)) == 0) + return NULL; buf = malloc(buf_len); if (buf == NULL) return NULL; - if (!BN_bn2bin(bn, buf)) - { + if (!BN_bn2bin(bn, buf)) { free(buf); return NULL; - } - - if (point == NULL) - { - if ((ret = EC_POINT_new(group)) == NULL) - { + } + if (point == NULL) { + if ((ret = EC_POINT_new(group)) == NULL) { free(buf); return NULL; - } } - else + } else ret = point; - if (!EC_POINT_oct2point(group, ret, buf, buf_len, ctx)) - { + if (!EC_POINT_oct2point(group, ret, buf, buf_len, ctx)) { if (point == NULL) EC_POINT_clear_free(ret); free(buf); return NULL; - } - + } free(buf); return ret; - } +} static const char *HEX_DIGITS = "0123456789ABCDEF"; /* the return value must be freed (using free()) */ -char *EC_POINT_point2hex(const EC_GROUP *group, - const EC_POINT *point, - point_conversion_form_t form, - BN_CTX *ctx) - { - char *ret, *p; - size_t buf_len=0,i; +char * +EC_POINT_point2hex(const EC_GROUP * group, const EC_POINT * point, + point_conversion_form_t form, BN_CTX * ctx) +{ + char *ret, *p; + size_t buf_len = 0, i; unsigned char *buf, *pbuf; buf_len = EC_POINT_point2oct(group, point, form, - NULL, 0, ctx); + NULL, 0, ctx); if (buf_len == 0) return NULL; if ((buf = malloc(buf_len)) == NULL) return NULL; - if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) - { + if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) { free(buf); return NULL; - } - - ret = (char *)malloc(buf_len*2+2); - if (ret == NULL) - { + } + ret = (char *) malloc(buf_len * 2 + 2); + if (ret == NULL) { free(buf); return NULL; - } + } p = ret; pbuf = buf; - for (i=buf_len; i > 0; i--) - { - int v = (int) *(pbuf++); - *(p++)=HEX_DIGITS[v>>4]; - *(p++)=HEX_DIGITS[v&0x0F]; - } - *p='\0'; + for (i = buf_len; i > 0; i--) { + int v = (int) *(pbuf++); + *(p++) = HEX_DIGITS[v >> 4]; + *(p++) = HEX_DIGITS[v & 0x0F]; + } + *p = '\0'; free(buf); return ret; - } +} -EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, - const char *buf, - EC_POINT *point, - BN_CTX *ctx) - { - EC_POINT *ret=NULL; - BIGNUM *tmp_bn=NULL; +EC_POINT * +EC_POINT_hex2point(const EC_GROUP * group, const char *buf, + EC_POINT * point, BN_CTX * ctx) +{ + EC_POINT *ret = NULL; + BIGNUM *tmp_bn = NULL; if (!BN_hex2bn(&tmp_bn, buf)) return NULL; @@ -192,4 +175,4 @@ EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, BN_clear_free(tmp_bn); return ret; - } +} diff --git a/lib/libcrypto/ec/eck_prn.c b/lib/libcrypto/ec/eck_prn.c index 4e8c748bbc0..86107d51424 100644 --- a/lib/libcrypto/ec/eck_prn.c +++ b/lib/libcrypto/ec/eck_prn.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Portions originally developed by SUN MICROSYSTEMS, INC., and + * Portions originally developed by SUN MICROSYSTEMS, INC., and * contributed to the OpenSSL project. */ @@ -68,113 +68,112 @@ #include #ifndef OPENSSL_NO_FP_API -int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off) - { +int +ECPKParameters_print_fp(FILE * fp, const EC_GROUP * x, int off) +{ BIO *b; int ret; - if ((b=BIO_new(BIO_s_file())) == NULL) - { - ECerr(EC_F_ECPKPARAMETERS_PRINT_FP,ERR_R_BUF_LIB); - return(0); - } + if ((b = BIO_new(BIO_s_file())) == NULL) { + ECerr(EC_F_ECPKPARAMETERS_PRINT_FP, ERR_R_BUF_LIB); + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = ECPKParameters_print(b, x, off); BIO_free(b); - return(ret); - } + return (ret); +} -int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off) - { +int +EC_KEY_print_fp(FILE * fp, const EC_KEY * x, int off) +{ BIO *b; int ret; - - if ((b=BIO_new(BIO_s_file())) == NULL) - { + + if ((b = BIO_new(BIO_s_file())) == NULL) { ECerr(EC_F_EC_KEY_PRINT_FP, ERR_R_BIO_LIB); - return(0); - } + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = EC_KEY_print(b, x, off); BIO_free(b); - return(ret); - } + return (ret); +} -int ECParameters_print_fp(FILE *fp, const EC_KEY *x) - { +int +ECParameters_print_fp(FILE * fp, const EC_KEY * x) +{ BIO *b; int ret; - - if ((b=BIO_new(BIO_s_file())) == NULL) - { + + if ((b = BIO_new(BIO_s_file())) == NULL) { ECerr(EC_F_ECPARAMETERS_PRINT_FP, ERR_R_BIO_LIB); - return(0); - } + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = ECParameters_print(b, x); BIO_free(b); - return(ret); - } + return (ret); +} #endif -int EC_KEY_print(BIO *bp, const EC_KEY *x, int off) - { +int +EC_KEY_print(BIO * bp, const EC_KEY * x, int off) +{ EVP_PKEY *pk; int ret; pk = EVP_PKEY_new(); - if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *) x)) return 0; ret = EVP_PKEY_print_private(bp, pk, off, NULL); EVP_PKEY_free(pk); return ret; - } +} -int ECParameters_print(BIO *bp, const EC_KEY *x) - { +int +ECParameters_print(BIO * bp, const EC_KEY * x) +{ EVP_PKEY *pk; int ret; pk = EVP_PKEY_new(); - if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *) x)) return 0; ret = EVP_PKEY_print_params(bp, pk, 4, NULL); EVP_PKEY_free(pk); return ret; - } - -static int print_bin(BIO *fp, const char *str, const unsigned char *num, - size_t len, int off); - -int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) - { - unsigned char *buffer=NULL; - size_t buf_len=0, i; - int ret=0, reason=ERR_R_BIO_LIB; - BN_CTX *ctx=NULL; - const EC_POINT *point=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *gen=NULL, - *order=NULL, *cofactor=NULL; +} + +static int +print_bin(BIO * fp, const char *str, const unsigned char *num, + size_t len, int off); + +int +ECPKParameters_print(BIO * bp, const EC_GROUP * x, int off) +{ + unsigned char *buffer = NULL; + size_t buf_len = 0, i; + int ret = 0, reason = ERR_R_BIO_LIB; + BN_CTX *ctx = NULL; + const EC_POINT *point = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *gen = NULL, *order = NULL, + *cofactor = NULL; const unsigned char *seed; - size_t seed_len=0; - + size_t seed_len = 0; + static const char *gen_compressed = "Generator (compressed):"; static const char *gen_uncompressed = "Generator (uncompressed):"; static const char *gen_hybrid = "Generator (hybrid):"; - - if (!x) - { + + if (!x) { reason = ERR_R_PASSED_NULL_PARAMETER; goto err; - } - + } ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - - if (EC_GROUP_get_asn1_flag(x)) - { + } + if (EC_GROUP_get_asn1_flag(x)) { /* the curve parameter are given by an asn1 OID */ int nid; @@ -189,9 +188,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) goto err; if (BIO_printf(bp, "\n") <= 0) goto err; - } - else - { + } else { /* explicit parameters */ int is_char_two = 0; point_conversion_form_t form; @@ -201,84 +198,71 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) is_char_two = 1; if ((p = BN_new()) == NULL || (a = BN_new()) == NULL || - (b = BN_new()) == NULL || (order = BN_new()) == NULL || - (cofactor = BN_new()) == NULL) - { + (b = BN_new()) == NULL || (order = BN_new()) == NULL || + (cofactor = BN_new()) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } + } #ifndef OPENSSL_NO_EC2M - if (is_char_two) - { - if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) - { + if (is_char_two) { + if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) { reason = ERR_R_EC_LIB; goto err; - } } - else /* prime field */ + } else /* prime field */ #endif - { - if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) - { + { + if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) { reason = ERR_R_EC_LIB; goto err; - } } + } - if ((point = EC_GROUP_get0_generator(x)) == NULL) - { + if ((point = EC_GROUP_get0_generator(x)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - if (!EC_GROUP_get_order(x, order, NULL) || - !EC_GROUP_get_cofactor(x, cofactor, NULL)) - { + } + if (!EC_GROUP_get_order(x, order, NULL) || + !EC_GROUP_get_cofactor(x, cofactor, NULL)) { reason = ERR_R_EC_LIB; goto err; - } - + } form = EC_GROUP_get_point_conversion_form(x); - if ((gen = EC_POINT_point2bn(x, point, - form, NULL, ctx)) == NULL) - { + if ((gen = EC_POINT_point2bn(x, point, + form, NULL, ctx)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - - buf_len = (size_t)BN_num_bytes(p); - if (buf_len < (i = (size_t)BN_num_bytes(a))) + } + buf_len = (size_t) BN_num_bytes(p); + if (buf_len < (i = (size_t) BN_num_bytes(a))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(b))) + if (buf_len < (i = (size_t) BN_num_bytes(b))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(gen))) + if (buf_len < (i = (size_t) BN_num_bytes(gen))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(order))) + if (buf_len < (i = (size_t) BN_num_bytes(order))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(cofactor))) + if (buf_len < (i = (size_t) BN_num_bytes(cofactor))) buf_len = i; if ((seed = EC_GROUP_get0_seed(x)) != NULL) seed_len = EC_GROUP_get_seed_len(x); buf_len += 10; - if ((buffer = malloc(buf_len)) == NULL) - { + if ((buffer = malloc(buf_len)) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - + } if (!BIO_indent(bp, off, 128)) goto err; /* print the 'short name' of the field type */ if (BIO_printf(bp, "Field Type: %s\n", OBJ_nid2sn(tmp_nid)) - <= 0) - goto err; + <= 0) + goto err; - if (is_char_two) - { + if (is_char_two) { /* print the 'short name' of the base type OID */ int basis_type = EC_GROUP_get_basis_type(x); if (basis_type == 0) @@ -287,7 +271,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) if (!BIO_indent(bp, off, 128)) goto err; - if (BIO_printf(bp, "Basis Type: %s\n", + if (BIO_printf(bp, "Basis Type: %s\n", OBJ_nid2sn(basis_type)) <= 0) goto err; @@ -295,48 +279,43 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) if ((p != NULL) && !ASN1_bn_print(bp, "Polynomial:", p, buffer, off)) goto err; - } - else - { - if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, buffer,off)) + } else { + if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, buffer, off)) goto err; - } - if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, buffer, off)) + } + if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, buffer, off)) goto err; if ((b != NULL) && !ASN1_bn_print(bp, "B: ", b, buffer, off)) goto err; - if (form == POINT_CONVERSION_COMPRESSED) - { + if (form == POINT_CONVERSION_COMPRESSED) { if ((gen != NULL) && !ASN1_bn_print(bp, gen_compressed, gen, buffer, off)) goto err; - } - else if (form == POINT_CONVERSION_UNCOMPRESSED) - { + } else if (form == POINT_CONVERSION_UNCOMPRESSED) { if ((gen != NULL) && !ASN1_bn_print(bp, gen_uncompressed, gen, buffer, off)) goto err; - } - else /* form == POINT_CONVERSION_HYBRID */ - { + } else { /* form == POINT_CONVERSION_HYBRID */ if ((gen != NULL) && !ASN1_bn_print(bp, gen_hybrid, gen, buffer, off)) goto err; - } - if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, - buffer, off)) goto err; - if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, - buffer, off)) goto err; + } + if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, + buffer, off)) + goto err; + if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, + buffer, off)) + goto err; if (seed && !print_bin(bp, "Seed:", seed, seed_len, off)) goto err; - } - ret=1; + } + ret = 1; err: if (!ret) - ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); - if (p) + ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); + if (p) BN_free(p); - if (a) + if (a) BN_free(a); if (b) BN_free(b); @@ -348,45 +327,42 @@ err: BN_free(cofactor); if (ctx) BN_CTX_free(ctx); - if (buffer != NULL) + if (buffer != NULL) free(buffer); - return(ret); - } + return (ret); +} -static int print_bin(BIO *fp, const char *name, const unsigned char *buf, - size_t len, int off) - { +static int +print_bin(BIO * fp, const char *name, const unsigned char *buf, + size_t len, int off) +{ size_t i; char str[128]; if (buf == NULL) return 1; - if (off) - { + if (off) { if (off > 128) - off=128; - memset(str,' ',off); + off = 128; + memset(str, ' ', off); if (BIO_write(fp, str, off) <= 0) return 0; - } - - if (BIO_printf(fp,"%s", name) <= 0) + } + if (BIO_printf(fp, "%s", name) <= 0) return 0; - for (i=0; ifield_data1 = NULL; group->field_data2 = NULL; return ok; - } +} -void ec_GFp_mont_group_finish(EC_GROUP *group) - { - if (group->field_data1 != NULL) - { +void +ec_GFp_mont_group_finish(EC_GROUP * group) +{ + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_free(group->field_data2); group->field_data2 = NULL; - } - ec_GFp_simple_group_finish(group); } + ec_GFp_simple_group_finish(group); +} -void ec_GFp_mont_group_clear_finish(EC_GROUP *group) - { - if (group->field_data1 != NULL) - { +void +ec_GFp_mont_group_clear_finish(EC_GROUP * group) +{ + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_clear_free(group->field_data2); group->field_data2 = NULL; - } - ec_GFp_simple_group_clear_finish(group); } + ec_GFp_simple_group_clear_finish(group); +} -int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { - if (dest->field_data1 != NULL) - { +int +ec_GFp_mont_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ + if (dest->field_data1 != NULL) { BN_MONT_CTX_free(dest->field_data1); dest->field_data1 = NULL; - } - if (dest->field_data2 != NULL) - { + } + if (dest->field_data2 != NULL) { BN_clear_free(dest->field_data2); dest->field_data2 = NULL; - } - - if (!ec_GFp_simple_group_copy(dest, src)) return 0; + } + if (!ec_GFp_simple_group_copy(dest, src)) + return 0; - if (src->field_data1 != NULL) - { + if (src->field_data1 != NULL) { dest->field_data1 = BN_MONT_CTX_new(); - if (dest->field_data1 == NULL) return 0; - if (!BN_MONT_CTX_copy(dest->field_data1, src->field_data1)) goto err; - } - if (src->field_data2 != NULL) - { + if (dest->field_data1 == NULL) + return 0; + if (!BN_MONT_CTX_copy(dest->field_data1, src->field_data1)) + goto err; + } + if (src->field_data2 != NULL) { dest->field_data2 = BN_dup(src->field_data2); - if (dest->field_data2 == NULL) goto err; - } - + if (dest->field_data2 == NULL) + goto err; + } return 1; - err: - if (dest->field_data1 != NULL) - { +err: + if (dest->field_data1 != NULL) { BN_MONT_CTX_free(dest->field_data1); dest->field_data1 = NULL; - } - return 0; } + return 0; +} -int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BN_MONT_CTX *mont = NULL; BIGNUM *one = NULL; int ret = 0; - if (group->field_data1 != NULL) - { + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_free(group->field_data2); group->field_data2 = NULL; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } mont = BN_MONT_CTX_new(); - if (mont == NULL) goto err; - if (!BN_MONT_CTX_set(mont, p, ctx)) - { + if (mont == NULL) + goto err; + if (!BN_MONT_CTX_set(mont, p, ctx)) { ECerr(EC_F_EC_GFP_MONT_GROUP_SET_CURVE, ERR_R_BN_LIB); goto err; - } + } one = BN_new(); - if (one == NULL) goto err; - if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) goto err; + if (one == NULL) + goto err; + if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) + goto err; group->field_data1 = mont; mont = NULL; @@ -238,79 +234,77 @@ int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM * ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); - if (!ret) - { + if (!ret) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; BN_free(group->field_data2); group->field_data2 = NULL; - } - - err: + } +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (mont != NULL) BN_MONT_CTX_free(mont); return ret; - } +} -int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_MUL, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_mod_mul_montgomery(r, a, b, group->field_data1, ctx); } + return BN_mod_mul_montgomery(r, a, b, group->field_data1, ctx); +} -int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_SQR, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_mod_mul_montgomery(r, a, a, group->field_data1, ctx); } + return BN_mod_mul_montgomery(r, a, a, group->field_data1, ctx); +} -int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_ENCODE, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_to_montgomery(r, a, (BN_MONT_CTX *)group->field_data1, ctx); } + return BN_to_montgomery(r, a, (BN_MONT_CTX *) group->field_data1, ctx); +} -int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_DECODE, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_from_montgomery(r, a, group->field_data1, ctx); } + return BN_from_montgomery(r, a, group->field_data1, ctx); +} -int ec_GFp_mont_field_set_to_one(const EC_GROUP *group, BIGNUM *r, BN_CTX *ctx) - { - if (group->field_data2 == NULL) - { +int +ec_GFp_mont_field_set_to_one(const EC_GROUP *group, BIGNUM *r, BN_CTX *ctx) +{ + if (group->field_data2 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE, EC_R_NOT_INITIALIZED); return 0; - } - - if (!BN_copy(r, group->field_data2)) return 0; - return 1; } + if (!BN_copy(r, group->field_data2)) + return 0; + return 1; +} diff --git a/lib/libcrypto/ec/ecp_nist.c b/lib/libcrypto/ec/ecp_nist.c index 479cff8fc93..60c4a2d790c 100644 --- a/lib/libcrypto/ec/ecp_nist.c +++ b/lib/libcrypto/ec/ecp_nist.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -81,20 +81,20 @@ EC_GFp_nist_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_simple_point_get_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -110,25 +110,29 @@ EC_GFp_nist_method(void) return &ret; } -int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +ec_GFp_nist_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ dest->field_mod_func = src->field_mod_func; return ec_GFp_simple_group_copy(dest, src); - } +} -int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_bn; - + if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); - if ((tmp_bn = BN_CTX_get(ctx)) == NULL) goto err; + if ((tmp_bn = BN_CTX_get(ctx)) == NULL) + goto err; if (BN_ucmp(BN_get0_nist_prime_192(), p) == 0) group->field_mod_func = BN_nist_mod_192; @@ -140,69 +144,72 @@ int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, group->field_mod_func = BN_nist_mod_384; else if (BN_ucmp(BN_get0_nist_prime_521(), p) == 0) group->field_mod_func = BN_nist_mod_521; - else - { + else { ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_NIST_PRIME); goto err; - } + } ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - const BIGNUM *b, BN_CTX *ctx) - { - int ret=0; - BN_CTX *ctx_new=NULL; +int +ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; - if (!group || !r || !a || !b) - { + if (!group || !r || !a || !b) { ECerr(EC_F_EC_GFP_NIST_FIELD_MUL, ERR_R_PASSED_NULL_PARAMETER); goto err; - } + } if (!ctx) - if ((ctx_new = ctx = BN_CTX_new()) == NULL) goto err; + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; - if (!BN_mul(r, a, b, ctx)) goto err; + if (!BN_mul(r, a, b, ctx)) + goto err; if (!group->field_mod_func(r, r, &group->field, ctx)) goto err; - ret=1; + ret = 1; err: if (ctx_new) BN_CTX_free(ctx_new); return ret; - } +} -int ec_GFp_nist_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - BN_CTX *ctx) - { - int ret=0; - BN_CTX *ctx_new=NULL; +int +ec_GFp_nist_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, + BN_CTX * ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; - if (!group || !r || !a) - { + if (!group || !r || !a) { ECerr(EC_F_EC_GFP_NIST_FIELD_SQR, EC_R_PASSED_NULL_PARAMETER); goto err; - } + } if (!ctx) - if ((ctx_new = ctx = BN_CTX_new()) == NULL) goto err; + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; - if (!BN_sqr(r, a, ctx)) goto err; + if (!BN_sqr(r, a, ctx)) + goto err; if (!group->field_mod_func(r, r, &group->field, ctx)) goto err; - ret=1; + ret = 1; err: if (ctx_new) BN_CTX_free(ctx_new); return ret; - } +} diff --git a/lib/libcrypto/ec/ecp_nistp224.c b/lib/libcrypto/ec/ecp_nistp224.c index 696024a5495..057670cf048 100644 --- a/lib/libcrypto/ec/ecp_nistp224.c +++ b/lib/libcrypto/ec/ecp_nistp224.c @@ -280,37 +280,40 @@ EC_GFp_nistp224_method(void) } /* Helper functions to convert field elements to/from internal representation */ -static void bin28_to_felem(felem out, const u8 in[28]) - { - out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; - out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; - out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; - out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; - } +static void +bin28_to_felem(felem out, const u8 in[28]) +{ + out[0] = *((const uint64_t *) (in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *) (in + 7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *) (in + 14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *) (in + 21))) & 0x00ffffffffffffff; +} -static void felem_to_bin28(u8 out[28], const felem in) - { +static void +felem_to_bin28(u8 out[28], const felem in) +{ unsigned i; - for (i = 0; i < 7; ++i) - { - out[i] = in[0]>>(8*i); - out[i+7] = in[1]>>(8*i); - out[i+14] = in[2]>>(8*i); - out[i+21] = in[3]>>(8*i); - } + for (i = 0; i < 7; ++i) { + out[i] = in[0] >> (8 * i); + out[i + 7] = in[1] >> (8 * i); + out[i + 14] = in[2] >> (8 * i); + out[i + 21] = in[3] >> (8 * i); } +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* From OpenSSL BIGNUM to internal representation */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -318,30 +321,29 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin28_to_felem(out, b_out); return 1; - } +} /* From internal representation to OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { +static BIGNUM * +felem_to_BN(BIGNUM * out, const felem in) +{ felem_bytearray b_in, b_out; felem_to_bin28(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /******************************************************************************/ /* FIELD OPERATIONS @@ -353,55 +355,60 @@ static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) * */ -static void felem_one(felem out) - { +static void +felem_one(felem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; out[3] = 0; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* Sum two field elements: out += in */ -static void felem_sum(felem out, const felem in) - { +static void +felem_sum(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* Get negative value: out = -in */ /* Assumes in[i] < 2^57 */ -static void felem_neg(felem out, const felem in) - { +static void +felem_neg(felem out, const felem in) +{ static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); + (((limb) 1) << 42) - (((limb) 1) << 2); /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ out[0] = two58p2 - in[0]; out[1] = two58m42m2 - in[1]; out[2] = two58m2 - in[2]; out[3] = two58m2 - in[3]; - } +} /* Subtract field elements: out -= in */ /* Assumes in[i] < 2^57 */ -static void felem_diff(felem out, const felem in) - { +static void +felem_diff(felem out, const felem in) +{ static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); + (((limb) 1) << 42) - (((limb) 1) << 2); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two58p2; @@ -413,17 +420,18 @@ static void felem_diff(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* Subtract in unreduced 128-bit mode: out -= in */ /* Assumes in[i] < 2^119 */ -static void widefelem_diff(widefelem out, const widefelem in) - { +static void +widefelem_diff(widefelem out, const widefelem in) +{ static const widelimb two120 = ((widelimb) 1) << 120; static const widelimb two120m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 64); + (((widelimb) 1) << 64); static const widelimb two120m104m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two120; @@ -441,18 +449,19 @@ static void widefelem_diff(widefelem out, const widefelem in) out[4] -= in[4]; out[5] -= in[5]; out[6] -= in[6]; - } +} /* Subtract in mixed mode: out128 -= in64 */ /* in[i] < 2^63 */ -static void felem_diff_128_64(widefelem out, const felem in) - { +static void +felem_diff_128_64(widefelem out, const felem in) +{ static const widelimb two64p8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 8); + (((widelimb) 1) << 8); static const widelimb two64m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 8); + (((widelimb) 1) << 8); static const widelimb two64m48m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two64p8; @@ -464,22 +473,24 @@ static void felem_diff_128_64(widefelem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* Multiply a field element by a scalar: out = out * scalar * The scalars we actually use are small, so results fit without overflow */ -static void felem_scalar(felem out, const limb scalar) - { +static void +felem_scalar(felem out, const limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; out[3] *= scalar; - } +} /* Multiply an unreduced field element by a scalar: out = out * scalar * The scalars we actually use are small, so results fit without overflow */ -static void widefelem_scalar(widefelem out, const widelimb scalar) - { +static void +widefelem_scalar(widefelem out, const widelimb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -487,49 +498,54 @@ static void widefelem_scalar(widefelem out, const widelimb scalar) out[4] *= scalar; out[5] *= scalar; out[6] *= scalar; - } +} /* Square a field element: out = in^2 */ -static void felem_square(widefelem out, const felem in) - { +static void +felem_square(widefelem out, const felem in) +{ limb tmp0, tmp1, tmp2; - tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; + tmp0 = 2 * in[0]; + tmp1 = 2 * in[1]; + tmp2 = 2 * in[2]; out[0] = ((widelimb) in[0]) * in[0]; out[1] = ((widelimb) in[0]) * tmp1; out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; out[3] = ((widelimb) in[3]) * tmp0 + - ((widelimb) in[1]) * tmp2; + ((widelimb) in[1]) * tmp2; out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; out[5] = ((widelimb) in[3]) * tmp2; out[6] = ((widelimb) in[3]) * in[3]; - } +} /* Multiply two field elements: out = in1 * in2 */ -static void felem_mul(widefelem out, const felem in1, const felem in2) - { +static void +felem_mul(widefelem out, const felem in1, const felem in2) +{ out[0] = ((widelimb) in1[0]) * in2[0]; out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + - ((widelimb) in1[2]) * in2[0]; + ((widelimb) in1[2]) * in2[0]; out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + - ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + - ((widelimb) in1[3]) * in2[1]; + ((widelimb) in1[3]) * in2[1]; out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; out[6] = ((widelimb) in1[3]) * in2[3]; - } +} /* Reduce seven 128-bit coefficients to four 64-bit coefficients. * Requires in[i] < 2^126, * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ -static void felem_reduce(felem out, const widefelem in) - { +static void +felem_reduce(felem out, const widefelem in) +{ static const widelimb two127p15 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 15); + (((widelimb) 1) << 15); static const widelimb two127m71 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71); + (((widelimb) 1) << 71); static const widelimb two127m71m55 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); widelimb output[5]; /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ @@ -578,30 +594,34 @@ static void felem_reduce(felem out, const widefelem in) /* output[3] <= 2^56 + 2^16 */ out[2] = output[2] & 0x00ffffffffffffff; - /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, - * out[3] <= 2^56 + 2^16 (due to final carry), - * so out < 2*p */ + /* + * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 + * (due to final carry), so out < 2*p + */ out[3] = output[3]; - } +} -static void felem_square_reduce(felem out, const felem in) - { +static void +felem_square_reduce(felem out, const felem in) +{ widefelem tmp; felem_square(tmp, in); felem_reduce(out, tmp); - } +} -static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { +static void +felem_mul_reduce(felem out, const felem in1, const felem in2) +{ widefelem tmp; felem_mul(tmp, in1, in2); felem_reduce(out, tmp); - } +} /* Reduce to unique minimal representation. * Requires 0 <= in < 2*p (always call felem_reduce first) */ -static void felem_contract(felem out, const felem in) - { +static void +felem_contract(felem out, const felem in) +{ static const int64_t two56 = ((limb) 1) << 56; /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ @@ -615,21 +635,25 @@ static void felem_contract(felem out, const felem in) tmp[0] -= a; tmp[1] += a << 40; tmp[3] &= 0x00ffffffffffffff; - /* Case 2: a = 0 iff p <= in < 2^224, i.e., - * the high 128 bits are all 1 and the lower part is non-zero */ + /* + * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all + * 1 and the lower part is non-zero + */ a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | - (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); a &= 0x00ffffffffffffff; /* turn a into an all-one mask (if a = 0) or an all-zero mask */ a = (a - 1) >> 63; - /* subtract 2^224 - 2^96 + 1 if a is all-one*/ + /* subtract 2^224 - 2^96 + 1 if a is all-one */ tmp[3] &= a ^ 0xffffffffffffffff; tmp[2] &= a ^ 0xffffffffffffffff; tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; tmp[0] -= 1 & a; - /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must - * be non-zero, so we only need one step */ + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] + * must be non-zero, so we only need one step + */ a = tmp[0] >> 63; tmp[0] += two56 & a; tmp[1] -= 1 & a; @@ -646,107 +670,131 @@ static void felem_contract(felem out, const felem in) out[1] = tmp[1]; out[2] = tmp[2]; out[3] = tmp[3]; - } +} /* Zero-check: returns 1 if input is 0, and 0 otherwise. * We know that field elements are reduced to in < 2^225, * so we only need to check three cases: 0, 2^224 - 2^96 + 1, * and 2^225 - 2^97 + 2 */ -static limb felem_is_zero(const felem in) - { +static limb +felem_is_zero(const felem in) +{ limb zero, two224m96p1, two225m97p2; zero = in[0] | in[1] | in[2] | in[3]; - zero = (((int64_t)(zero) - 1) >> 63) & 1; + zero = (((int64_t) (zero) - 1) >> 63) & 1; two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); - two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); - two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; return (zero | two224m96p1 | two225m97p2); - } +} -static limb felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +static limb +felem_is_zero_int(const felem in) +{ + return (int) (felem_is_zero(in) & ((limb) 1)); +} /* Invert a field element */ /* Computation chain copied from djb's code */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2, ftmp3, ftmp4; widefelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ - for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ - for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ - for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ - for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ - for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ - for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ - for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ - { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } - felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp);/* 2^6 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); + felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp);/* 2^126 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp);/* 2^127 - 1 */ + for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); } + felem_mul(tmp, ftmp, ftmp3); + felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ +} /* Copy in constant time: * if icopy == 1, copy in to out, * if icopy == 0, copy out to itself. */ static void copy_conditional(felem out, const felem in, limb icopy) - { +{ unsigned i; /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ const limb copy = -icopy; - for (i = 0; i < 4; ++i) - { + for (i = 0; i < 4; ++i) { const limb tmp = copy & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /******************************************************************************/ /* ELLIPTIC CURVE POINT OPERATIONS @@ -766,8 +814,8 @@ copy_conditional(felem out, const felem in, limb icopy) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ widefelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; @@ -833,7 +881,7 @@ point_double(felem x_out, felem y_out, felem z_out, widefelem_diff(tmp, tmp2); /* tmp[i] < 2^119 + 2^120 < 2^121 */ felem_reduce(y_out, tmp); - } +} /* Add two elliptic curve points: * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where @@ -851,16 +899,16 @@ point_double(felem x_out, felem y_out, felem z_out, * (while not equal to the point at infinity). * This case never happens during single point multiplication, * so there is no timing leak for ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; widefelem tmp, tmp2; limb z1_is_zero, z2_is_zero, x_equal, y_equal; - if (!mixed) - { + if (!mixed) { /* ftmp2 = z2^2 */ felem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -876,9 +924,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp2 = z2^2*x1 */ felem_mul(tmp2, ftmp2, x1); felem_reduce(ftmp2, tmp2); - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* ftmp4 = z2^3*y1 */ @@ -886,7 +932,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp2 = z2^2*x1 */ felem_assign(ftmp2, x1); - } + } /* ftmp = z1^2 */ felem_square(tmp, z1); @@ -914,30 +960,27 @@ static void point_add(felem x3, felem y3, felem z3, /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ felem_reduce(ftmp, tmp); - /* the formulae are incorrect if the points are equal - * so we check for this and do doubling if this happens */ + /* + * the formulae are incorrect if the points are equal so we check for + * this and do doubling if this happens + */ x_equal = felem_is_zero(ftmp); y_equal = felem_is_zero(ftmp3); z1_is_zero = felem_is_zero(z1); z2_is_zero = felem_is_zero(z2); /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* ftmp5 = z1*z2 */ - if (!mixed) - { + if (!mixed) { felem_mul(tmp, z1, z2); felem_reduce(ftmp5, tmp); - } - else - { + } else { /* special case z2 = 0 is handled later */ felem_assign(ftmp5, z1); - } + } /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ felem_mul(tmp, ftmp, ftmp5); @@ -973,8 +1016,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar(ftmp5, 2); /* ftmp5[i] < 2 * 2^57 = 2^58 */ - /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - - 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + /* + * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 + */ felem_diff_128_64(tmp2, ftmp5); /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ felem_reduce(x_out, tmp2); @@ -987,14 +1032,18 @@ static void point_add(felem x3, felem y3, felem z3, felem_mul(tmp2, ftmp3, ftmp2); /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ - /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - - z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + /* + * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - + * x_out) - z2^3*y1*(z1^2*x2 - z2^2*x1)^3 + */ widefelem_diff(tmp2, tmp); /* tmp2[i] < 2^118 + 2^120 < 2^121 */ felem_reduce(y_out, tmp2); - /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is - * the point at infinity, so we need to check for this separately */ + /* + * the result (x_out, y_out, z_out) is incorrect if one of the inputs + * is the point at infinity, so we need to check for this separately + */ /* if point 1 is at infinity, copy point 2 to output, and vice versa */ copy_conditional(x_out, x2, z1_is_zero); @@ -1006,18 +1055,18 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) - { +static void +select_point(const u64 idx, unsigned int size, const felem pre_comp[ /* size */ ][3], felem out[3]) +{ unsigned i, j; limb *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(felem)); - for (i = 0; i < size; i++) - { + for (i = 0; i < size; i++) { const limb *inlimbs = &pre_comp[i][0][0]; u64 mask = i ^ idx; mask |= mask >> 4; @@ -1027,26 +1076,28 @@ static void select_point(const u64 idx, unsigned int size, const felem pre_comp[ mask--; for (j = 0; j < 4 * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, unsigned i) - { +static char +get_bit(const felem_bytearray in, unsigned i) +{ if (i >= 224) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) +{ int i, skip; unsigned num; unsigned gen_mul = (g_scalar != NULL); @@ -1057,20 +1108,20 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (two in each of the last 28 rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (two in each of the last 28 rounds) and + * additions of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 220 : 27); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 27)) - { + if (gen_mul && (i <= 27)) { /* first, look 28 bits upwards */ bits = get_bit(g_scalar, i + 196) << 3; bits |= get_bit(g_scalar, i + 140) << 2; @@ -1079,17 +1130,14 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[1], tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } + } /* second, look at the current position */ bits = get_bit(g_scalar, i + 168) << 3; @@ -1099,16 +1147,13 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[0], tmp); point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1119,58 +1164,58 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add or subtract */ select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_conditional(tmp[1], tmp[3], sign); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /******************************************************************************/ /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP224_PRE_COMP *nistp224_pre_comp_new() - { +static NISTP224_PRE_COMP * +nistp224_pre_comp_new() +{ NISTP224_PRE_COMP *ret = NULL; ret = (NISTP224_PRE_COMP *) malloc(sizeof *ret); - if (!ret) - { + if (!ret) { ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp224_pre_comp_dup(void *src_) - { +static void * +nistp224_pre_comp_dup(void *src_) +{ NISTP224_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp224_pre_comp_free(void *pre_) - { +static void +nistp224_pre_comp_free(void *pre_) +{ int i; NISTP224_PRE_COMP *pre = pre_; @@ -1182,10 +1227,11 @@ static void nistp224_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp224_pre_comp_clear_free(void *pre_) - { +static void +nistp224_pre_comp_clear_free(void *pre_) +{ int i; NISTP224_PRE_COMP *pre = pre_; @@ -1198,43 +1244,46 @@ static void nistp224_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp224_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp224_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp224_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_224; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1242,74 +1291,81 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in, x_out, y_out; widefelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { + if (x != NULL) { if (!felem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { + if (y != NULL) { if (!felem_to_BN(y, y_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - return 1; } + return 1; +} -static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } + num, + points, + sizeof(felem), + tmp_felems, + (void (*) (void *)) felem_one, + (int (*) (const void *)) felem_is_zero_int, + (void (*) (void *, const void *)) felem_assign, + (void (*) (void *, const void *)) felem_square_reduce, + (void (*) (void *, const void *, const void *)) felem_mul_reduce, + (void (*) (void *, const void *)) felem_inv, + (void (*) (void *, const void *)) felem_contract); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp224_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; unsigned i; @@ -1318,7 +1374,7 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; + felem(*pre_comp)[17][3] = NULL; felem *tmp_felems = NULL; felem_bytearray tmp; unsigned num_bytes; @@ -1326,28 +1382,28 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, size_t num_points = num; felem x_in, y_in, z_in, x_out, y_out, z_out; NISTP224_PRE_COMP *pre = NULL; - const felem (*g_pre_comp)[16][3] = NULL; + const felem(*g_pre_comp)[16][3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp224_pre_comp_dup, nistp224_pre_comp_free, - nistp224_pre_comp_clear_free); + nistp224_pre_comp_dup, nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ - g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; + g_pre_comp = (const felem(*)[16][3]) pre->g_pre_comp; else /* try to use the standard precomputation */ g_pre_comp = &gmul[0]; @@ -1356,147 +1412,137 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, goto err; /* get the generator from precomputation */ if (!felem_to_BN(x, g_pre_comp[0][1][0]) || - !felem_to_BN(y, g_pre_comp[0][1][1]) || - !felem_to_BN(z, g_pre_comp[0][1][2])) - { + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points = num_points + 1; - } - - if (num_points > 0) - { - if (num_points >= 3) - { - /* unless we precompute multiples for just one or two points, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two + * points, converting those into affine form is time + * well spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); if (mixed) tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) /* the generator */ - { + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; felem_assign(pre_comp[i][1][0], x_out); felem_assign(pre_comp[i][1][1], y_out); felem_assign(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof g_secret); /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3]) pre_comp, + g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { + (!felem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -1512,10 +1558,11 @@ err: if (tmp_felems != NULL) free(tmp_felems); return ret; - } +} -int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp224_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP224_PRE_COMP *pre = NULL; int i, j; @@ -1526,113 +1573,113 @@ int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free); + nistp224_pre_comp_free, nistp224_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp224_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) + (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) goto err; - /* compute 2^56*G, 2^112*G, 2^168*G for the first table, - * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one + /* + * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, + * 2^84*G, 2^140*G, 2^196*G for the second one */ - for (i = 1; i <= 8; i <<= 1) - { + for (i = 1; i <= 8; i <<= 1) { point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); - for (j = 0; j < 27; ++j) - { + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) { point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - } + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } if (i == 8) break; point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - for (j = 0; j < 27; ++j) - { + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) { point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); - } + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]); } - for (i = 0; i < 2; i++) - { + } + for (i = 0; i < 2; i++) { /* g_pre_comp[i][0] is the point at infinity */ memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); /* the remaining multiples */ /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ point_add( - pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], - pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], - pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ point_add( - pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], - pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ point_add( - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], - pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], - pre->g_pre_comp[i][4][2]); - /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + + * 2^196*G + */ point_add( - pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], - pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], - pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); - for (j = 1; j < 8; ++j) - { + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { /* odd multiples: add G resp. 2^28*G */ point_add( - pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], - pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], - pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], - 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], - pre->g_pre_comp[i][1][2]); - } + pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2], + 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); } + } make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) + nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -1641,18 +1688,19 @@ int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp224_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp224_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free) - != NULL) + nistp224_pre_comp_free, nistp224_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libcrypto/ec/ecp_nistp256.c b/lib/libcrypto/ec/ecp_nistp256.c index 132ca0d2507..345f67d5207 100644 --- a/lib/libcrypto/ec/ecp_nistp256.c +++ b/lib/libcrypto/ec/ecp_nistp256.c @@ -112,41 +112,45 @@ typedef limb longfelem[NLIMBS * 2]; typedef u64 smallfelem[NLIMBS]; /* This is the value of the prime as four 64-bit words, little-endian. */ -static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; +static const u64 kPrime[4] = {0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul}; static const limb bottom32bits = 0xffffffff; static const u64 bottom63bits = 0x7ffffffffffffffful; /* bin32_to_felem takes a little-endian byte array and converts it into felem * form. This assumes that the CPU is little-endian. */ -static void bin32_to_felem(felem out, const u8 in[32]) - { - out[0] = *((u64*) &in[0]); - out[1] = *((u64*) &in[8]); - out[2] = *((u64*) &in[16]); - out[3] = *((u64*) &in[24]); - } +static void +bin32_to_felem(felem out, const u8 in[32]) +{ + out[0] = *((u64 *) & in[0]); + out[1] = *((u64 *) & in[8]); + out[2] = *((u64 *) & in[16]); + out[3] = *((u64 *) & in[24]); +} /* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, * 32 byte array. This assumes that the CPU is little-endian. */ -static void smallfelem_to_bin32(u8 out[32], const smallfelem in) - { - *((u64*) &out[0]) = in[0]; - *((u64*) &out[8]) = in[1]; - *((u64*) &out[16]) = in[2]; - *((u64*) &out[24]) = in[3]; - } +static void +smallfelem_to_bin32(u8 out[32], const smallfelem in) +{ + *((u64 *) & out[0]) = in[0]; + *((u64 *) & out[8]) = in[1]; + *((u64 *) & out[16]) = in[2]; + *((u64 *) & out[24]) = in[3]; +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -154,89 +158,95 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin32_to_felem(out, b_out); return 1; - } +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ -static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) - { +static BIGNUM * +smallfelem_to_BN(BIGNUM * out, const smallfelem in) +{ felem_bytearray b_in, b_out; smallfelem_to_bin32(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /* Field operations * ---------------- */ -static void smallfelem_one(smallfelem out) - { +static void +smallfelem_one(smallfelem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; out[3] = 0; - } +} -static void smallfelem_assign(smallfelem out, const smallfelem in) - { +static void +smallfelem_assign(smallfelem out, const smallfelem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* felem_sum sets out = out + in. */ -static void felem_sum(felem out, const felem in) - { +static void +felem_sum(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* felem_small_sum sets out = out + in. */ -static void felem_small_sum(felem out, const smallfelem in) - { +static void +felem_small_sum(felem out, const smallfelem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* felem_scalar sets out = out * scalar */ -static void felem_scalar(felem out, const u64 scalar) - { +static void +felem_scalar(felem out, const u64 scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; out[3] *= scalar; - } +} /* longfelem_scalar sets out = out * scalar */ -static void longfelem_scalar(longfelem out, const u64 scalar) - { +static void +longfelem_scalar(longfelem out, const u64 scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -245,27 +255,28 @@ static void longfelem_scalar(longfelem out, const u64 scalar) out[5] *= scalar; out[6] *= scalar; out[7] *= scalar; - } +} #define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) #define two105 (((limb)1) << 105) #define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) /* zero105 is 0 mod p */ -static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; +static const felem zero105 = {two105m41m9, two105, two105m41p9, two105m41p9}; /* smallfelem_neg sets |out| to |-small| * On exit: * out[i] < out[i] + 2^105 */ -static void smallfelem_neg(felem out, const smallfelem small) - { +static void +smallfelem_neg(felem out, const smallfelem small) +{ /* In order to prevent underflow, we subtract from 0 mod p. */ out[0] = zero105[0] - small[0]; out[1] = zero105[1] - small[1]; out[2] = zero105[2] - small[2]; out[3] = zero105[3] - small[3]; - } +} /* felem_diff subtracts |in| from |out| * On entry: @@ -273,8 +284,9 @@ static void smallfelem_neg(felem out, const smallfelem small) * On exit: * out[i] < out[i] + 2^105 */ -static void felem_diff(felem out, const felem in) - { +static void +felem_diff(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ out[0] += zero105[0]; out[1] += zero105[1]; @@ -285,14 +297,14 @@ static void felem_diff(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} #define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) #define two107 (((limb)1) << 107) #define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) /* zero107 is 0 mod p */ -static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; +static const felem zero107 = {two107m43m11, two107, two107m43p11, two107m43p11}; /* An alternative felem_diff for larger inputs |in| * felem_diff_zero107 subtracts |in| from |out| @@ -301,8 +313,9 @@ static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 * On exit: * out[i] < out[i] + 2^107 */ -static void felem_diff_zero107(felem out, const felem in) - { +static void +felem_diff_zero107(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ out[0] += zero107[0]; out[1] += zero107[1]; @@ -313,7 +326,7 @@ static void felem_diff_zero107(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* longfelem_diff subtracts |in| from |out| * On entry: @@ -321,13 +334,14 @@ static void felem_diff_zero107(felem out, const felem in) * On exit: * out[i] < out[i] + 2^70 + 2^40 */ -static void longfelem_diff(longfelem out, const longfelem in) - { - static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); - static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); - static const limb two70 = (((limb)1) << 70); - static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); - static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); +static void +longfelem_diff(longfelem out, const longfelem in) +{ + static const limb two70m8p6 = (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); + static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); + static const limb two70 = (((limb) 1) << 70); + static const limb two70m40m38p6 = (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + (((limb) 1) << 6); + static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); /* add 0 mod p to avoid underflow */ out[0] += two70m8p6; @@ -348,7 +362,7 @@ static void longfelem_diff(longfelem out, const longfelem in) out[5] -= in[5]; out[6] -= in[6]; out[7] -= in[7]; - } +} #define two64m0 (((limb)1) << 64) - 1 #define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 @@ -356,7 +370,7 @@ static void longfelem_diff(longfelem out, const longfelem in) #define two64m32 (((limb)1) << 64) - (((limb)1) << 32) /* zero110 is 0 mod p */ -static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; +static const felem zero110 = {two64m0, two110p32m0, two64m46, two64m32}; /* felem_shrink converts an felem into a smallfelem. The result isn't quite * minimal as the value may be greater than p. @@ -366,12 +380,13 @@ static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; * On exit: * out[i] < 2^64 */ -static void felem_shrink(smallfelem out, const felem in) - { +static void +felem_shrink(smallfelem out, const felem in) +{ felem tmp; u64 a, b, mask; s64 high, low; - static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ /* Carry 2->3 */ tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); @@ -382,50 +397,58 @@ static void felem_shrink(smallfelem out, const felem in) tmp[1] = zero110[1] + in[1]; /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ - /* We perform two partial reductions where we eliminate the - * high-word of tmp[3]. We don't update the other words till the end. + /* + * We perform two partial reductions where we eliminate the high-word + * of tmp[3]. We don't update the other words till the end. */ - a = tmp[3] >> 64; /* a < 2^46 */ + a = tmp[3] >> 64; /* a < 2^46 */ tmp[3] = (u64) tmp[3]; tmp[3] -= a; - tmp[3] += ((limb)a) << 32; + tmp[3] += ((limb) a) << 32; /* tmp[3] < 2^79 */ b = a; - a = tmp[3] >> 64; /* a < 2^15 */ - b += a; /* b < 2^46 + 2^15 < 2^47 */ + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ tmp[3] = (u64) tmp[3]; tmp[3] -= a; - tmp[3] += ((limb)a) << 32; + tmp[3] += ((limb) a) << 32; /* tmp[3] < 2^64 + 2^47 */ - /* This adjusts the other two words to complete the two partial - * reductions. */ + /* + * This adjusts the other two words to complete the two partial + * reductions. + */ tmp[0] += b; - tmp[1] -= (((limb)b) << 32); + tmp[1] -= (((limb) b) << 32); - /* In order to make space in tmp[3] for the carry from 2 -> 3, we - * conditionally subtract kPrime if tmp[3] is large enough. */ + /* + * In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. + */ high = tmp[3] >> 64; /* As tmp[3] < 2^65, high is either 1 or 0 */ high <<= 63; high >>= 63; - /* high is: - * all ones if the high word of tmp[3] is 1 - * all zeros if the high word of tmp[3] if 0 */ + /* + * high is: all ones if the high word of tmp[3] is 1 all zeros if + * the high word of tmp[3] if 0 + */ low = tmp[3]; mask = low >> 63; - /* mask is: - * all ones if the MSB of low is 1 - * all zeros if the MSB of low if 0 */ + /* + * mask is: all ones if the MSB of low is 1 all zeros if the MSB + * of low if 0 + */ low &= bottom63bits; low -= kPrime3Test; /* if low was greater than kPrime3Test then the MSB is zero */ low = ~low; low >>= 63; - /* low is: - * all ones if low was > kPrime3Test - * all zeros if low was <= kPrime3Test */ + /* + * low is: all ones if low was > kPrime3Test all zeros if low was + * <= kPrime3Test + */ mask = (mask & low) | high; tmp[0] -= mask & kPrime[0]; tmp[1] -= mask & kPrime[1]; @@ -433,25 +456,29 @@ static void felem_shrink(smallfelem out, const felem in) tmp[3] -= mask & kPrime[3]; /* tmp[3] < 2**64 - 2**32 + 1 */ - tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; - tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; - tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; + tmp[1] += ((u64) (tmp[0] >> 64)); + tmp[0] = (u64) tmp[0]; + tmp[2] += ((u64) (tmp[1] >> 64)); + tmp[1] = (u64) tmp[1]; + tmp[3] += ((u64) (tmp[2] >> 64)); + tmp[2] = (u64) tmp[2]; /* tmp[i] < 2^64 */ out[0] = tmp[0]; out[1] = tmp[1]; out[2] = tmp[2]; out[3] = tmp[3]; - } +} /* smallfelem_expand converts a smallfelem to an felem */ -static void smallfelem_expand(felem out, const smallfelem in) - { +static void +smallfelem_expand(felem out, const smallfelem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* smallfelem_square sets |out| = |small|^2 * On entry: @@ -459,8 +486,9 @@ static void smallfelem_expand(felem out, const smallfelem in) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void smallfelem_square(longfelem out, const smallfelem small) - { +static void +smallfelem_square(longfelem out, const smallfelem small) +{ limb a; u64 high, low; @@ -529,7 +557,7 @@ static void smallfelem_square(longfelem out, const smallfelem small) high = a >> 64; out[6] += low; out[7] = high; - } +} /* felem_square sets |out| = |in|^2 * On entry: @@ -537,12 +565,13 @@ static void smallfelem_square(longfelem out, const smallfelem small) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_square(longfelem out, const felem in) - { +static void +felem_square(longfelem out, const felem in) +{ u64 small[4]; felem_shrink(small, in); smallfelem_square(out, small); - } +} /* smallfelem_mul sets |out| = |small1| * |small2| * On entry: @@ -551,8 +580,9 @@ static void felem_square(longfelem out, const felem in) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) - { +static void +smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) +{ limb a; u64 high, low; @@ -657,7 +687,7 @@ static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfe high = a >> 64; out[6] += low; out[7] = high; - } +} /* felem_mul sets |out| = |in1| * |in2| * On entry: @@ -666,13 +696,14 @@ static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfe * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_mul(longfelem out, const felem in1, const felem in2) - { +static void +felem_mul(longfelem out, const felem in1, const felem in2) +{ smallfelem small1, small2; felem_shrink(small1, in1); felem_shrink(small2, in2); smallfelem_mul(out, small1, small2); - } +} /* felem_small_mul sets |out| = |small1| * |in2| * On entry: @@ -681,23 +712,24 @@ static void felem_mul(longfelem out, const felem in1, const felem in2) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) - { +static void +felem_small_mul(longfelem out, const smallfelem small1, const felem in2) +{ smallfelem small2; felem_shrink(small2, in2); smallfelem_mul(out, small1, small2); - } +} #define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) #define two100 (((limb)1) << 100) #define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) /* zero100 is 0 mod p */ -static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; +static const felem zero100 = {two100m36m4, two100, two100m36p4, two100m36p4}; /* Internal function for the different flavours of felem_reduce. * felem_reduce_ reduces the higher coefficients in[4]-in[7]. * On entry: - * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] * out[1] >= in[7] + 2^32*in[4] * out[2] >= in[5] + 2^32*in[5] * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] @@ -707,8 +739,9 @@ static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] * out[3] <= out[3] + 2^32*in[4] + 3*in[7] */ -static void felem_reduce_(felem out, const longfelem in) - { +static void +felem_reduce_(felem out, const longfelem in) +{ int128_t c; /* combine common terms from below */ c = in[4] + (in[5] << 32); @@ -739,7 +772,7 @@ static void felem_reduce_(felem out, const longfelem in) out[0] -= (in[7] << 32); out[2] += (in[7] << 33); out[3] += (in[7] * 3); - } +} /* felem_reduce converts a longfelem into an felem. * To be called directly after felem_square or felem_mul. @@ -749,8 +782,9 @@ static void felem_reduce_(felem out, const longfelem in) * On exit: * out[i] < 2^101 */ -static void felem_reduce(felem out, const longfelem in) - { +static void +felem_reduce(felem out, const longfelem in) +{ out[0] = zero100[0] + in[0]; out[1] = zero100[1] + in[1]; out[2] = zero100[2] + in[2]; @@ -758,17 +792,18 @@ static void felem_reduce(felem out, const longfelem in) felem_reduce_(out, in); - /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 - * out[1] > 2^100 - 2^64 - 7*2^96 > 0 - * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 - * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 - * - * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 - * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 - * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 - * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + /* + * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 out[2] > 2^100 - 2^36 + 2^4 - + * 5*2^64 - 5*2^96 > 0 out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 + * - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 out[1] < 2^100 + + * 3*2^64 + 5*2^64 + 3*2^97 < 2^101 out[2] < 2^100 + 5*2^64 + 2^64 + + * 3*2^65 + 2^97 < 2^101 out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < + * 2^101 */ - } +} /* felem_reduce_zero105 converts a larger longfelem into an felem. * On entry: @@ -776,8 +811,9 @@ static void felem_reduce(felem out, const longfelem in) * On exit: * out[i] < 2^106 */ -static void felem_reduce_zero105(felem out, const longfelem in) - { +static void +felem_reduce_zero105(felem out, const longfelem in) +{ out[0] = zero105[0] + in[0]; out[1] = zero105[1] + in[1]; out[2] = zero105[2] + in[2]; @@ -785,34 +821,36 @@ static void felem_reduce_zero105(felem out, const longfelem in) felem_reduce_(out, in); - /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 - * out[1] > 2^105 - 2^71 - 2^103 > 0 - * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 - * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 - * - * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 - * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + /* + * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 out[2] > 2^105 - 2^41 + 2^9 - + * 2^71 - 2^103 > 0 out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - + * 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 out[1] < 2^105 + 2^71 + + * 2^71 + 2^103 < 2^106 out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < + * 2^106 out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 */ - } +} /* subtract_u64 sets *result = *result - v and *carry to one if the subtraction * underflowed. */ -static void subtract_u64(u64* result, u64* carry, u64 v) - { +static void +subtract_u64(u64 * result, u64 * carry, u64 v) +{ uint128_t r = *result; r -= v; *carry = (r >> 64) & 1; *result = (u64) r; - } +} /* felem_contract converts |in| to its unique, minimal representation. * On entry: * in[i] < 2^109 */ -static void felem_contract(smallfelem out, const felem in) - { +static void +felem_contract(smallfelem out, const felem in) +{ unsigned i; u64 all_equal_so_far = 0, result = 0, carry; @@ -820,20 +858,25 @@ static void felem_contract(smallfelem out, const felem in) /* small is minimal except that the value might be > p */ all_equal_so_far--; - /* We are doing a constant time test if out >= kPrime. We need to + /* + * We are doing a constant time test if out >= kPrime. We need to * compare each u64, from most-significant to least significant. For - * each one, if all words so far have been equal (m is all ones) then a - * non-equal result is the answer. Otherwise we continue. */ - for (i = 3; i < 4; i--) - { + * each one, if all words so far have been equal (m is all ones) then + * a non-equal result is the answer. Otherwise we continue. + */ + for (i = 3; i < 4; i--) { u64 equal; uint128_t a = ((uint128_t) kPrime[i]) - out[i]; - /* if out[i] > kPrime[i] then a will underflow and the high - * 64-bits will all be set. */ + /* + * if out[i] > kPrime[i] then a will underflow and the high + * 64-bits will all be set. + */ result |= all_equal_so_far & ((u64) (a >> 64)); - /* if kPrime[i] == out[i] then |equal| will be all zeros and - * the decrement will make it all ones. */ + /* + * if kPrime[i] == out[i] then |equal| will be all zeros and + * the decrement will make it all ones. + */ equal = kPrime[i] ^ out[i]; equal--; equal &= equal << 32; @@ -845,10 +888,12 @@ static void felem_contract(smallfelem out, const felem in) equal = ((s64) equal) >> 63; all_equal_so_far &= equal; - } + } - /* if all_equal_so_far is still all ones then the two values are equal - * and so out >= kPrime is true. */ + /* + * if all_equal_so_far is still all ones then the two values are + * equal and so out >= kPrime is true. + */ result |= all_equal_so_far; /* if out >= kPrime then we subtract kPrime. */ @@ -865,35 +910,38 @@ static void felem_contract(smallfelem out, const felem in) subtract_u64(&out[3], &carry, carry); subtract_u64(&out[3], &carry, result & kPrime[3]); - } +} -static void smallfelem_square_contract(smallfelem out, const smallfelem in) - { +static void +smallfelem_square_contract(smallfelem out, const smallfelem in) +{ longfelem longtmp; felem tmp; smallfelem_square(longtmp, in); felem_reduce(tmp, longtmp); felem_contract(out, tmp); - } +} -static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) - { +static void +smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) +{ longfelem longtmp; felem tmp; smallfelem_mul(longtmp, in1, in2); felem_reduce(tmp, longtmp); felem_contract(out, tmp); - } +} /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * small[i] < 2^64 */ -static limb smallfelem_is_zero(const smallfelem small) - { +static limb +smallfelem_is_zero(const smallfelem small) +{ limb result; u64 is_p; @@ -908,9 +956,9 @@ static limb smallfelem_is_zero(const smallfelem small) is_zero = ((s64) is_zero) >> 63; is_p = (small[0] ^ kPrime[0]) | - (small[1] ^ kPrime[1]) | - (small[2] ^ kPrime[2]) | - (small[3] ^ kPrime[3]); + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | + (small[3] ^ kPrime[3]); is_p--; is_p &= is_p << 32; is_p &= is_p << 16; @@ -925,12 +973,13 @@ static limb smallfelem_is_zero(const smallfelem small) result = is_zero; result |= ((limb) is_zero) << 64; return result; - } +} -static int smallfelem_is_zero_int(const smallfelem small) - { - return (int) (smallfelem_is_zero(small) & ((limb)1)); - } +static int +smallfelem_is_zero_int(const smallfelem small) +{ + return (int) (smallfelem_is_zero(small) & ((limb) 1)); +} /* felem_inv calculates |out| = |in|^{-1} * @@ -939,77 +988,110 @@ static int smallfelem_is_zero_int(const smallfelem small) * a^{p-1} = 1 (mod p) * a^{p-2} = a^{-1} (mod p) */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2; /* each e_I will hold |in|^{2^I - 1} */ felem e2, e4, e8, e16, e32, e64; longfelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */ felem_assign(e2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); + felem_reduce(ftmp, tmp);/* 2^4 - 2^0 */ felem_assign(e4, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ - felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^5 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^6 - 2^2 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^7 - 2^3 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); + felem_reduce(ftmp, tmp);/* 2^8 - 2^0 */ felem_assign(e8, ftmp); for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^16 - 2^8 */ - felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); + felem_reduce(ftmp, tmp);/* 2^16 - 2^0 */ felem_assign(e16, ftmp); for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^32 - 2^16 */ - felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); + felem_reduce(ftmp, tmp);/* 2^32 - 2^0 */ felem_assign(e32, ftmp); for (i = 0; i < 32; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^64 - 2^32 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ felem_assign(e64, ftmp); - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp);/* 2^64 - 2^32 + 2^0 */ for (i = 0; i < 192; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^256 - 2^224 + 2^192 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ - felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + felem_mul(tmp, e64, e32); + felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^80 - 2^16 */ - felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); + felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^88 - 2^8 */ - felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); + felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ for (i = 0; i < 4; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^92 - 2^4 */ - felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ - felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ - felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ - - felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ - } + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); + felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); + felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ +} -static void smallfelem_inv_contract(smallfelem out, const smallfelem in) - { +static void +smallfelem_inv_contract(smallfelem out, const smallfelem in) +{ felem tmp; smallfelem_expand(tmp, in); felem_inv(tmp, tmp); felem_contract(out, tmp); - } +} /* Group operations * ---------------- @@ -1027,8 +1109,8 @@ static void smallfelem_inv_contract(smallfelem out, const smallfelem in) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ longfelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; smallfelem small1, small2; @@ -1101,14 +1183,14 @@ point_double(felem x_out, felem y_out, felem z_out, /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ felem_reduce_zero105(y_out, tmp); /* y_out[i] < 2^106 */ - } +} /* point_double_small is the same as point_double, except that it operates on * smallfelems */ static void point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, - const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) - { + const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) +{ felem felem_x_out, felem_y_out, felem_z_out; felem felem_x_in, felem_y_in, felem_z_in; @@ -1116,35 +1198,33 @@ point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, smallfelem_expand(felem_y_in, y_in); smallfelem_expand(felem_z_in, z_in); point_double(felem_x_out, felem_y_out, felem_z_out, - felem_x_in, felem_y_in, felem_z_in); + felem_x_in, felem_y_in, felem_z_in); felem_shrink(x_out, felem_x_out); felem_shrink(y_out, felem_y_out); felem_shrink(z_out, felem_z_out); - } +} /* copy_conditional copies in to out iff mask is all ones. */ static void copy_conditional(felem out, const felem in, limb mask) - { +{ unsigned i; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { const limb tmp = mask & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /* copy_small_conditional copies in to out iff mask is all ones. */ static void copy_small_conditional(felem out, const smallfelem in, limb mask) - { +{ unsigned i; const u64 mask64 = mask; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); - } } +} /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) * @@ -1156,10 +1236,11 @@ copy_small_conditional(felem out, const smallfelem in, limb mask) * are equal, (while not equal to the point at infinity). This case never * happens during single point multiplication, so there is no timing leak for * ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; longfelem tmp, tmp2; smallfelem small1, small2, small3, small4, small5; @@ -1176,8 +1257,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp[i] < 2^101 */ felem_shrink(small1, ftmp); - if(!mixed) - { + if (!mixed) { /* ftmp2 = z2z2 = z2**2 */ smallfelem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -1213,9 +1293,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_mul(tmp, y1, ftmp2); felem_reduce(ftmp6, tmp); /* ftmp6[i] < 2^101 */ - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* u1 = ftmp3 = x1*z2z2 */ @@ -1230,7 +1308,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp2 = y1 * z2**3 */ felem_assign(ftmp6, y1); /* ftmp6[i] < 2^106 */ - } + } /* u2 = x2*z1z1 */ smallfelem_mul(tmp, x2, small1); @@ -1258,18 +1336,16 @@ static void point_add(felem x3, felem y3, felem z3, /* r = ftmp5 = (s2 - s1)*2 */ felem_diff_zero107(ftmp5, ftmp6); - /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ + /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ felem_scalar(ftmp5, 2); /* ftmp5[i] < 2^109 */ felem_shrink(small1, ftmp5); y_equal = smallfelem_is_zero(small1); - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* I = ftmp = (2h)**2 */ felem_assign(ftmp, ftmp4); felem_scalar(ftmp, 2); @@ -1316,14 +1392,15 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* point_add_small is the same as point_add, except that it operates on * smallfelems */ -static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, - smallfelem x1, smallfelem y1, smallfelem z1, - smallfelem x2, smallfelem y2, smallfelem z2) - { +static void +point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) +{ felem felem_x3, felem_y3, felem_z3; felem felem_x1, felem_y1, felem_z1; smallfelem_expand(felem_x1, x1); @@ -1333,7 +1410,7 @@ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, felem_shrink(x3, felem_x3); felem_shrink(y3, felem_y3); felem_shrink(z3, felem_z3); - } +} /* Base point pre computation * -------------------------- @@ -1373,113 +1450,113 @@ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, /* gmul is the table of precomputed base points */ static const smallfelem gmul[2][16][3] = {{{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, - {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, - {1, 0, 0, 0}}, - {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, - {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, - {1, 0, 0, 0}}, - {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, - {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, - {1, 0, 0, 0}}, - {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, - {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, - {1, 0, 0, 0}}, - {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, - {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, - {1, 0, 0, 0}}, - {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, - {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, - {1, 0, 0, 0}}, - {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, - {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, - {1, 0, 0, 0}}, - {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, - {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, - {1, 0, 0, 0}}, - {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, - {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, - {1, 0, 0, 0}}, - {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, - {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, - {1, 0, 0, 0}}, - {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, - {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, - {1, 0, 0, 0}}, - {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, - {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, - {1, 0, 0, 0}}, - {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, - {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, - {1, 0, 0, 0}}, - {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, - {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, - {1, 0, 0, 0}}, - {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, - {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, - {1, 0, 0, 0}}}, - {{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, - {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, - {1, 0, 0, 0}}, - {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, - {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, - {1, 0, 0, 0}}, - {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, - {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, - {1, 0, 0, 0}}, - {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, - {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, - {1, 0, 0, 0}}, - {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, - {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, - {1, 0, 0, 0}}, - {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, - {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, - {1, 0, 0, 0}}, - {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, - {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, - {1, 0, 0, 0}}, - {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, - {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, - {1, 0, 0, 0}}, - {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, - {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, - {1, 0, 0, 0}}, - {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, - {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, - {1, 0, 0, 0}}, - {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, - {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, - {1, 0, 0, 0}}, - {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, - {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, - {1, 0, 0, 0}}, - {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, - {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, - {1, 0, 0, 0}}, - {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, - {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, - {1, 0, 0, 0}}, - {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, - {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, - {1, 0, 0, 0}}}}; +{0, 0, 0, 0}, +{0, 0, 0, 0}}, +{{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, +{0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, +{1, 0, 0, 0}}, +{{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, +{0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, +{1, 0, 0, 0}}, +{{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, +{0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, +{1, 0, 0, 0}}, +{{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, +{0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, +{1, 0, 0, 0}}, +{{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, +{0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, +{1, 0, 0, 0}}, +{{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, +{0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, +{1, 0, 0, 0}}, +{{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, +{0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, +{1, 0, 0, 0}}, +{{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, +{0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, +{1, 0, 0, 0}}, +{{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, +{0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, +{1, 0, 0, 0}}, +{{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, +{0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, +{1, 0, 0, 0}}, +{{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, +{0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, +{1, 0, 0, 0}}, +{{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, +{0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, +{1, 0, 0, 0}}, +{{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, +{0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, +{1, 0, 0, 0}}, +{{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, +{0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, +{1, 0, 0, 0}}, +{{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, +{0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, +{1, 0, 0, 0}}}, +{{{0, 0, 0, 0}, +{0, 0, 0, 0}, +{0, 0, 0, 0}}, +{{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, +{0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, +{1, 0, 0, 0}}, +{{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, +{0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, +{1, 0, 0, 0}}, +{{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, +{0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, +{1, 0, 0, 0}}, +{{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, +{0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, +{1, 0, 0, 0}}, +{{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, +{0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, +{1, 0, 0, 0}}, +{{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, +{0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, +{1, 0, 0, 0}}, +{{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, +{0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, +{1, 0, 0, 0}}, +{{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, +{0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, +{1, 0, 0, 0}}, +{{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, +{0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, +{1, 0, 0, 0}}, +{{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, +{0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, +{1, 0, 0, 0}}, +{{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, +{0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, +{1, 0, 0, 0}}, +{{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, +{0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, +{1, 0, 0, 0}}, +{{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, +{0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, +{1, 0, 0, 0}}, +{{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, +{0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, +{1, 0, 0, 0}}, +{{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, +{0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, +{1, 0, 0, 0}}}}; /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) - { +static void +select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) +{ unsigned i, j; u64 *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(smallfelem)); - for (i = 0; i < size; i++) - { - const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; + for (i = 0; i < size; i++) { + const u64 *inlimbs = (u64 *) & pre_comp[i][0][0]; u64 mask = i ^ idx; mask |= mask >> 4; mask |= mask >> 2; @@ -1488,26 +1565,28 @@ static void select_point(const u64 idx, unsigned int size, const smallfelem pre_ mask--; for (j = 0; j < NLIMBS * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, int i) - { +static char +get_bit(const felem_bytearray in, int i) +{ if ((i < 0) || (i >= 256)) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) +{ int i, skip; unsigned num, gen_mul = (g_scalar != NULL); felem nq[3], ftmp; @@ -1518,20 +1597,20 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (two in each of the last 32 rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (two in each of the last 32 rounds) and + * additions of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 255 : 31); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 255 : 31); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 31)) - { + if (gen_mul && (i <= 31)) { /* first, look 32 bits upwards */ bits = get_bit(g_scalar, i + 224) << 3; bits |= get_bit(g_scalar, i + 160) << 2; @@ -1540,19 +1619,16 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[1], tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { smallfelem_expand(nq[0], tmp[0]); smallfelem_expand(nq[1], tmp[1]); smallfelem_expand(nq[2], tmp[2]); skip = 0; - } + } /* second, look at the current position */ bits = get_bit(g_scalar, i + 192) << 3; @@ -1562,16 +1638,13 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[0], tmp); point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1580,32 +1653,33 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, bits |= get_bit(scalars[num], i - 1); ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - /* select the point to add or subtract, in constant time */ + /* + * select the point to add or subtract, in + * constant time + */ select_point(digit, 17, pre_comp[num], tmp); - smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); felem_contract(tmp[1], ftmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { smallfelem_expand(nq[0], tmp[0]); smallfelem_expand(nq[1], tmp[1]); smallfelem_expand(nq[2], tmp[2]); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /* Precomputation for the group generator. */ typedef struct { @@ -1627,20 +1701,20 @@ EC_GFp_nistp256_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_nistp256_point_get_affine_coordinates, + ec_GFp_nistp256_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -1663,32 +1737,34 @@ EC_GFp_nistp256_method(void) /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP256_PRE_COMP *nistp256_pre_comp_new() - { +static NISTP256_PRE_COMP * +nistp256_pre_comp_new() +{ NISTP256_PRE_COMP *ret = NULL; ret = (NISTP256_PRE_COMP *) malloc(sizeof *ret); - if (!ret) - { + if (!ret) { ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp256_pre_comp_dup(void *src_) - { +static void * +nistp256_pre_comp_dup(void *src_) +{ NISTP256_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp256_pre_comp_free(void *pre_) - { +static void +nistp256_pre_comp_free(void *pre_) +{ int i; NISTP256_PRE_COMP *pre = pre_; @@ -1700,10 +1776,11 @@ static void nistp256_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp256_pre_comp_clear_free(void *pre_) - { +static void +nistp256_pre_comp_clear_free(void *pre_) +{ int i; NISTP256_PRE_COMP *pre = pre_; @@ -1716,43 +1793,46 @@ static void nistp256_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp256_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp256_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp256_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_256; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1760,76 +1840,82 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in; smallfelem x_out, y_out; longfelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { + if (x != NULL) { if (!smallfelem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { - if (!smallfelem_to_BN(y, y_out)) - { + if (y != NULL) { + if (!smallfelem_to_BN(y, y_out)) { ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); + ERR_R_BN_LIB); return 0; - } } - return 1; } + return 1; +} -static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, smallfelem points[ /* num */ ][3], smallfelem tmp_smallfelems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(smallfelem), - tmp_smallfelems, - (void (*)(void *)) smallfelem_one, - (int (*)(const void *)) smallfelem_is_zero_int, - (void (*)(void *, const void *)) smallfelem_assign, - (void (*)(void *, const void *)) smallfelem_square_contract, - (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, - (void (*)(void *, const void *)) smallfelem_inv_contract, - (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); - } + num, + points, + sizeof(smallfelem), + tmp_smallfelems, + (void (*) (void *)) smallfelem_one, + (int (*) (const void *)) smallfelem_is_zero_int, + (void (*) (void *, const void *)) smallfelem_assign, + (void (*) (void *, const void *)) smallfelem_square_contract, + (void (*) (void *, const void *, const void *)) smallfelem_mul_contract, + (void (*) (void *, const void *)) smallfelem_inv_contract, + (void (*) (void *, const void *)) smallfelem_assign /* nothing to contract */ ); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp256_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; int mixed = 0; @@ -1837,7 +1923,7 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - smallfelem (*pre_comp)[17][3] = NULL; + smallfelem(*pre_comp)[17][3] = NULL; smallfelem *tmp_smallfelems = NULL; felem_bytearray tmp; unsigned i, num_bytes; @@ -1846,28 +1932,28 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, smallfelem x_in, y_in, z_in; felem x_out, y_out, z_out; NISTP256_PRE_COMP *pre = NULL; - const smallfelem (*g_pre_comp)[16][3] = NULL; + const smallfelem(*g_pre_comp)[16][3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp256_pre_comp_dup, nistp256_pre_comp_free, - nistp256_pre_comp_clear_free); + nistp256_pre_comp_dup, nistp256_pre_comp_free, + nistp256_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ - g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; + g_pre_comp = (const smallfelem(*)[16][3]) pre->g_pre_comp; else /* try to use the standard precomputation */ g_pre_comp = &gmul[0]; @@ -1876,147 +1962,140 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, goto err; /* get the generator from precomputation */ if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || - !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || - !smallfelem_to_BN(z, g_pre_comp[0][1][2])) - { + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points++; - } - if (num_points > 0) - { - if (num_points >= 3) - { - /* unless we precompute multiples for just one or two points, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two + * points, converting those into affine form is time + * well spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(smallfelem)); if (mixed) tmp_smallfelems = malloc((num_points * 17 + 1) * sizeof(smallfelem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) - /* we didn't have a valid precomputation, so we pick - * the generator */ - { + /* + * we didn't have a valid precomputation, so + * we pick the generator + */ + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^256 */ - if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; felem_shrink(pre_comp[i][1][0], x_out); felem_shrink(pre_comp[i][1][1], y_out); felem_shrink(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add_small( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double_small( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof(g_secret)); /* reduce scalar to 0 <= scalar < 2^256 */ - if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const smallfelem (*)[17][3]) pre_comp, - g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const smallfelem(*)[17][3]) pre_comp, + g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const smallfelem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || - (!smallfelem_to_BN(z, z_in))) - { + (!smallfelem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -2032,10 +2111,11 @@ err: if (tmp_smallfelems != NULL) free(tmp_smallfelems); return ret; - } +} -int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp256_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP256_PRE_COMP *pre = NULL; int i, j; @@ -2047,106 +2127,106 @@ int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free); + nistp256_pre_comp_free, nistp256_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp256_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(x_tmp, &group->generator->X)) || - (!BN_to_felem(y_tmp, &group->generator->Y)) || - (!BN_to_felem(z_tmp, &group->generator->Z))) + (!BN_to_felem(y_tmp, &group->generator->Y)) || + (!BN_to_felem(z_tmp, &group->generator->Z))) goto err; felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); - /* compute 2^64*G, 2^128*G, 2^192*G for the first table, - * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one + /* + * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, + * 2^96*G, 2^160*G, 2^224*G for the second one */ - for (i = 1; i <= 8; i <<= 1) - { + for (i = 1; i <= 8; i <<= 1) { point_double_small( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); - for (j = 0; j < 31; ++j) - { + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 31; ++j) { point_double_small( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - } + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } if (i == 8) break; point_double_small( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - for (j = 0; j < 31; ++j) - { + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 31; ++j) { point_double_small( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); - } + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]); } - for (i = 0; i < 2; i++) - { + } + for (i = 0; i < 2; i++) { /* g_pre_comp[i][0] is the point at infinity */ memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); /* the remaining multiples */ /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ point_add_small( - pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], - pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ point_add_small( - pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], - pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ point_add_small( - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); - /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); + /* + * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + + * 2^224*G + */ point_add_small( - pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); - for (j = 1; j < 8; ++j) - { + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { /* odd multiples: add G resp. 2^32*G */ point_add_small( - pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], pre->g_pre_comp[i][2*j+1][2], - pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], - pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); - } + pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1], pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2], + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); } + } make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) + nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -2155,17 +2235,18 @@ int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp256_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp256_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free) - != NULL) + nistp256_pre_comp_free, nistp256_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libcrypto/ec/ecp_nistp521.c b/lib/libcrypto/ec/ecp_nistp521.c index c34c38b7e83..f5b72a4c0d3 100644 --- a/lib/libcrypto/ec/ecp_nistp521.c +++ b/lib/libcrypto/ec/ecp_nistp521.c @@ -133,46 +133,50 @@ static const limb bottom58bits = 0x3ffffffffffffff; /* bin66_to_felem takes a little-endian byte array and converts it into felem * form. This assumes that the CPU is little-endian. */ -static void bin66_to_felem(felem out, const u8 in[66]) - { - out[0] = (*((limb*) &in[0])) & bottom58bits; - out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; - out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; - out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; - out[4] = (*((limb*) &in[29])) & bottom58bits; - out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; - out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; - out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; - out[8] = (*((limb*) &in[58])) & bottom57bits; - } +static void +bin66_to_felem(felem out, const u8 in[66]) +{ + out[0] = (*((limb *) & in[0])) & bottom58bits; + out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits; + out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits; + out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits; + out[4] = (*((limb *) & in[29])) & bottom58bits; + out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits; + out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits; + out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits; + out[8] = (*((limb *) & in[58])) & bottom57bits; +} /* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte * array. This assumes that the CPU is little-endian. */ -static void felem_to_bin66(u8 out[66], const felem in) - { +static void +felem_to_bin66(u8 out[66], const felem in) +{ memset(out, 0, 66); - (*((limb*) &out[0])) = in[0]; - (*((limb*) &out[7])) |= in[1] << 2; - (*((limb*) &out[14])) |= in[2] << 4; - (*((limb*) &out[21])) |= in[3] << 6; - (*((limb*) &out[29])) = in[4]; - (*((limb*) &out[36])) |= in[5] << 2; - (*((limb*) &out[43])) |= in[6] << 4; - (*((limb*) &out[50])) |= in[7] << 6; - (*((limb*) &out[58])) = in[8]; - } + (*((limb *) & out[0])) = in[0]; + (*((limb *) & out[7])) |= in[1] << 2; + (*((limb *) & out[14])) |= in[2] << 4; + (*((limb *) & out[21])) |= in[3] << 6; + (*((limb *) & out[29])) = in[4]; + (*((limb *) & out[36])) |= in[5] << 2; + (*((limb *) & out[43])) |= in[6] << 4; + (*((limb *) & out[50])) |= in[7] << 6; + (*((limb *) & out[58])) = in[8]; +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -180,37 +184,37 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin66_to_felem(out, b_out); return 1; - } +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { +static BIGNUM * +felem_to_BN(BIGNUM * out, const felem in) +{ felem_bytearray b_in, b_out; felem_to_bin66(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /* Field operations * ---------------- */ -static void felem_one(felem out) - { +static void +felem_one(felem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; @@ -220,10 +224,11 @@ static void felem_one(felem out) out[6] = 0; out[7] = 0; out[8] = 0; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; @@ -233,11 +238,12 @@ static void felem_assign(felem out, const felem in) out[6] = in[6]; out[7] = in[7]; out[8] = in[8]; - } +} /* felem_sum64 sets out = out + in. */ -static void felem_sum64(felem out, const felem in) - { +static void +felem_sum64(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; @@ -247,11 +253,12 @@ static void felem_sum64(felem out, const felem in) out[6] += in[6]; out[7] += in[7]; out[8] += in[8]; - } +} /* felem_scalar sets out = in * scalar */ -static void felem_scalar(felem out, const felem in, limb scalar) - { +static void +felem_scalar(felem out, const felem in, limb scalar) +{ out[0] = in[0] * scalar; out[1] = in[1] * scalar; out[2] = in[2] * scalar; @@ -261,11 +268,12 @@ static void felem_scalar(felem out, const felem in, limb scalar) out[6] = in[6] * scalar; out[7] = in[7] * scalar; out[8] = in[8] * scalar; - } +} /* felem_scalar64 sets out = out * scalar */ -static void felem_scalar64(felem out, limb scalar) - { +static void +felem_scalar64(felem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -275,11 +283,12 @@ static void felem_scalar64(felem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_scalar128 sets out = out * scalar */ -static void felem_scalar128(largefelem out, limb scalar) - { +static void +felem_scalar128(largefelem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -289,7 +298,7 @@ static void felem_scalar128(largefelem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_neg sets |out| to |-in| * On entry: @@ -297,11 +306,12 @@ static void felem_scalar128(largefelem out, limb scalar) * On exit: * out[i] < 2^62 */ -static void felem_neg(felem out, const felem in) - { +static void +felem_neg(felem out, const felem in) +{ /* In order to prevent underflow, we subtract from 0 mod p. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] = two62m3 - in[0]; out[1] = two62m2 - in[1]; @@ -312,7 +322,7 @@ static void felem_neg(felem out, const felem in) out[6] = two62m2 - in[6]; out[7] = two62m2 - in[7]; out[8] = two62m2 - in[8]; - } +} /* felem_diff64 subtracts |in| from |out| * On entry: @@ -320,11 +330,12 @@ static void felem_neg(felem out, const felem in) * On exit: * out[i] < out[i] + 2^62 */ -static void felem_diff64(felem out, const felem in) - { +static void +felem_diff64(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two62m3 - in[0]; out[1] += two62m2 - in[1]; @@ -335,7 +346,7 @@ static void felem_diff64(felem out, const felem in) out[6] += two62m2 - in[6]; out[7] += two62m2 - in[7]; out[8] += two62m2 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -343,11 +354,12 @@ static void felem_diff64(felem out, const felem in) * On exit: * out[i] < out[i] + 2^63 */ -static void felem_diff_128_64(largefelem out, const felem in) - { +static void +felem_diff_128_64(largefelem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two63m6 - in[0]; out[1] += two63m5 - in[1]; @@ -358,7 +370,7 @@ static void felem_diff_128_64(largefelem out, const felem in) out[6] += two63m5 - in[6]; out[7] += two63m5 - in[7]; out[8] += two63m5 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -366,11 +378,12 @@ static void felem_diff_128_64(largefelem out, const felem in) * On exit: * out[i] < out[i] + 2^127 - 2^69 */ -static void felem_diff128(largefelem out, const largefelem in) - { +static void +felem_diff128(largefelem out, const largefelem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); - static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); + static const uint128_t two127m70 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70); + static const uint128_t two127m69 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69); out[0] += (two127m70 - in[0]); out[1] += (two127m69 - in[1]); @@ -381,7 +394,7 @@ static void felem_diff128(largefelem out, const largefelem in) out[6] += (two127m69 - in[6]); out[7] += (two127m69 - in[7]); out[8] += (two127m69 - in[8]); - } +} /* felem_square sets |out| = |in|^2 * On entry: @@ -389,90 +402,92 @@ static void felem_diff128(largefelem out, const largefelem in) * On exit: * out[i] < 17 * max(in[i]) * max(in[i]) */ -static void felem_square(largefelem out, const felem in) - { +static void +felem_square(largefelem out, const felem in) +{ felem inx2, inx4; felem_scalar(inx2, in, 2); felem_scalar(inx4, in, 4); - /* We have many cases were we want to do - * in[x] * in[y] + - * in[y] * in[x] - * This is obviously just - * 2 * in[x] * in[y] - * However, rather than do the doubling on the 128 bit result, we - * double one of the inputs to the multiplication by reading from - * |inx2| */ + /* + * We have many cases were we want to do in[x] * in[y] + in[y] * + * in[x] This is obviously just 2 * in[x] * in[y] However, rather + * than do the doubling on the 128 bit result, we double one of the + * inputs to the multiplication by reading from |inx2| + */ out[0] = ((uint128_t) in[0]) * in[0]; out[1] = ((uint128_t) in[0]) * inx2[1]; out[2] = ((uint128_t) in[0]) * inx2[2] + - ((uint128_t) in[1]) * in[1]; + ((uint128_t) in[1]) * in[1]; out[3] = ((uint128_t) in[0]) * inx2[3] + - ((uint128_t) in[1]) * inx2[2]; + ((uint128_t) in[1]) * inx2[2]; out[4] = ((uint128_t) in[0]) * inx2[4] + - ((uint128_t) in[1]) * inx2[3] + - ((uint128_t) in[2]) * in[2]; + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; out[5] = ((uint128_t) in[0]) * inx2[5] + - ((uint128_t) in[1]) * inx2[4] + - ((uint128_t) in[2]) * inx2[3]; + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; out[6] = ((uint128_t) in[0]) * inx2[6] + - ((uint128_t) in[1]) * inx2[5] + - ((uint128_t) in[2]) * inx2[4] + - ((uint128_t) in[3]) * in[3]; + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; out[7] = ((uint128_t) in[0]) * inx2[7] + - ((uint128_t) in[1]) * inx2[6] + - ((uint128_t) in[2]) * inx2[5] + - ((uint128_t) in[3]) * inx2[4]; + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; out[8] = ((uint128_t) in[0]) * inx2[8] + - ((uint128_t) in[1]) * inx2[7] + - ((uint128_t) in[2]) * inx2[6] + - ((uint128_t) in[3]) * inx2[5] + - ((uint128_t) in[4]) * in[4]; + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; - /* The remaining limbs fall above 2^521, with the first falling at + /* + * The remaining limbs fall above 2^521, with the first falling at * 2^522. They correspond to locations one bit up from the limbs * produced above so we would have to multiply by two to align them. * Again, rather than operate on the 128-bit result, we double one of - * the inputs to the multiplication. If we want to double for both this - * reason, and the reason above, then we end up multiplying by four. */ + * the inputs to the multiplication. If we want to double for both + * this reason, and the reason above, then we end up multiplying by + * four. + */ /* 9 */ out[0] += ((uint128_t) in[1]) * inx4[8] + - ((uint128_t) in[2]) * inx4[7] + - ((uint128_t) in[3]) * inx4[6] + - ((uint128_t) in[4]) * inx4[5]; + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + + ((uint128_t) in[4]) * inx4[5]; /* 10 */ out[1] += ((uint128_t) in[2]) * inx4[8] + - ((uint128_t) in[3]) * inx4[7] + - ((uint128_t) in[4]) * inx4[6] + - ((uint128_t) in[5]) * inx2[5]; + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + + ((uint128_t) in[5]) * inx2[5]; /* 11 */ out[2] += ((uint128_t) in[3]) * inx4[8] + - ((uint128_t) in[4]) * inx4[7] + - ((uint128_t) in[5]) * inx4[6]; + ((uint128_t) in[4]) * inx4[7] + + ((uint128_t) in[5]) * inx4[6]; /* 12 */ out[3] += ((uint128_t) in[4]) * inx4[8] + - ((uint128_t) in[5]) * inx4[7] + - ((uint128_t) in[6]) * inx2[6]; + ((uint128_t) in[5]) * inx4[7] + + ((uint128_t) in[6]) * inx2[6]; /* 13 */ out[4] += ((uint128_t) in[5]) * inx4[8] + - ((uint128_t) in[6]) * inx4[7]; + ((uint128_t) in[6]) * inx4[7]; /* 14 */ out[5] += ((uint128_t) in[6]) * inx4[8] + - ((uint128_t) in[7]) * inx2[7]; + ((uint128_t) in[7]) * inx2[7]; /* 15 */ out[6] += ((uint128_t) in[7]) * inx4[8]; /* 16 */ out[7] += ((uint128_t) in[8]) * inx2[8]; - } +} /* felem_mul sets |out| = |in1| * |in2| * On entry: @@ -481,111 +496,112 @@ static void felem_square(largefelem out, const felem in) * On exit: * out[i] < 17 * max(in1[i]) * max(in2[i]) */ -static void felem_mul(largefelem out, const felem in1, const felem in2) - { +static void +felem_mul(largefelem out, const felem in1, const felem in2) +{ felem in2x2; felem_scalar(in2x2, in2, 2); out[0] = ((uint128_t) in1[0]) * in2[0]; out[1] = ((uint128_t) in1[0]) * in2[1] + - ((uint128_t) in1[1]) * in2[0]; + ((uint128_t) in1[1]) * in2[0]; out[2] = ((uint128_t) in1[0]) * in2[2] + - ((uint128_t) in1[1]) * in2[1] + - ((uint128_t) in1[2]) * in2[0]; + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; out[3] = ((uint128_t) in1[0]) * in2[3] + - ((uint128_t) in1[1]) * in2[2] + - ((uint128_t) in1[2]) * in2[1] + - ((uint128_t) in1[3]) * in2[0]; + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; out[4] = ((uint128_t) in1[0]) * in2[4] + - ((uint128_t) in1[1]) * in2[3] + - ((uint128_t) in1[2]) * in2[2] + - ((uint128_t) in1[3]) * in2[1] + - ((uint128_t) in1[4]) * in2[0]; + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; out[5] = ((uint128_t) in1[0]) * in2[5] + - ((uint128_t) in1[1]) * in2[4] + - ((uint128_t) in1[2]) * in2[3] + - ((uint128_t) in1[3]) * in2[2] + - ((uint128_t) in1[4]) * in2[1] + - ((uint128_t) in1[5]) * in2[0]; + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; out[6] = ((uint128_t) in1[0]) * in2[6] + - ((uint128_t) in1[1]) * in2[5] + - ((uint128_t) in1[2]) * in2[4] + - ((uint128_t) in1[3]) * in2[3] + - ((uint128_t) in1[4]) * in2[2] + - ((uint128_t) in1[5]) * in2[1] + - ((uint128_t) in1[6]) * in2[0]; + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; out[7] = ((uint128_t) in1[0]) * in2[7] + - ((uint128_t) in1[1]) * in2[6] + - ((uint128_t) in1[2]) * in2[5] + - ((uint128_t) in1[3]) * in2[4] + - ((uint128_t) in1[4]) * in2[3] + - ((uint128_t) in1[5]) * in2[2] + - ((uint128_t) in1[6]) * in2[1] + - ((uint128_t) in1[7]) * in2[0]; + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; out[8] = ((uint128_t) in1[0]) * in2[8] + - ((uint128_t) in1[1]) * in2[7] + - ((uint128_t) in1[2]) * in2[6] + - ((uint128_t) in1[3]) * in2[5] + - ((uint128_t) in1[4]) * in2[4] + - ((uint128_t) in1[5]) * in2[3] + - ((uint128_t) in1[6]) * in2[2] + - ((uint128_t) in1[7]) * in2[1] + - ((uint128_t) in1[8]) * in2[0]; + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; /* See comment in felem_square about the use of in2x2 here */ out[0] += ((uint128_t) in1[1]) * in2x2[8] + - ((uint128_t) in1[2]) * in2x2[7] + - ((uint128_t) in1[3]) * in2x2[6] + - ((uint128_t) in1[4]) * in2x2[5] + - ((uint128_t) in1[5]) * in2x2[4] + - ((uint128_t) in1[6]) * in2x2[3] + - ((uint128_t) in1[7]) * in2x2[2] + - ((uint128_t) in1[8]) * in2x2[1]; + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; out[1] += ((uint128_t) in1[2]) * in2x2[8] + - ((uint128_t) in1[3]) * in2x2[7] + - ((uint128_t) in1[4]) * in2x2[6] + - ((uint128_t) in1[5]) * in2x2[5] + - ((uint128_t) in1[6]) * in2x2[4] + - ((uint128_t) in1[7]) * in2x2[3] + - ((uint128_t) in1[8]) * in2x2[2]; + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; out[2] += ((uint128_t) in1[3]) * in2x2[8] + - ((uint128_t) in1[4]) * in2x2[7] + - ((uint128_t) in1[5]) * in2x2[6] + - ((uint128_t) in1[6]) * in2x2[5] + - ((uint128_t) in1[7]) * in2x2[4] + - ((uint128_t) in1[8]) * in2x2[3]; + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; out[3] += ((uint128_t) in1[4]) * in2x2[8] + - ((uint128_t) in1[5]) * in2x2[7] + - ((uint128_t) in1[6]) * in2x2[6] + - ((uint128_t) in1[7]) * in2x2[5] + - ((uint128_t) in1[8]) * in2x2[4]; + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; out[4] += ((uint128_t) in1[5]) * in2x2[8] + - ((uint128_t) in1[6]) * in2x2[7] + - ((uint128_t) in1[7]) * in2x2[6] + - ((uint128_t) in1[8]) * in2x2[5]; + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; out[5] += ((uint128_t) in1[6]) * in2x2[8] + - ((uint128_t) in1[7]) * in2x2[7] + - ((uint128_t) in1[8]) * in2x2[6]; + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; out[6] += ((uint128_t) in1[7]) * in2x2[8] + - ((uint128_t) in1[8]) * in2x2[7]; + ((uint128_t) in1[8]) * in2x2[7]; out[7] += ((uint128_t) in1[8]) * in2x2[8]; - } +} static const limb bottom52bits = 0xfffffffffffff; @@ -595,8 +611,9 @@ static const limb bottom52bits = 0xfffffffffffff; * On exit: * out[i] < 2^59 + 2^14 */ -static void felem_reduce(felem out, const largefelem in) - { +static void +felem_reduce(felem out, const largefelem in) +{ u64 overflow1, overflow2; out[0] = ((limb) in[0]) & bottom58bits; @@ -613,8 +630,9 @@ static void felem_reduce(felem out, const largefelem in) out[1] += ((limb) in[0]) >> 58; out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; - /* out[1] < 2^58 + 2^6 + 2^58 - * = 2^59 + 2^6 */ + /* + * out[1] < 2^58 + 2^6 + 2^58 = 2^59 + 2^6 + */ out[2] += ((limb) (in[0] >> 64)) >> 52; out[2] += ((limb) in[1]) >> 58; @@ -643,39 +661,43 @@ static void felem_reduce(felem out, const largefelem in) out[8] += ((limb) in[7]) >> 58; out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; - /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 - * < 2^59 + 2^13 */ + /* + * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 < 2^59 + 2^13 + */ overflow1 = ((limb) (in[7] >> 64)) >> 52; overflow1 += ((limb) in[8]) >> 58; overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; overflow2 = ((limb) (in[8] >> 64)) >> 52; - overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ - overflow2 <<= 1; /* overflow2 < 2^13 */ + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ - out[0] += overflow1; /* out[0] < 2^60 */ - out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - /* out[0] < 2^58 - * out[1] < 2^59 + 2^6 + 2^13 + 2^2 - * < 2^59 + 2^14 */ - } + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + /* + * out[0] < 2^58 out[1] < 2^59 + 2^6 + 2^13 + 2^2 < 2^59 + 2^14 + */ +} -static void felem_square_reduce(felem out, const felem in) - { +static void +felem_square_reduce(felem out, const felem in) +{ largefelem tmp; felem_square(tmp, in); felem_reduce(out, tmp); - } +} -static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { +static void +felem_mul_reduce(felem out, const felem in1, const felem in2) +{ largefelem tmp; felem_mul(tmp, in1, in2); felem_reduce(out, tmp); - } +} /* felem_inv calculates |out| = |in|^{-1} * @@ -684,117 +706,153 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2) * a^{p-1} = 1 (mod p) * a^{p-2} = a^{-1} (mod p) */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2, ftmp3, ftmp4; largefelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */ felem_assign(ftmp2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^4 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ felem_assign(ftmp2, ftmp3); - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ felem_assign(ftmp4, ftmp3); - felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 8; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 16; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 32; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 64; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + for (i = 0; i < 64; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 128; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + for (i = 0; i < 128; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 256; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + for (i = 0; i < 256; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ - for (i = 0; i < 9; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ - felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ + for (i = 0; i < 9; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); + felem_reduce(out, tmp); /* 2^512 - 3 */ } /* This is 2^521-1, expressed as an felem */ static const felem kPrime = - { +{ 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff - }; +}; /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * in[i] < 2^59 + 2^14 */ -static limb felem_is_zero(const felem in) - { +static limb +felem_is_zero(const felem in) +{ felem ftmp; limb is_zero, is_p; felem_assign(ftmp, in); - ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; + ftmp[0] += ftmp[8] >> 57; + ftmp[8] &= bottom57bits; /* ftmp[8] < 2^57 */ - ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; - ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; - ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; - ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; - ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; - ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; - ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; - ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; + ftmp[1] += ftmp[0] >> 58; + ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; + ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; + ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; + ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; + ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; + ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; + ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; + ftmp[7] &= bottom58bits; /* ftmp[8] < 2^57 + 4 */ - /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is - * greater than our bound for ftmp[8]. Therefore we only have to check - * if the zero is zero or 2^521-1. */ + /* + * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is + * greater than our bound for ftmp[8]. Therefore we only have to + * check if the zero is zero or 2^521-1. + */ is_zero = 0; is_zero |= ftmp[0]; @@ -808,8 +866,10 @@ static limb felem_is_zero(const felem in) is_zero |= ftmp[8]; is_zero--; - /* We know that ftmp[i] < 2^63, therefore the only way that the top bit - * can be set is if is_zero was 0 before the decrement. */ + /* + * We know that ftmp[i] < 2^63, therefore the only way that the top + * bit can be set is if is_zero was 0 before the decrement. + */ is_zero = ((s64) is_zero) >> 63; is_p = ftmp[0] ^ kPrime[0]; @@ -827,41 +887,57 @@ static limb felem_is_zero(const felem in) is_zero |= is_p; return is_zero; - } +} -static int felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +static int +felem_is_zero_int(const felem in) +{ + return (int) (felem_is_zero(in) & ((limb) 1)); +} /* felem_contract converts |in| to its unique, minimal representation. * On entry: * in[i] < 2^59 + 2^14 */ -static void felem_contract(felem out, const felem in) - { +static void +felem_contract(felem out, const felem in) +{ limb is_p, is_greater, sign; - static const limb two58 = ((limb)1) << 58; + static const limb two58 = ((limb) 1) << 58; felem_assign(out, in); - out[0] += out[8] >> 57; out[8] &= bottom57bits; + out[0] += out[8] >> 57; + out[8] &= bottom57bits; /* out[8] < 2^57 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - out[2] += out[1] >> 58; out[1] &= bottom58bits; - out[3] += out[2] >> 58; out[2] &= bottom58bits; - out[4] += out[3] >> 58; out[3] &= bottom58bits; - out[5] += out[4] >> 58; out[4] &= bottom58bits; - out[6] += out[5] >> 58; out[5] &= bottom58bits; - out[7] += out[6] >> 58; out[6] &= bottom58bits; - out[8] += out[7] >> 58; out[7] &= bottom58bits; + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + out[2] += out[1] >> 58; + out[1] &= bottom58bits; + out[3] += out[2] >> 58; + out[2] &= bottom58bits; + out[4] += out[3] >> 58; + out[3] &= bottom58bits; + out[5] += out[4] >> 58; + out[4] &= bottom58bits; + out[6] += out[5] >> 58; + out[5] &= bottom58bits; + out[7] += out[6] >> 58; + out[6] &= bottom58bits; + out[8] += out[7] >> 58; + out[7] &= bottom58bits; /* out[8] < 2^57 + 4 */ - /* If the value is greater than 2^521-1 then we have to subtract + /* + * If the value is greater than 2^521-1 then we have to subtract * 2^521-1 out. See the comments in felem_is_zero regarding why we - * don't test for other multiples of the prime. */ + * don't test for other multiples of the prime. + */ - /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ + /* + * First, if |out| is equal to 2^521-1, we subtract it out to get + * zero. + */ is_p = out[0] ^ kPrime[0]; is_p |= out[1] ^ kPrime[1]; @@ -895,8 +971,10 @@ static void felem_contract(felem out, const felem in) out[7] &= is_p; out[8] &= is_p; - /* In order to test that |out| >= 2^521-1 we need only test if out[8] - * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ + /* + * In order to test that |out| >= 2^521-1 we need only test if out[8] + * >> 57 is greater than zero as (2^521-1) + x >= 2^522 + */ is_greater = out[8] >> 57; is_greater |= is_greater << 32; is_greater |= is_greater << 16; @@ -917,18 +995,40 @@ static void felem_contract(felem out, const felem in) out[8] -= kPrime[8] & is_greater; /* Eliminate negative coefficients */ - sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); - sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); - sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); - sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); - sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); - sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - } + sign = -(out[0] >> 63); + out[0] += (two58 & sign); + out[1] -= (1 & sign); + sign = -(out[1] >> 63); + out[1] += (two58 & sign); + out[2] -= (1 & sign); + sign = -(out[2] >> 63); + out[2] += (two58 & sign); + out[3] -= (1 & sign); + sign = -(out[3] >> 63); + out[3] += (two58 & sign); + out[4] -= (1 & sign); + sign = -(out[4] >> 63); + out[4] += (two58 & sign); + out[5] -= (1 & sign); + sign = -(out[0] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); + sign = -(out[5] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); +} /* Group operations * ---------------- @@ -946,8 +1046,8 @@ static void felem_contract(felem out, const felem in) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ largefelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; @@ -956,15 +1056,15 @@ point_double(felem x_out, felem y_out, felem z_out, /* delta = z^2 */ felem_square(tmp, z_in); - felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ /* gamma = y^2 */ felem_square(tmp, y_in); - felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ /* beta = x*gamma */ felem_mul(tmp, x_in, gamma); - felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + felem_reduce(beta, tmp);/* beta[i] < 2^59 + 2^14 */ /* alpha = 3*(x-delta)*(x+delta) */ felem_diff64(ftmp, delta); @@ -974,17 +1074,17 @@ point_double(felem x_out, felem y_out, felem z_out, felem_scalar64(ftmp2, 3); /* ftmp2[i] < 3*2^60 + 3*2^15 */ felem_mul(tmp, ftmp, ftmp2); - /* tmp[i] < 17(3*2^121 + 3*2^76) - * = 61*2^121 + 61*2^76 - * < 64*2^121 + 64*2^76 - * = 2^127 + 2^82 - * < 2^128 */ + /* + * tmp[i] < 17(3*2^121 + 3*2^76) = 61*2^121 + 61*2^76 < 64*2^121 + + * 64*2^76 = 2^127 + 2^82 < 2^128 + */ felem_reduce(alpha, tmp); /* x' = alpha^2 - 8*beta */ felem_square(tmp, alpha); - /* tmp[i] < 17*2^120 - * < 2^125 */ + /* + * tmp[i] < 17*2^120 < 2^125 + */ felem_assign(ftmp, beta); felem_scalar64(ftmp, 8); /* ftmp[i] < 2^62 + 2^17 */ @@ -999,8 +1099,9 @@ point_double(felem x_out, felem y_out, felem z_out, felem_sum64(ftmp, z_in); /* ftmp[i] < 2^60 + 2^15 */ felem_square(tmp, ftmp); - /* tmp[i] < 17(2^122) - * < 2^127 */ + /* + * tmp[i] < 17(2^122) < 2^127 + */ felem_diff_128_64(tmp, delta); /* tmp[i] < 2^127 + 2^63 */ felem_reduce(z_out, tmp); @@ -1011,36 +1112,39 @@ point_double(felem x_out, felem y_out, felem z_out, felem_diff64(beta, x_out); /* beta[i] < 2^61 + 2^60 + 2^16 */ felem_mul(tmp, alpha, beta); - /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) - * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) - * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * < 2^128 */ + /* + * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) = 17*(2^120 + 2^75 + * + 2^119 + 2^74 + 2^75 + 2^30) = 17*(2^120 + 2^119 + 2^76 + 2^74 + + * 2^30) < 2^128 + */ felem_square(tmp2, gamma); - /* tmp2[i] < 17*(2^59 + 2^14)^2 - * = 17*(2^118 + 2^74 + 2^28) */ + /* + * tmp2[i] < 17*(2^59 + 2^14)^2 = 17*(2^118 + 2^74 + 2^28) + */ felem_scalar128(tmp2, 8); - /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) - * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 - * < 2^126 */ + /* + * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) = 2^125 + 2^121 + 2^81 + 2^77 + * + 2^35 + 2^31 < 2^126 + */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + - * 2^74 + 2^69 + 2^34 + 2^30 - * < 2^128 */ + /* + * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) = + * 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + 2^74 + * + 2^69 + 2^34 + 2^30 < 2^128 + */ felem_reduce(y_out, tmp); - } +} /* copy_conditional copies in to out iff mask is all ones. */ static void copy_conditional(felem out, const felem in, limb mask) - { +{ unsigned i; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { const limb tmp = mask & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) * @@ -1052,10 +1156,11 @@ copy_conditional(felem out, const felem in, limb mask) * are equal (while not equal to the point at infinity). This case never * happens during single point multiplication, so there is no timing leak for * ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; largefelem tmp, tmp2; limb x_equal, y_equal, z1_is_zero, z2_is_zero; @@ -1067,8 +1172,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_square(tmp, z1); felem_reduce(ftmp, tmp); - if (!mixed) - { + if (!mixed) { /* ftmp2 = z2z2 = z2**2 */ felem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -1098,9 +1202,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_mul(tmp, y1, ftmp2); felem_reduce(ftmp6, tmp); - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* u1 = ftmp3 = x1*z2z2 */ @@ -1111,7 +1213,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_assign(ftmp6, y1); - } + } /* u2 = x2*z1z1 */ felem_mul(tmp, x2, ftmp); @@ -1144,12 +1246,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar64(ftmp5, 2); /* ftmp5[i] < 2^61 */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* I = ftmp = (2h)**2 */ felem_assign(ftmp, ftmp4); felem_scalar64(ftmp, 2); @@ -1180,8 +1280,9 @@ static void point_add(felem x3, felem y3, felem z3, /* y_out = r(V-x_out) - 2 * s1 * J */ felem_diff64(ftmp3, x_out); - /* ftmp3[i] < 2^60 + 2^60 - * = 2^61 */ + /* + * ftmp3[i] < 2^60 + 2^60 = 2^61 + */ felem_mul(tmp, ftmp5, ftmp3); /* tmp[i] < 17*2^122 */ felem_mul(tmp2, ftmp6, ftmp2); @@ -1189,9 +1290,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar128(tmp2, 2); /* tmp2[i] < 17*2^121 */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17*2^122 - * = 2^126 - 2^122 - 2^6 - 2^2 - 1 - * < 2^127 */ + /* + * tmp[i] < 2^127 - 2^69 + 17*2^122 = 2^126 - 2^122 - 2^6 - 2^2 - 1 < + * 2^127 + */ felem_reduce(y_out, tmp); copy_conditional(x_out, x2, z1_is_zero); @@ -1203,7 +1305,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* Base point pre computation * -------------------------- @@ -1240,126 +1342,126 @@ static void point_add(felem x3, felem y3, felem z3, /* gmul is the table of precomputed base points */ static const felem gmul[16][3] = - {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, - 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, - 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, - {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, - 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, - 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, - 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, - 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, - {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, - 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, - 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, - 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, - 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, - {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, - 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, - 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, - 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, - 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, - {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, - 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, - 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, - 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, - 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, - {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, - 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, - 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, - 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, - 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, - {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, - 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, - 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, - 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, - 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, - {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, - 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, - 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, - 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, - 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, - {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, - 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, - 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, - 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, - 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, - {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, - 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, - 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, - 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, - 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, - {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, - 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, - 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, - 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, - 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, - {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, - 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, - 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, - 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, - 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, - {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, - 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, - 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, - 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, - 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, - {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, - 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, - 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, - 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, - 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, - {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, - 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, - 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, - 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, - 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, - {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, - 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, - 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; +{{{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, +0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, +{0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, +0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, +0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, +{0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, +0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, +0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, +{0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, +0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, +0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, +{0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, +0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, +0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, +{0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, +0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, +0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, +{0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, +0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, +0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, +{0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, +0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, +0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, +{0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, +0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, +0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, +{0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, +0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, +0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, +{0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, +0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, +0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, +{0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, +0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, +0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, +{0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, +0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, +0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, +{0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, +0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, +0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, +{0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, +0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, +0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, +{0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, +0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}}; /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], - felem out[3]) - { +static void +select_point(const limb idx, unsigned int size, const felem pre_comp[ /* size */ ][3], + felem out[3]) +{ unsigned i, j; limb *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(felem)); - for (i = 0; i < size; i++) - { + for (i = 0; i < size; i++) { const limb *inlimbs = &pre_comp[i][0][0]; limb mask = i ^ idx; mask |= mask >> 4; @@ -1369,26 +1471,28 @@ static void select_point(const limb idx, unsigned int size, const felem pre_comp mask--; for (j = 0; j < NLIMBS * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, int i) - { +static char +get_bit(const felem_bytearray in, int i) +{ if (i < 0) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) +{ int i, skip; unsigned num, gen_mul = (g_scalar != NULL); felem nq[3], tmp[4]; @@ -1398,48 +1502,41 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (last quarter of rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (last quarter of rounds) and additions + * of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 520 : 130); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 520 : 130); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 130)) - { + if (gen_mul && (i <= 130)) { bits = get_bit(g_scalar, i + 390) << 3; - if (i < 130) - { + if (i < 130) { bits |= get_bit(g_scalar, i + 260) << 2; bits |= get_bit(g_scalar, i + 130) << 1; bits |= get_bit(g_scalar, i); - } + } /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp, tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } - + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1448,29 +1545,30 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, bits |= get_bit(scalars[num], i - 1); ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - /* select the point to add or subtract, in constant time */ + /* + * select the point to add or subtract, in + * constant time + */ select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_conditional(tmp[1], tmp[3], (-(limb) sign)); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /* Precomputation for the group generator. */ @@ -1493,20 +1591,20 @@ EC_GFp_nistp521_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_nistp521_point_get_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -1530,32 +1628,34 @@ EC_GFp_nistp521_method(void) /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP521_PRE_COMP *nistp521_pre_comp_new() - { +static NISTP521_PRE_COMP * +nistp521_pre_comp_new() +{ NISTP521_PRE_COMP *ret = NULL; - ret = (NISTP521_PRE_COMP *)malloc(sizeof(NISTP521_PRE_COMP)); - if (!ret) - { + ret = (NISTP521_PRE_COMP *) malloc(sizeof(NISTP521_PRE_COMP)); + if (!ret) { ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp521_pre_comp_dup(void *src_) - { +static void * +nistp521_pre_comp_dup(void *src_) +{ NISTP521_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp521_pre_comp_free(void *pre_) - { +static void +nistp521_pre_comp_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1567,10 +1667,11 @@ static void nistp521_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp521_pre_comp_clear_free(void *pre_) - { +static void +nistp521_pre_comp_clear_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1583,43 +1684,46 @@ static void nistp521_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof(*pre)); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp521_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp521_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp521_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_521; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1627,74 +1731,79 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in, x_out, y_out; largefelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { - if (!felem_to_BN(x, x_out)) - { + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); return 0; - } } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { - if (!felem_to_BN(y, y_out)) - { + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); return 0; - } } - return 1; } + return 1; +} -static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } + num, + points, + sizeof(felem), + tmp_felems, + (void (*) (void *)) felem_one, + (int (*) (const void *)) felem_is_zero_int, + (void (*) (void *, const void *)) felem_assign, + (void (*) (void *, const void *)) felem_square_reduce, + (void (*) (void *, const void *, const void *)) felem_mul_reduce, + (void (*) (void *, const void *)) felem_inv, + (void (*) (void *, const void *)) felem_contract); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp521_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; int mixed = 0; @@ -1702,7 +1811,7 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; + felem(*pre_comp)[17][3] = NULL; felem *tmp_felems = NULL; felem_bytearray tmp; unsigned i, num_bytes; @@ -1710,178 +1819,170 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, size_t num_points = num; felem x_in, y_in, z_in, x_out, y_out, z_out; NISTP521_PRE_COMP *pre = NULL; - felem (*g_pre_comp)[3] = NULL; + felem(*g_pre_comp)[3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp521_pre_comp_dup, nistp521_pre_comp_free, - nistp521_pre_comp_clear_free); + nistp521_pre_comp_dup, nistp521_pre_comp_free, + nistp521_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ g_pre_comp = &pre->g_pre_comp[0]; else /* try to use the standard precomputation */ - g_pre_comp = (felem (*)[3]) gmul; + g_pre_comp = (felem(*)[3]) gmul; generator = EC_POINT_new(group); if (generator == NULL) goto err; /* get the generator from precomputation */ if (!felem_to_BN(x, g_pre_comp[1][0]) || - !felem_to_BN(y, g_pre_comp[1][1]) || - !felem_to_BN(z, g_pre_comp[1][2])) - { + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points++; - } - - if (num_points > 0) - { - if (num_points >= 2) - { - /* unless we precompute multiples for just one point, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 2) { + /* + * unless we precompute multiples for just one point, + * converting those into affine form is time well + * spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); if (mixed) tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) - /* we didn't have a valid precomputation, so we pick - * the generator */ - { + /* + * we didn't have a valid precomputation, so + * we pick the generator + */ + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof(g_secret)); /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - (const felem (*)[3]) g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3]) pre_comp, + (const felem(*)[3]) g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { + (!felem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -1897,10 +1998,11 @@ err: if (tmp_felems != NULL) free(tmp_felems); return ret; - } +} -int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp521_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP521_PRE_COMP *pre = NULL; int i, j; @@ -1911,95 +2013,93 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free); + nistp521_pre_comp_free, nistp521_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp521_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) + (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) goto err; /* compute 2^130*G, 2^260*G, 2^390*G */ - for (i = 1; i <= 4; i <<= 1) - { - point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], - pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); - for (j = 0; j < 129; ++j) - { - point_double(pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], - pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2]); - } + for (i = 1; i <= 4; i <<= 1) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) { + point_double(pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2]); } + } /* g_pre_comp[0] is the point at infinity */ memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); /* the remaining multiples */ /* 2^130*G + 2^260*G */ point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], - pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], - pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^130*G + 2^390*G */ point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], - pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], - pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], - pre->g_pre_comp[4][2]); + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); /* 2^130*G + 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], - pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], - pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - for (i = 1; i < 8; ++i) - { + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) { /* odd multiples: add G */ - point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], - pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], - 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], - pre->g_pre_comp[1][2]); - } + point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1], + pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], + 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -2008,18 +2108,19 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp521_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp521_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free) - != NULL) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libcrypto/ec/ecp_nistputil.c b/lib/libcrypto/ec/ecp_nistputil.c index c8140c807fb..0312fb16add 100644 --- a/lib/libcrypto/ec/ecp_nistputil.c +++ b/lib/libcrypto/ec/ecp_nistputil.c @@ -41,16 +41,17 @@ * tmp_felems needs to point to a temporary array of 'num'+1 field elements * for storage of intermediate values. */ -void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, - size_t felem_size, void *tmp_felems, - void (*felem_one)(void *out), - int (*felem_is_zero)(const void *in), - void (*felem_assign)(void *out, const void *in), - void (*felem_square)(void *out, const void *in), - void (*felem_mul)(void *out, const void *in1, const void *in2), - void (*felem_inv)(void *out, const void *in), - void (*felem_contract)(void *out, const void *in)) - { +void +ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one) (void *out), + int (*felem_is_zero) (const void *in), + void (*felem_assign) (void *out, const void *in), + void (*felem_square) (void *out, const void *in), + void (*felem_mul) (void *out, const void *in1, const void *in2), + void (*felem_inv) (void *out, const void *in), + void (*felem_contract) (void *out, const void *in)) +{ int i = 0; #define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) @@ -62,50 +63,59 @@ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, felem_assign(tmp_felem(0), Z(0)); else felem_one(tmp_felem(0)); - for (i = 1; i < (int)num; i++) - { + for (i = 1; i < (int) num; i++) { if (!felem_is_zero(Z(i))) - felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); + felem_mul(tmp_felem(i), tmp_felem(i - 1), Z(i)); else - felem_assign(tmp_felem(i), tmp_felem(i-1)); - } - /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: - * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ + felem_assign(tmp_felem(i), tmp_felem(i - 1)); + } + /* + * Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any + * zero-valued factors: if Z(i) = 0, we essentially pretend that Z(i) + * = 1 + */ - felem_inv(tmp_felem(num-1), tmp_felem(num-1)); - for (i = num - 1; i >= 0; i--) - { + felem_inv(tmp_felem(num - 1), tmp_felem(num - 1)); + for (i = num - 1; i >= 0; i--) { if (i > 0) - /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), - * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) + /* + * tmp_felem(i-1) is the product of Z(0) .. Z(i-1), + * tmp_felem(i) is the inverse of the product of Z(0) + * .. Z(i) */ - felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ + felem_mul(tmp_felem(num), tmp_felem(i - 1), tmp_felem(i)); /* 1/Z(i) */ else - felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ - if (!felem_is_zero(Z(i))) - { + if (!felem_is_zero(Z(i))) { if (i > 0) - /* For next iteration, replace tmp_felem(i-1) by its inverse */ - felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); + /* + * For next iteration, replace tmp_felem(i-1) + * by its inverse + */ + felem_mul(tmp_felem(i - 1), tmp_felem(i), Z(i)); - /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ - felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ - felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ - felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ - felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + /* + * Convert point (X, Y, Z) into affine form (X/(Z^2), + * Y/(Z^3), 1) + */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ felem_contract(X(i), X(i)); felem_contract(Y(i), Y(i)); felem_one(Z(i)); - } - else - { + } else { if (i > 0) - /* For next iteration, replace tmp_felem(i-1) by its inverse */ - felem_assign(tmp_felem(i-1), tmp_felem(i)); - } + /* + * For next iteration, replace tmp_felem(i-1) + * by its inverse + */ + felem_assign(tmp_felem(i - 1), tmp_felem(i)); } } +} /* * This function looks at 5+1 scalar bits (5 current, 1 adjacent less @@ -180,18 +190,20 @@ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, * has to be b_4 b_3 b_2 b_1 b_0 0. * */ -void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) - { +void +ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) +{ unsigned char s, d; - s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as + * 6-bit value */ d = (1 << 6) - in - 1; d = (d & s) | (in & ~s); d = (d >> 1) + (d & 1); *sign = s & 1; *digit = d; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libcrypto/ec/ecp_oct.c b/lib/libcrypto/ec/ecp_oct.c index a06abbc8cd6..c7719c74132 100644 --- a/lib/libcrypto/ec/ecp_oct.c +++ b/lib/libcrypto/ec/ecp_oct.c @@ -1,6 +1,6 @@ /* crypto/ec/ecp_oct.c */ /* Includes code written by Lenka Fibikova - * for the OpenSSL project. + * for the OpenSSL project. * Includes code written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== @@ -11,7 +11,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -66,23 +66,22 @@ #include "ec_lcl.h" -int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { +int +ec_GFp_simple_set_compressed_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x_, int y_bit, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp1, *tmp2, *x, *y; int ret = 0; - /* clear error queue*/ + /* clear error queue */ ERR_clear_error(); - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } y_bit = (y_bit != 0); BN_CTX_start(ctx); @@ -90,114 +89,117 @@ int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *po tmp2 = BN_CTX_get(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - /* Recover y. We have a Weierstrass equation - * y^2 = x^3 + a*x + b, - * so y is one of the square roots of x^3 + a*x + b. + /* + * Recover y. We have a Weierstrass equation y^2 = x^3 + a*x + b, so + * y is one of the square roots of x^3 + a*x + b. */ /* tmp1 := x^3 */ - if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; - if (group->meth->field_decode == 0) - { + if (!BN_nnmod(x, x_, &group->field, ctx)) + goto err; + if (group->meth->field_decode == 0) { /* field_{sqr,mul} work on standard representation */ - if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; - if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; - } - + if (!group->meth->field_sqr(group, tmp2, x_, ctx)) + goto err; + if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) + goto err; + } else { + if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) + goto err; + if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) + goto err; + } + /* tmp1 := tmp1 + a*x */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; - if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; - if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; - } - else - { + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) + goto err; + if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) + goto err; + if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } else { + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) + goto err; + if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) + goto err; + } else { /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; - } - - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) + goto err; } - + + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } + /* tmp1 := tmp1 + b */ - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; - } - - if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) - { + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) + goto err; + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } else { + if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) + goto err; + } + + if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) { unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) - { + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) { ERR_clear_error(); ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else + } else ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); goto err; - } - - if (y_bit != BN_is_odd(y)) - { - if (BN_is_zero(y)) - { + } + if (y_bit != BN_is_odd(y)) { + if (BN_is_zero(y)) { int kron; kron = BN_kronecker(x, &group->field, ctx); - if (kron == -2) goto err; + if (kron == -2) + goto err; if (kron == 1) ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); else - /* BN_mod_sqrt() should have cought this error (not a square) */ + /* + * BN_mod_sqrt() should have cought this + * error (not a square) + */ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); goto err; - } - if (!BN_usub(y, &group->field, y)) goto err; } - if (y_bit != BN_is_odd(y)) - { + if (!BN_usub(y, &group->field, y)) + goto err; + } + if (y_bit != BN_is_odd(y)) { ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); goto err; - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + } + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +ec_GFp_simple_point2oct(const EC_GROUP * group, const EC_POINT * point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX * ctx) +{ size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; @@ -205,125 +207,106 @@ size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, poi size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { + } + if (EC_POINT_is_at_infinity(group, point)) { /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { + if (buf != NULL) { + if (len < 1) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); return 0; - } - buf[0] = 0; } - return 1; + buf[0] = 0; } - - + return 1; + } /* ret := required output buffer length */ field_len = BN_num_bytes(&group->field); - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { + if (buf != NULL) { + if (len < ret) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); used_ctx = 1; x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) buf[0] = form + 1; else buf[0] = form; - + i = 1; - + skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(x, buf + i); i += skip; - if (i != 1 + field_len) - { + if (i != 1 + field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { + } + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(y, buf + i); i += skip; - } - - if (i != ret) - { + } + if (i != ret) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } } - + } if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - err: +err: if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return 0; - } +} -int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { +int +ec_GFp_simple_oct2point(const EC_GROUP * group, EC_POINT * point, + const unsigned char *buf, size_t len, BN_CTX * ctx) +{ point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; @@ -331,102 +314,84 @@ int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, size_t field_len, enc_len; int ret = 0; - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); return 0; - } + } form = buf[0]; y_bit = form & 1; form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (form == 0) - { - if (len != 1) - { + } + if (form == 0) { + if (len != 1) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - return EC_POINT_set_to_infinity(group, point); } - + return EC_POINT_set_to_infinity(group, point); + } field_len = BN_num_bytes(&group->field); - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; - if (len != enc_len) - { + if (len != enc_len) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, &group->field) >= 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { + } + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, &group->field) >= 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (y_bit != BN_is_odd(y)) - { + } + if (form == POINT_CONVERSION_HYBRID) { + if (y_bit != BN_is_odd(y)) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) { /* test required by + * X9.62 */ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } - +} diff --git a/lib/libcrypto/ec/ecp_smpl.c b/lib/libcrypto/ec/ecp_smpl.c index c99348f08f5..b87410120df 100644 --- a/lib/libcrypto/ec/ecp_smpl.c +++ b/lib/libcrypto/ec/ecp_smpl.c @@ -1,6 +1,6 @@ /* crypto/ec/ecp_smpl.c */ /* Includes code written by Lenka Fibikova - * for the OpenSSL project. + * for the OpenSSL project. * Includes code written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== @@ -11,7 +11,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -80,20 +80,20 @@ EC_GFp_simple_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, - .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, - .point_get_affine_coordinates = - ec_GFp_simple_point_get_affine_coordinates, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + .point_set_affine_coordinates = + ec_GFp_simple_point_set_affine_coordinates, + .point_get_affine_coordinates = + ec_GFp_simple_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -124,212 +124,225 @@ EC_GFp_simple_method(void) */ -int ec_GFp_simple_group_init(EC_GROUP *group) - { +int +ec_GFp_simple_group_init(EC_GROUP * group) +{ BN_init(&group->field); BN_init(&group->a); BN_init(&group->b); group->a_is_minus3 = 0; return 1; - } +} -void ec_GFp_simple_group_finish(EC_GROUP *group) - { +void +ec_GFp_simple_group_finish(EC_GROUP * group) +{ BN_free(&group->field); BN_free(&group->a); BN_free(&group->b); - } +} -void ec_GFp_simple_group_clear_finish(EC_GROUP *group) - { +void +ec_GFp_simple_group_clear_finish(EC_GROUP * group) +{ BN_clear_free(&group->field); BN_clear_free(&group->a); BN_clear_free(&group->b); - } +} -int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { - if (!BN_copy(&dest->field, &src->field)) return 0; - if (!BN_copy(&dest->a, &src->a)) return 0; - if (!BN_copy(&dest->b, &src->b)) return 0; +int +ec_GFp_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ + if (!BN_copy(&dest->field, &src->field)) + return 0; + if (!BN_copy(&dest->a, &src->a)) + return 0; + if (!BN_copy(&dest->b, &src->b)) + return 0; dest->a_is_minus3 = src->a_is_minus3; return 1; - } +} -int ec_GFp_simple_group_set_curve(EC_GROUP *group, - const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_group_set_curve(EC_GROUP * group, + const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_a; - + /* p must be a prime > 3 */ - if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) - { + if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); tmp_a = BN_CTX_get(ctx); - if (tmp_a == NULL) goto err; + if (tmp_a == NULL) + goto err; /* group->field */ - if (!BN_copy(&group->field, p)) goto err; + if (!BN_copy(&group->field, p)) + goto err; BN_set_negative(&group->field, 0); /* group->a */ - if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; - if (group->meth->field_encode) - { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; } - else - if (!BN_copy(&group->a, tmp_a)) goto err; - + if (!BN_nnmod(tmp_a, a, p, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) + goto err; + } else if (!BN_copy(&group->a, tmp_a)) + goto err; + /* group->b */ - if (!BN_nnmod(&group->b, b, p, ctx)) goto err; + if (!BN_nnmod(&group->b, b, p, ctx)) + goto err; if (group->meth->field_encode) - if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err; - + if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) + goto err; + /* group->a_is_minus3 */ - if (!BN_add_word(tmp_a, 3)) goto err; + if (!BN_add_word(tmp_a, 3)) + goto err; group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_group_get_curve(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; - - if (p != NULL) - { - if (!BN_copy(p, &group->field)) return 0; - } - if (a != NULL || b != NULL) - { - if (group->meth->field_decode) - { - if (ctx == NULL) - { + if (p != NULL) { + if (!BN_copy(p, &group->field)) + return 0; + } + if (a != NULL || b != NULL) { + if (group->meth->field_decode) { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - if (a != NULL) - { - if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; - } - if (b != NULL) - { - if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; - } } - else - { - if (a != NULL) - { - if (!BN_copy(a, &group->a)) goto err; - } - if (b != NULL) - { - if (!BN_copy(b, &group->b)) goto err; - } + if (a != NULL) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + } + if (b != NULL) { + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } + } else { + if (a != NULL) { + if (!BN_copy(a, &group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, &group->b)) + goto err; } } - + } ret = 1; - - err: + +err: if (new_ctx) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_group_get_degree(const EC_GROUP *group) - { +int +ec_GFp_simple_group_get_degree(const EC_GROUP * group) +{ return BN_num_bits(&group->field); - } +} -int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; - BIGNUM *a,*b,*order,*tmp_1,*tmp_2; + BIGNUM *a, *b, *order, *tmp_1, *tmp_2; const BIGNUM *p = &group->field; BN_CTX *new_ctx = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); a = BN_CTX_get(ctx); b = BN_CTX_get(ctx); tmp_1 = BN_CTX_get(ctx); tmp_2 = BN_CTX_get(ctx); order = BN_CTX_get(ctx); - if (order == NULL) goto err; + if (order == NULL) + goto err; - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; - if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; - } - else - { - if (!BN_copy(a, &group->a)) goto err; - if (!BN_copy(b, &group->b)) goto err; - } - - /* check the discriminant: - * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) - * 0 =< a, b < p */ - if (BN_is_zero(a)) - { - if (BN_is_zero(b)) goto err; - } - else if (!BN_is_zero(b)) - { - if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err; - if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err; - if (!BN_lshift(tmp_1, tmp_2, 2)) goto err; + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } else { + if (!BN_copy(a, &group->a)) + goto err; + if (!BN_copy(b, &group->b)) + goto err; + } + + /* + * check the discriminant: y^2 = x^3 + a*x + b is an elliptic curve + * <=> 4*a^3 + 27*b^2 != 0 (mod p) 0 =< a, b < p + */ + if (BN_is_zero(a)) { + if (BN_is_zero(b)) + goto err; + } else if (!BN_is_zero(b)) { + if (!BN_mod_sqr(tmp_1, a, p, ctx)) + goto err; + if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) + goto err; + if (!BN_lshift(tmp_1, tmp_2, 2)) + goto err; /* tmp_1 = 4*a^3 */ - if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err; - if (!BN_mul_word(tmp_2, 27)) goto err; + if (!BN_mod_sqr(tmp_2, b, p, ctx)) + goto err; + if (!BN_mul_word(tmp_2, 27)) + goto err; /* tmp_2 = 27*b^2 */ - if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err; - if (BN_is_zero(a)) goto err; - } + if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) + goto err; + if (BN_is_zero(a)) + goto err; + } ret = 1; err: @@ -338,325 +351,312 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_point_init(EC_POINT *point) - { +int +ec_GFp_simple_point_init(EC_POINT * point) +{ BN_init(&point->X); BN_init(&point->Y); BN_init(&point->Z); point->Z_is_one = 0; return 1; - } +} -void ec_GFp_simple_point_finish(EC_POINT *point) - { +void +ec_GFp_simple_point_finish(EC_POINT * point) +{ BN_free(&point->X); BN_free(&point->Y); BN_free(&point->Z); - } +} -void ec_GFp_simple_point_clear_finish(EC_POINT *point) - { +void +ec_GFp_simple_point_clear_finish(EC_POINT * point) +{ BN_clear_free(&point->X); BN_clear_free(&point->Y); BN_clear_free(&point->Z); point->Z_is_one = 0; - } +} -int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) - { - if (!BN_copy(&dest->X, &src->X)) return 0; - if (!BN_copy(&dest->Y, &src->Y)) return 0; - if (!BN_copy(&dest->Z, &src->Z)) return 0; +int +ec_GFp_simple_point_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (!BN_copy(&dest->X, &src->X)) + return 0; + if (!BN_copy(&dest->Y, &src->Y)) + return 0; + if (!BN_copy(&dest->Z, &src->Z)) + return 0; dest->Z_is_one = src->Z_is_one; return 1; - } +} -int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { +int +ec_GFp_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ point->Z_is_one = 0; BN_zero(&point->Z); return 1; - } +} -int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) - { +int +ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, const BIGNUM * z, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; - - if (ctx == NULL) - { + + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; + } + if (x != NULL) { + if (!BN_nnmod(&point->X, x, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) + goto err; } - - if (x != NULL) - { - if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err; - if (group->meth->field_encode) - { - if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err; - } - } - - if (y != NULL) - { - if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err; - if (group->meth->field_encode) - { - if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err; - } + } + if (y != NULL) { + if (!BN_nnmod(&point->Y, y, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) + goto err; } - - if (z != NULL) - { + } + if (z != NULL) { int Z_is_one; - if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err; + if (!BN_nnmod(&point->Z, z, &group->field, ctx)) + goto err; Z_is_one = BN_is_one(&point->Z); - if (group->meth->field_encode) - { - if (Z_is_one && (group->meth->field_set_to_one != 0)) - { - if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err; - } - else - { - if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err; - } + if (group->meth->field_encode) { + if (Z_is_one && (group->meth->field_set_to_one != 0)) { + if (!group->meth->field_set_to_one(group, &point->Z, ctx)) + goto err; + } else { + if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) + goto err; } - point->Z_is_one = Z_is_one; } - + point->Z_is_one = Z_is_one; + } ret = 1; - - err: + +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) - { +int +ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP * group, const EC_POINT * point, + BIGNUM * x, BIGNUM * y, BIGNUM * z, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; - - if (group->meth->field_decode != 0) - { - if (ctx == NULL) - { + + if (group->meth->field_decode != 0) { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - - if (x != NULL) - { - if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; - } - if (y != NULL) - { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; - } - if (z != NULL) - { - if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err; - } } - else - { - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; - } - if (z != NULL) - { - if (!BN_copy(z, &point->Z)) goto err; - } + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + if (z != NULL) { + if (!group->meth->field_decode(group, z, &point->Z, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; } - + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; + } + if (z != NULL) { + if (!BN_copy(z, &point->Z)) + goto err; + } + } + ret = 1; - err: +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (x == NULL || y == NULL) - { +int +ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) +{ + if (x == NULL || y == NULL) { /* unlike for projective coordinates, we do not tolerate this */ ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); } + return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); +} -int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP * group, const EC_POINT * point, + BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *Z, *Z_1, *Z_2, *Z_3; const BIGNUM *Z_; int ret = 0; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); Z = BN_CTX_get(ctx); Z_1 = BN_CTX_get(ctx); Z_2 = BN_CTX_get(ctx); Z_3 = BN_CTX_get(ctx); - if (Z_3 == NULL) goto err; + if (Z_3 == NULL) + goto err; /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ - - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err; + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, Z, &point->Z, ctx)) + goto err; Z_ = Z; - } - else - { + } else { Z_ = &point->Z; - } - - if (BN_is_one(Z_)) - { - if (group->meth->field_decode) - { - if (x != NULL) - { - if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; - } - if (y != NULL) - { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; - } + } + + if (BN_is_one(Z_)) { + if (group->meth->field_decode) { + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; } - else - { - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; - } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; } } - else - { - if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) - { + } else { + if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); goto err; - } - - if (group->meth->field_encode == 0) - { + } + if (group->meth->field_encode == 0) { /* field_sqr works on standard representation */ - if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err; - } - - if (x != NULL) - { - /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */ - if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err; - } + if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) + goto err; + } - if (y != NULL) - { - if (group->meth->field_encode == 0) - { + if (x != NULL) { + /* + * in the Montgomery case, field_mul will cancel out + * Montgomery factor in X: + */ + if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) + goto err; + } + if (y != NULL) { + if (group->meth->field_encode == 0) { /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err; - } - else - { - if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err; - } - - /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */ - if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err; + if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) + goto err; } + + /* + * in the Montgomery case, field_mul will cancel out + * Montgomery factor in Y: + */ + if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) + goto err; } + } ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_add(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; int ret = 0; - + if (a == b) return EC_POINT_dbl(group, r, a, ctx); if (EC_POINT_is_at_infinity(group, a)) return EC_POINT_copy(r, b); if (EC_POINT_is_at_infinity(group, b)) return EC_POINT_copy(r, a); - + field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); @@ -665,272 +665,321 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con n4 = BN_CTX_get(ctx); n5 = BN_CTX_get(ctx); n6 = BN_CTX_get(ctx); - if (n6 == NULL) goto end; + if (n6 == NULL) + goto end; - /* Note that in this function we must not read components of 'a' or 'b' - * once we have written the corresponding components of 'r'. - * ('r' might be one of 'a' or 'b'.) + /* + * Note that in this function we must not read components of 'a' or + * 'b' once we have written the corresponding components of 'r'. ('r' + * might be one of 'a' or 'b'.) */ /* n1, n2 */ - if (b->Z_is_one) - { - if (!BN_copy(n1, &a->X)) goto end; - if (!BN_copy(n2, &a->Y)) goto end; + if (b->Z_is_one) { + if (!BN_copy(n1, &a->X)) + goto end; + if (!BN_copy(n2, &a->Y)) + goto end; /* n1 = X_a */ /* n2 = Y_a */ - } - else - { - if (!field_sqr(group, n0, &b->Z, ctx)) goto end; - if (!field_mul(group, n1, &a->X, n0, ctx)) goto end; + } else { + if (!field_sqr(group, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n1, &a->X, n0, ctx)) + goto end; /* n1 = X_a * Z_b^2 */ - if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end; - if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end; + if (!field_mul(group, n0, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n2, &a->Y, n0, ctx)) + goto end; /* n2 = Y_a * Z_b^3 */ - } + } /* n3, n4 */ - if (a->Z_is_one) - { - if (!BN_copy(n3, &b->X)) goto end; - if (!BN_copy(n4, &b->Y)) goto end; + if (a->Z_is_one) { + if (!BN_copy(n3, &b->X)) + goto end; + if (!BN_copy(n4, &b->Y)) + goto end; /* n3 = X_b */ /* n4 = Y_b */ - } - else - { - if (!field_sqr(group, n0, &a->Z, ctx)) goto end; - if (!field_mul(group, n3, &b->X, n0, ctx)) goto end; + } else { + if (!field_sqr(group, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n3, &b->X, n0, ctx)) + goto end; /* n3 = X_b * Z_a^2 */ - if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end; - if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end; + if (!field_mul(group, n0, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n4, &b->Y, n0, ctx)) + goto end; /* n4 = Y_b * Z_a^3 */ - } + } /* n5, n6 */ - if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; - if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; + if (!BN_mod_sub_quick(n5, n1, n3, p)) + goto end; + if (!BN_mod_sub_quick(n6, n2, n4, p)) + goto end; /* n5 = n1 - n3 */ /* n6 = n2 - n4 */ - if (BN_is_zero(n5)) - { - if (BN_is_zero(n6)) - { + if (BN_is_zero(n5)) { + if (BN_is_zero(n6)) { /* a is the same point as b */ BN_CTX_end(ctx); ret = EC_POINT_dbl(group, r, a, ctx); ctx = NULL; goto end; - } - else - { + } else { /* a is the inverse of b */ BN_zero(&r->Z); r->Z_is_one = 0; ret = 1; goto end; - } } - + } /* 'n7', 'n8' */ - if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; - if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; + if (!BN_mod_add_quick(n1, n1, n3, p)) + goto end; + if (!BN_mod_add_quick(n2, n2, n4, p)) + goto end; /* 'n7' = n1 + n3 */ /* 'n8' = n2 + n4 */ /* Z_r */ - if (a->Z_is_one && b->Z_is_one) - { - if (!BN_copy(&r->Z, n5)) goto end; - } - else - { - if (a->Z_is_one) - { if (!BN_copy(n0, &b->Z)) goto end; } - else if (b->Z_is_one) - { if (!BN_copy(n0, &a->Z)) goto end; } - else - { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; } - if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end; + if (a->Z_is_one && b->Z_is_one) { + if (!BN_copy(&r->Z, n5)) + goto end; + } else { + if (a->Z_is_one) { + if (!BN_copy(n0, &b->Z)) + goto end; + } else if (b->Z_is_one) { + if (!BN_copy(n0, &a->Z)) + goto end; + } else { + if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) + goto end; } + if (!field_mul(group, &r->Z, n0, n5, ctx)) + goto end; + } r->Z_is_one = 0; /* Z_r = Z_a * Z_b * n5 */ /* X_r */ - if (!field_sqr(group, n0, n6, ctx)) goto end; - if (!field_sqr(group, n4, n5, ctx)) goto end; - if (!field_mul(group, n3, n1, n4, ctx)) goto end; - if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end; + if (!field_sqr(group, n0, n6, ctx)) + goto end; + if (!field_sqr(group, n4, n5, ctx)) + goto end; + if (!field_mul(group, n3, n1, n4, ctx)) + goto end; + if (!BN_mod_sub_quick(&r->X, n0, n3, p)) + goto end; /* X_r = n6^2 - n5^2 * 'n7' */ - + /* 'n9' */ - if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end; - if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; + if (!BN_mod_lshift1_quick(n0, &r->X, p)) + goto end; + if (!BN_mod_sub_quick(n0, n3, n0, p)) + goto end; /* n9 = n5^2 * 'n7' - 2 * X_r */ /* Y_r */ - if (!field_mul(group, n0, n0, n6, ctx)) goto end; - if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ - if (!field_mul(group, n1, n2, n5, ctx)) goto end; - if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; + if (!field_mul(group, n0, n0, n6, ctx)) + goto end; + if (!field_mul(group, n5, n4, n5, ctx)) + goto end; /* now n5 is n5^3 */ + if (!field_mul(group, n1, n2, n5, ctx)) + goto end; + if (!BN_mod_sub_quick(n0, n0, n1, p)) + goto end; if (BN_is_odd(n0)) - if (!BN_add(n0, n0, p)) goto end; + if (!BN_add(n0, n0, p)) + goto end; /* now 0 <= n0 < 2*p, and n0 is even */ - if (!BN_rshift1(&r->Y, n0)) goto end; + if (!BN_rshift1(&r->Y, n0)) + goto end; /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ ret = 1; - end: - if (ctx) /* otherwise we already called BN_CTX_end */ +end: + if (ctx) /* otherwise we already called BN_CTX_end */ BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_dbl(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3; int ret = 0; - - if (EC_POINT_is_at_infinity(group, a)) - { + + if (EC_POINT_is_at_infinity(group, a)) { BN_zero(&r->Z); r->Z_is_one = 0; return 1; - } - + } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); - if (n3 == NULL) goto err; + if (n3 == NULL) + goto err; - /* Note that in this function we must not read components of 'a' - * once we have written the corresponding components of 'r'. - * ('r' might the same as 'a'.) + /* + * Note that in this function we must not read components of 'a' once + * we have written the corresponding components of 'r'. ('r' might + * the same as 'a'.) */ /* n1 */ - if (a->Z_is_one) - { - if (!field_sqr(group, n0, &a->X, ctx)) goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; - if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err; + if (a->Z_is_one) { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, &group->a, p)) + goto err; /* n1 = 3 * X_a^2 + a_curve */ - } - else if (group->a_is_minus3) - { - if (!field_sqr(group, n1, &a->Z, ctx)) goto err; - if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err; - if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err; - if (!field_mul(group, n1, n0, n2, ctx)) goto err; - if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; - if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; - /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) - * = 3 * X_a^2 - 3 * Z_a^4 */ - } - else - { - if (!field_sqr(group, n0, &a->X, ctx)) goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; - if (!field_sqr(group, n1, &a->Z, ctx)) goto err; - if (!field_sqr(group, n1, n1, ctx)) goto err; - if (!field_mul(group, n1, n1, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; + } else if (group->a_is_minus3) { + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!BN_mod_add_quick(n0, &a->X, n1, p)) + goto err; + if (!BN_mod_sub_quick(n2, &a->X, n1, p)) + goto err; + if (!field_mul(group, n1, n0, n2, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, n1, p)) + goto err; + /* + * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) = 3 * X_a^2 - 3 * + * Z_a^4 + */ + } else { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!field_sqr(group, n1, n1, ctx)) + goto err; + if (!field_mul(group, n1, n1, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(n1, n1, n0, p)) + goto err; /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ - } + } /* Z_r */ - if (a->Z_is_one) - { - if (!BN_copy(n0, &a->Y)) goto err; - } - else - { - if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err; - } - if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err; + if (a->Z_is_one) { + if (!BN_copy(n0, &a->Y)) + goto err; + } else { + if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) + goto err; + } + if (!BN_mod_lshift1_quick(&r->Z, n0, p)) + goto err; r->Z_is_one = 0; /* Z_r = 2 * Y_a * Z_a */ /* n2 */ - if (!field_sqr(group, n3, &a->Y, ctx)) goto err; - if (!field_mul(group, n2, &a->X, n3, ctx)) goto err; - if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; + if (!field_sqr(group, n3, &a->Y, ctx)) + goto err; + if (!field_mul(group, n2, &a->X, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n2, n2, 2, p)) + goto err; /* n2 = 4 * X_a * Y_a^2 */ /* X_r */ - if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; - if (!field_sqr(group, &r->X, n1, ctx)) goto err; - if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err; + if (!BN_mod_lshift1_quick(n0, n2, p)) + goto err; + if (!field_sqr(group, &r->X, n1, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) + goto err; /* X_r = n1^2 - 2 * n2 */ - + /* n3 */ - if (!field_sqr(group, n0, n3, ctx)) goto err; - if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; + if (!field_sqr(group, n0, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n3, n0, 3, p)) + goto err; /* n3 = 8 * Y_a^4 */ - + /* Y_r */ - if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err; - if (!field_mul(group, n0, n1, n0, ctx)) goto err; - if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err; + if (!BN_mod_sub_quick(n0, n2, &r->X, p)) + goto err; + if (!field_mul(group, n0, n1, n0, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) + goto err; /* Y_r = n1 * (n2 - X_r) - n3 */ ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GFp_simple_invert(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) /* point is its own inverse */ return 1; - + return BN_usub(&point->Y, &group->field, &point->Y); - } +} -int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { +int +ec_GFp_simple_is_at_infinity(const EC_GROUP * group, const EC_POINT * point) +{ return BN_is_zero(&point->Z); - } +} -int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *rh, *tmp, *Z4, *Z6; @@ -938,199 +987,200 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C if (EC_POINT_is_at_infinity(group, point)) return 1; - + field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); rh = BN_CTX_get(ctx); tmp = BN_CTX_get(ctx); Z4 = BN_CTX_get(ctx); Z6 = BN_CTX_get(ctx); - if (Z6 == NULL) goto err; - - /* We have a curve defined by a Weierstrass equation - * y^2 = x^3 + a*x + b. - * The point to consider is given in Jacobian projective coordinates - * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). - * Substituting this and multiplying by Z^6 transforms the above equation into - * Y^2 = X^3 + a*X*Z^4 + b*Z^6. - * To test this, we add up the right-hand side in 'rh'. + if (Z6 == NULL) + goto err; + + /* + * We have a curve defined by a Weierstrass equation y^2 = x^3 + a*x + * + b. The point to consider is given in Jacobian projective + * coordinates where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). + * Substituting this and multiplying by Z^6 transforms the above + * equation into Y^2 = X^3 + a*X*Z^4 + b*Z^6. To test this, we add up + * the right-hand side in 'rh'. */ /* rh := X^2 */ - if (!field_sqr(group, rh, &point->X, ctx)) goto err; + if (!field_sqr(group, rh, &point->X, ctx)) + goto err; - if (!point->Z_is_one) - { - if (!field_sqr(group, tmp, &point->Z, ctx)) goto err; - if (!field_sqr(group, Z4, tmp, ctx)) goto err; - if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; + if (!point->Z_is_one) { + if (!field_sqr(group, tmp, &point->Z, ctx)) + goto err; + if (!field_sqr(group, Z4, tmp, ctx)) + goto err; + if (!field_mul(group, Z6, Z4, tmp, ctx)) + goto err; /* rh := (rh + a*Z^4)*X */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; - if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; - if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; - } - else - { - if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; - } + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp, Z4, p)) + goto err; + if (!BN_mod_add_quick(tmp, tmp, Z4, p)) + goto err; + if (!BN_mod_sub_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } else { + if (!field_mul(group, tmp, Z4, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } /* rh := rh + b*Z^6 */ - if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; - } - else - { + if (!field_mul(group, tmp, &group->b, Z6, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + } else { /* point->Z_is_one */ /* rh := (rh + a)*X */ - if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; + if (!BN_mod_add_quick(rh, rh, &group->a, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; /* rh := rh + b */ - if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; - } + if (!BN_mod_add_quick(rh, rh, &group->b, p)) + goto err; + } /* 'lh' := Y^2 */ - if (!field_sqr(group, tmp, &point->Y, ctx)) goto err; + if (!field_sqr(group, tmp, &point->Y, ctx)) + goto err; ret = (0 == BN_ucmp(tmp, rh)); - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - /* return values: - * -1 error - * 0 equal (in affine coordinates) - * 1 not equal +int +ec_GFp_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ + /* + * return values: -1 error 0 equal (in affine coordinates) 1 + * not equal */ - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); BN_CTX *new_ctx = NULL; BIGNUM *tmp1, *tmp2, *Za23, *Zb23; const BIGNUM *tmp1_, *tmp2_; int ret = -1; - - if (EC_POINT_is_at_infinity(group, a)) - { - return EC_POINT_is_at_infinity(group, b) ? 0 : 1; - } + if (EC_POINT_is_at_infinity(group, a)) { + return EC_POINT_is_at_infinity(group, b) ? 0 : 1; + } if (EC_POINT_is_at_infinity(group, b)) return 1; - - if (a->Z_is_one && b->Z_is_one) - { - return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; - } + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; + } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); tmp1 = BN_CTX_get(ctx); tmp2 = BN_CTX_get(ctx); Za23 = BN_CTX_get(ctx); Zb23 = BN_CTX_get(ctx); - if (Zb23 == NULL) goto end; + if (Zb23 == NULL) + goto end; - /* We have to decide whether - * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), - * or equivalently, whether - * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). + /* + * We have to decide whether (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, + * Y_b/Z_b^3), or equivalently, whether (X_a*Z_b^2, Y_a*Z_b^3) = + * (X_b*Z_a^2, Y_b*Z_a^3). */ - if (!b->Z_is_one) - { - if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end; - if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end; + if (!b->Z_is_one) { + if (!field_sqr(group, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) + goto end; tmp1_ = tmp1; - } - else + } else tmp1_ = &a->X; - if (!a->Z_is_one) - { - if (!field_sqr(group, Za23, &a->Z, ctx)) goto end; - if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end; + if (!a->Z_is_one) { + if (!field_sqr(group, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->X, Za23, ctx)) + goto end; tmp2_ = tmp2; - } - else + } else tmp2_ = &b->X; - + /* compare X_a*Z_b^2 with X_b*Z_a^2 */ - if (BN_cmp(tmp1_, tmp2_) != 0) - { - ret = 1; /* points differ */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ goto end; - } - - - if (!b->Z_is_one) - { - if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end; - if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end; + } + if (!b->Z_is_one) { + if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) + goto end; /* tmp1_ = tmp1 */ - } - else + } else tmp1_ = &a->Y; - if (!a->Z_is_one) - { - if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end; - if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end; + if (!a->Z_is_one) { + if (!field_mul(group, Za23, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) + goto end; /* tmp2_ = tmp2 */ - } - else + } else tmp2_ = &b->Y; /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ - if (BN_cmp(tmp1_, tmp2_) != 0) - { - ret = 1; /* points differ */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ goto end; - } - + } /* points are equal */ ret = 0; - end: +end: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GFp_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; @@ -1138,38 +1188,38 @@ int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - if (!point->Z_is_one) - { + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!point->Z_is_one) { ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); goto err; - } - + } ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +ec_GFp_simple_points_make_affine(const EC_GROUP * group, size_t num, EC_POINT * points[], BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp0, *tmp1; size_t pow2 = 0; @@ -1180,171 +1230,179 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT if (num == 0) return 1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); tmp0 = BN_CTX_get(ctx); tmp1 = BN_CTX_get(ctx); - if (tmp0 == NULL || tmp1 == NULL) goto err; + if (tmp0 == NULL || tmp1 == NULL) + goto err; - /* Before converting the individual points, compute inverses of all Z values. - * Modular inversion is rather slow, but luckily we can do with a single - * explicit inversion, plus about 3 multiplications per input value. + /* + * Before converting the individual points, compute inverses of all Z + * values. Modular inversion is rather slow, but luckily we can do + * with a single explicit inversion, plus about 3 multiplications per + * input value. */ pow2 = 1; while (num > pow2) pow2 <<= 1; - /* Now pow2 is the smallest power of 2 satifsying pow2 >= num. - * We need twice that. */ + /* + * Now pow2 is the smallest power of 2 satifsying pow2 >= num. We + * need twice that. + */ pow2 <<= 1; heap = malloc(pow2 * sizeof heap[0]); - if (heap == NULL) goto err; - - /* The array is used as a binary tree, exactly as in heapsort: - * - * heap[1] - * heap[2] heap[3] - * heap[4] heap[5] heap[6] heap[7] - * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15] - * - * We put the Z's in the last line; - * then we set each other node to the product of its two child-nodes (where - * empty or 0 entries are treated as ones); - * then we invert heap[1]; - * then we invert each other node by replacing it by the product of its - * parent (after inversion) and its sibling (before inversion). + if (heap == NULL) + goto err; + + /* + * The array is used as a binary tree, exactly as in heapsort: + * + * heap[1] heap[2] heap[3] heap[4] heap[5] + * heap[6] heap[7] heap[8]heap[9] heap[10]heap[11] + * heap[12]heap[13] heap[14] heap[15] + * + * We put the Z's in the last line; then we set each other node to the + * product of its two child-nodes (where empty or 0 entries are + * treated as ones); then we invert heap[1]; then we invert each + * other node by replacing it by the product of its parent (after + * inversion) and its sibling (before inversion). */ heap[0] = NULL; - for (i = pow2/2 - 1; i > 0; i--) + for (i = pow2 / 2 - 1; i > 0; i--) heap[i] = NULL; for (i = 0; i < num; i++) - heap[pow2/2 + i] = &points[i]->Z; - for (i = pow2/2 + num; i < pow2; i++) + heap[pow2 / 2 + i] = &points[i]->Z; + for (i = pow2 / 2 + num; i < pow2; i++) heap[i] = NULL; - + /* set each node to the product of its children */ - for (i = pow2/2 - 1; i > 0; i--) - { + for (i = pow2 / 2 - 1; i > 0; i--) { heap[i] = BN_new(); - if (heap[i] == NULL) goto err; - - if (heap[2*i] != NULL) - { - if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1])) - { - if (!BN_copy(heap[i], heap[2*i])) goto err; - } - else - { - if (BN_is_zero(heap[2*i])) - { - if (!BN_copy(heap[i], heap[2*i + 1])) goto err; - } - else - { + if (heap[i] == NULL) + goto err; + + if (heap[2 * i] != NULL) { + if ((heap[2 * i + 1] == NULL) || BN_is_zero(heap[2 * i + 1])) { + if (!BN_copy(heap[i], heap[2 * i])) + goto err; + } else { + if (BN_is_zero(heap[2 * i])) { + if (!BN_copy(heap[i], heap[2 * i + 1])) + goto err; + } else { if (!group->meth->field_mul(group, heap[i], - heap[2*i], heap[2*i + 1], ctx)) goto err; - } + heap[2 * i], heap[2 * i + 1], ctx)) + goto err; } } } + } /* invert heap[1] */ - if (!BN_is_zero(heap[1])) - { - if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) - { + if (!BN_is_zero(heap[1])) { + if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) { ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); goto err; - } } - if (group->meth->field_encode != 0) - { - /* in the Montgomery case, we just turned R*H (representing H) - * into 1/(R*H), but we need R*(1/H) (representing 1/H); - * i.e. we have need to multiply by the Montgomery factor twice */ - if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; - if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; - } - + } + if (group->meth->field_encode != 0) { + /* + * in the Montgomery case, we just turned R*H (representing + * H) into 1/(R*H), but we need R*(1/H) (representing + * 1/H); i.e. we have need to multiply by the Montgomery + * factor twice + */ + if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) + goto err; + if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) + goto err; + } /* set other heap[i]'s to their inverses */ - for (i = 2; i < pow2/2 + num; i += 2) - { + for (i = 2; i < pow2 / 2 + num; i += 2) { /* i is even */ - if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) - { - if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err; - if (!BN_copy(heap[i], tmp0)) goto err; - if (!BN_copy(heap[i + 1], tmp1)) goto err; - } - else - { - if (!BN_copy(heap[i], heap[i/2])) goto err; - } + if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) { + if (!group->meth->field_mul(group, tmp0, heap[i / 2], heap[i + 1], ctx)) + goto err; + if (!group->meth->field_mul(group, tmp1, heap[i / 2], heap[i], ctx)) + goto err; + if (!BN_copy(heap[i], tmp0)) + goto err; + if (!BN_copy(heap[i + 1], tmp1)) + goto err; + } else { + if (!BN_copy(heap[i], heap[i / 2])) + goto err; } + } - /* we have replaced all non-zero Z's by their inverses, now fix up all the points */ - for (i = 0; i < num; i++) - { + /* + * we have replaced all non-zero Z's by their inverses, now fix up + * all the points + */ + for (i = 0; i < num; i++) { EC_POINT *p = points[i]; - - if (!BN_is_zero(&p->Z)) - { - /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ - if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err; - if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err; + if (!BN_is_zero(&p->Z)) { + /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ - if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err; - if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err; - - if (group->meth->field_set_to_one != 0) - { - if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err; - } - else - { - if (!BN_one(&p->Z)) goto err; - } - p->Z_is_one = 1; + if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) + goto err; + + if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) + goto err; + + if (group->meth->field_set_to_one != 0) { + if (!group->meth->field_set_to_one(group, &p->Z, ctx)) + goto err; + } else { + if (!BN_one(&p->Z)) + goto err; } + p->Z_is_one = 1; } + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); - if (heap != NULL) - { - /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */ - for (i = pow2/2 - 1; i > 0; i--) - { + if (heap != NULL) { + /* + * heap[pow2/2] .. heap[pow2-1] have not been allocated + * locally! + */ + for (i = pow2 / 2 - 1; i > 0; i--) { if (heap[i] != NULL) BN_clear_free(heap[i]); - } - free(heap); } - return ret; + free(heap); } + return ret; +} -int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_field_mul(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ return BN_mod_mul(r, a, b, &group->field, ctx); - } +} -int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { +int +ec_GFp_simple_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, BN_CTX * ctx) +{ return BN_mod_sqr(r, a, &group->field, ctx); - } +} diff --git a/lib/libssl/src/crypto/ec/ec2_mult.c b/lib/libssl/src/crypto/ec/ec2_mult.c index 1c575dc47ad..040d7bb2782 100644 --- a/lib/libssl/src/crypto/ec/ec2_mult.c +++ b/lib/libssl/src/crypto/ec/ec2_mult.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -74,178 +74,215 @@ #ifndef OPENSSL_NO_EC2M -/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective +/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective * coordinates. - * Uses algorithm Mdouble in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Uses algorithm Mdouble in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * modified to not require precomputation of c=b^{2^{m-1}}. */ -static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) - { +static int +gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) +{ BIGNUM *t1; int ret = 0; - + /* Since Mdouble is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t1 = BN_CTX_get(ctx); - if (t1 == NULL) goto err; + if (t1 == NULL) + goto err; - if (!group->meth->field_sqr(group, x, x, ctx)) goto err; - if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; - if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; - if (!group->meth->field_sqr(group, x, x, ctx)) goto err; - if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; - if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; - if (!BN_GF2m_add(x, x, t1)) goto err; + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, z, ctx)) + goto err; + if (!group->meth->field_mul(group, z, x, t1, ctx)) + goto err; + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, t1, ctx)) + goto err; + if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) + goto err; + if (!BN_GF2m_add(x, x, t1)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} -/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery +/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery * projective coordinates. - * Uses algorithm Madd in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Uses algorithm Madd in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). */ -static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, - const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) - { +static int +gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, + const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) +{ BIGNUM *t1, *t2; int ret = 0; - + /* Since Madd is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t1 = BN_CTX_get(ctx); t2 = BN_CTX_get(ctx); - if (t2 == NULL) goto err; + if (t2 == NULL) + goto err; - if (!BN_copy(t1, x)) goto err; - if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; - if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; - if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; - if (!BN_GF2m_add(z1, z1, x1)) goto err; - if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; - if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; - if (!BN_GF2m_add(x1, x1, t2)) goto err; + if (!BN_copy(t1, x)) + goto err; + if (!group->meth->field_mul(group, x1, x1, z2, ctx)) + goto err; + if (!group->meth->field_mul(group, z1, z1, x2, ctx)) + goto err; + if (!group->meth->field_mul(group, t2, x1, z1, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_sqr(group, z1, z1, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z1, t1, ctx)) + goto err; + if (!BN_GF2m_add(x1, x1, t2)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} -/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) - * using Montgomery point multiplication algorithm Mxy() in appendix of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over +/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) + * using Montgomery point multiplication algorithm Mxy() in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * Returns: * 0 on error * 1 if return value should be the point at infinity * 2 otherwise */ -static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, - BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) - { +static int +gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, + BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) +{ BIGNUM *t3, *t4, *t5; int ret = 0; - - if (BN_is_zero(z1)) - { + + if (BN_is_zero(z1)) { BN_zero(x2); BN_zero(z2); return 1; - } - - if (BN_is_zero(z2)) - { - if (!BN_copy(x2, x)) return 0; - if (!BN_GF2m_add(z2, x, y)) return 0; + } + if (BN_is_zero(z2)) { + if (!BN_copy(x2, x)) + return 0; + if (!BN_GF2m_add(z2, x, y)) + return 0; return 2; - } - + } /* Since Mxy is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); t3 = BN_CTX_get(ctx); t4 = BN_CTX_get(ctx); t5 = BN_CTX_get(ctx); - if (t5 == NULL) goto err; + if (t5 == NULL) + goto err; - if (!BN_one(t5)) goto err; + if (!BN_one(t5)) + goto err; - if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; + if (!group->meth->field_mul(group, t3, z1, z2, ctx)) + goto err; - if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; - if (!BN_GF2m_add(z1, z1, x1)) goto err; - if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; - if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; - if (!BN_GF2m_add(z2, z2, x2)) goto err; + if (!group->meth->field_mul(group, z1, z1, x, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_mul(group, z2, z2, x, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z2, x1, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, x2)) + goto err; - if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; - if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; - if (!BN_GF2m_add(t4, t4, y)) goto err; - if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; - if (!BN_GF2m_add(t4, t4, z2)) goto err; + if (!group->meth->field_mul(group, z2, z2, z1, ctx)) + goto err; + if (!group->meth->field_sqr(group, t4, x, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, y)) + goto err; + if (!group->meth->field_mul(group, t4, t4, t3, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, z2)) + goto err; - if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; - if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; - if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; - if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; - if (!BN_GF2m_add(z2, x2, x)) goto err; + if (!group->meth->field_mul(group, t3, t3, x, ctx)) + goto err; + if (!group->meth->field_div(group, t3, t5, t3, ctx)) + goto err; + if (!group->meth->field_mul(group, t4, t3, t4, ctx)) + goto err; + if (!group->meth->field_mul(group, x2, x1, t3, ctx)) + goto err; + if (!BN_GF2m_add(z2, x2, x)) + goto err; - if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; - if (!BN_GF2m_add(z2, z2, y)) goto err; + if (!group->meth->field_mul(group, z2, z2, t4, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, y)) + goto err; ret = 2; - err: +err: BN_CTX_end(ctx); return ret; - } +} /* Computes scalar*point and stores the result in r. * point can not equal r. * Uses a modified algorithm 2P of - * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * * To protect against side-channel attack the function uses constant time swap, * avoiding conditional branches. */ -static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - const EC_POINT *point, BN_CTX *ctx) - { +static int +ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) +{ BIGNUM *x1, *x2, *z1, *z2; int ret = 0, i; - BN_ULONG mask,word; + BN_ULONG mask, word; - if (r == point) - { + if (r == point) { ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); return 0; - } - + } /* if result should be point at infinity */ - if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || - EC_POINT_is_at_infinity(group, point)) - { + if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || + EC_POINT_is_at_infinity(group, point)) { return EC_POINT_set_to_infinity(group, r); - } - + } /* only support affine coordinates */ - if (!point->Z_is_one) return 0; + if (!point->Z_is_one) + return 0; /* Since point_multiply is static we can guarantee that ctx != NULL. */ BN_CTX_start(ctx); x1 = BN_CTX_get(ctx); z1 = BN_CTX_get(ctx); - if (z1 == NULL) goto err; + if (z1 == NULL) + goto err; x2 = &r->X; z2 = &r->Y; @@ -255,53 +292,57 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, bn_wexpand(x2, group->field.top); bn_wexpand(z2, group->field.top); - if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ - if (!BN_one(z1)) goto err; /* z1 = 1 */ - if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ - if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ + if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) + goto err; /* x1 = x */ + if (!BN_one(z1)) + goto err; /* z1 = 1 */ + if (!group->meth->field_sqr(group, z2, x1, ctx)) + goto err; /* z2 = x1^2 = x^2 */ + if (!group->meth->field_sqr(group, x2, z2, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->b)) + goto err; /* x2 = x^4 + b */ /* find top most bit and go one past it */ i = scalar->top - 1; mask = BN_TBIT; word = scalar->d[i]; - while (!(word & mask)) mask >>= 1; + while (!(word & mask)) + mask >>= 1; mask >>= 1; /* if top most bit was at word break, go to next word */ - if (!mask) - { + if (!mask) { i--; mask = BN_TBIT; - } - - for (; i >= 0; i--) - { + } + for (; i >= 0; i--) { word = scalar->d[i]; - while (mask) - { + while (mask) { BN_consttime_swap(word & mask, x1, x2, group->field.top); BN_consttime_swap(word & mask, z1, z2, group->field.top); - if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; - if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; + if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) + goto err; + if (!gf2m_Mdouble(group, x1, z1, ctx)) + goto err; BN_consttime_swap(word & mask, x1, x2, group->field.top); BN_consttime_swap(word & mask, z1, z2, group->field.top); mask >>= 1; - } - mask = BN_TBIT; } + mask = BN_TBIT; + } /* convert out of "projective" coordinates */ i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); - if (i == 0) goto err; - else if (i == 1) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; - } - else - { - if (!BN_one(&r->Z)) goto err; + if (i == 0) + goto err; + else if (i == 1) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { + if (!BN_one(&r->Z)) + goto err; r->Z_is_one = 1; - } + } /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ BN_set_negative(&r->X, 0); @@ -309,87 +350,98 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, ret = 1; - err: +err: BN_CTX_end(ctx); return ret; - } +} /* Computes the sum * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] * gracefully ignoring NULL scalar values. */ -int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; size_t i; - EC_POINT *p=NULL; + EC_POINT *p = NULL; EC_POINT *acc = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - - /* This implementation is more efficient than the wNAF implementation for 2 - * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, - * or if we can perform a fast multiplication based on precomputation. + } + /* + * This implementation is more efficient than the wNAF implementation + * for 2 or fewer points. Use the ec_wNAF_mul implementation for 3 + * or more points, or if we can perform a fast multiplication based + * on precomputation. */ - if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) - { + if ((scalar && (num > 1)) || (num > 2) || + (num == 0 && EC_GROUP_have_precompute_mult(group))) { ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); goto err; - } - - if ((p = EC_POINT_new(group)) == NULL) goto err; - if ((acc = EC_POINT_new(group)) == NULL) goto err; + } + if ((p = EC_POINT_new(group)) == NULL) + goto err; + if ((acc = EC_POINT_new(group)) == NULL) + goto err; - if (!EC_POINT_set_to_infinity(group, acc)) goto err; + if (!EC_POINT_set_to_infinity(group, acc)) + goto err; - if (scalar) - { - if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; + if (scalar) { + if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) + goto err; if (BN_is_negative(scalar)) - if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, acc, acc, p, ctx)) goto err; - } - - for (i = 0; i < num; i++) - { - if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } + for (i = 0; i < num; i++) { + if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) + goto err; if (BN_is_negative(scalars[i])) - if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, acc, acc, p, ctx)) goto err; - } + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } - if (!EC_POINT_copy(r, acc)) goto err; + if (!EC_POINT_copy(r, acc)) + goto err; ret = 1; - err: - if (p) EC_POINT_free(p); - if (acc) EC_POINT_free(acc); +err: + if (p) + EC_POINT_free(p); + if (acc) + EC_POINT_free(acc); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Precomputation for point multiplication: fall back to wNAF methods * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ -int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ return ec_wNAF_precompute_mult(group, ctx); - } +} -int ec_GF2m_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GF2m_have_precompute_mult(const EC_GROUP * group) +{ return ec_wNAF_have_precompute_mult(group); - } +} #endif diff --git a/lib/libssl/src/crypto/ec/ec2_oct.c b/lib/libssl/src/crypto/ec/ec2_oct.c index f1d75e5ddf6..a856a5b1a7b 100644 --- a/lib/libssl/src/crypto/ec/ec2_oct.c +++ b/lib/libssl/src/crypto/ec/ec2_oct.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -74,11 +74,11 @@ #ifndef OPENSSL_NO_EC2M /* Calculates and sets the affine coordinates of an EC_POINT from the given - * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. + * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. * Note that the simple implementation only uses affine coordinates. * * The method is from the following publication: - * + * * Harper, Menezes, Vanstone: * "Public-Key Cryptosystems with Very Small Key Lengths", * EUROCRYPT '92, Springer-Verlag LNCS 658, @@ -88,9 +88,10 @@ * the same method, but claim no priority date earlier than July 29, 1994 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). */ -int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { +int +ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp, *x, *y, *z; int ret = 0, z0; @@ -98,13 +99,11 @@ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p /* clear error queue */ ERR_clear_error(); - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } y_bit = (y_bit != 0) ? 1 : 0; BN_CTX_start(ctx); @@ -112,59 +111,65 @@ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); z = BN_CTX_get(ctx); - if (z == NULL) goto err; + if (z == NULL) + goto err; - if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; - if (BN_is_zero(x)) - { - if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; - } - else - { - if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; - if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; - if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; - if (!BN_GF2m_add(tmp, x, tmp)) goto err; - if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) - { + if (!BN_GF2m_mod_arr(x, x_, group->poly)) + goto err; + if (BN_is_zero(x)) { + if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) + goto err; + } else { + if (!group->meth->field_sqr(group, tmp, x, ctx)) + goto err; + if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) + goto err; + if (!BN_GF2m_add(tmp, &group->a, tmp)) + goto err; + if (!BN_GF2m_add(tmp, x, tmp)) + goto err; + if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) { unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) - { + + if (ERR_GET_LIB(err) == ERR_LIB_BN && + ERR_GET_REASON(err) == BN_R_NO_SOLUTION) { ERR_clear_error(); ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else + } else ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); goto err; - } + } z0 = (BN_is_odd(z)) ? 1 : 0; - if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; - if (z0 != y_bit) - { - if (!BN_GF2m_add(y, y, x)) goto err; - } + if (!group->meth->field_mul(group, y, x, z, ctx)) + goto err; + if (z0 != y_bit) { + if (!BN_GF2m_add(y, y, x)) + goto err; } + } - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -/* Converts an EC_POINT to an octet string. +/* Converts an EC_POINT to an octet string. * If buf is NULL, the encoded length will be returned. * If the length len of buf is smaller than required an error will be returned. */ -size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX * ctx) +{ size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; @@ -172,131 +177,114 @@ size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, po size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { + } + if (EC_POINT_is_at_infinity(group, point)) { /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { + if (buf != NULL) { + if (len < 1) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); return 0; - } - buf[0] = 0; } - return 1; + buf[0] = 0; } - - + return 1; + } /* ret := required output buffer length */ field_len = (EC_GROUP_get_degree(group) + 7) / 8; - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : + 1 + 2 * field_len; /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { + if (buf != NULL) { + if (len < ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); used_ctx = 1; x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; + if (yxi == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; buf[0] = form; - if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (BN_is_odd(yxi)) buf[0]++; - } - + if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (BN_is_odd(yxi)) + buf[0]++; + } i = 1; - + skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(x, buf + i); i += skip; - if (i != 1 + field_len) - { + if (i != 1 + field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { + } + if (form == POINT_CONVERSION_UNCOMPRESSED || + form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(y, buf + i); i += skip; - } - - if (i != ret) - { + } + if (i != ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } } - + } if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - err: +err: if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return 0; - } +} -/* Converts an octet string representation to an EC_POINT. +/* Converts an octet string representation to an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { +int +ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; @@ -304,104 +292,89 @@ int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, size_t field_len, enc_len; int ret = 0; - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); return 0; - } + } form = buf[0]; y_bit = form & 1; form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) && + (form != POINT_CONVERSION_UNCOMPRESSED) && + (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (form == 0) - { - if (len != 1) - { + } + if (form == 0) { + if (len != 1) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - return EC_POINT_set_to_infinity(group, point); } - + return EC_POINT_set_to_infinity(group, point); + } field_len = (EC_GROUP_get_degree(group) + 7) / 8; - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : + 1 + 2 * field_len; - if (len != enc_len) - { + if (len != enc_len) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; + if (yxi == NULL) + goto err; - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { + } + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (y_bit != BN_is_odd(yxi)) - { + } + if (form == POINT_CONVERSION_HYBRID) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (y_bit != BN_is_odd(yxi)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) { + /* test required by X9.62 */ ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} #endif diff --git a/lib/libssl/src/crypto/ec/ec2_smpl.c b/lib/libssl/src/crypto/ec/ec2_smpl.c index 5682bfab377..71bacf71dd9 100644 --- a/lib/libssl/src/crypto/ec/ec2_smpl.c +++ b/lib/libssl/src/crypto/ec/ec2_smpl.c @@ -21,7 +21,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -87,16 +87,16 @@ EC_GF2m_simple_method(void) .group_get_curve = ec_GF2m_simple_group_get_curve, .group_get_degree = ec_GF2m_simple_group_get_degree, .group_check_discriminant = - ec_GF2m_simple_group_check_discriminant, + ec_GF2m_simple_group_check_discriminant, .point_init = ec_GF2m_simple_point_init, .point_finish = ec_GF2m_simple_point_finish, .point_clear_finish = ec_GF2m_simple_point_clear_finish, .point_copy = ec_GF2m_simple_point_copy, .point_set_to_infinity = ec_GF2m_simple_point_set_to_infinity, .point_set_affine_coordinates = - ec_GF2m_simple_point_set_affine_coordinates, + ec_GF2m_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GF2m_simple_point_get_affine_coordinates, + ec_GF2m_simple_point_get_affine_coordinates, .add = ec_GF2m_simple_add, .dbl = ec_GF2m_simple_dbl, .invert = ec_GF2m_simple_invert, @@ -106,7 +106,10 @@ EC_GF2m_simple_method(void) .make_affine = ec_GF2m_simple_make_affine, .points_make_affine = ec_GF2m_simple_points_make_affine, - /* the following three method functions are defined in ec2_mult.c */ + /* + * the following three method functions are defined in + * ec2_mult.c + */ .mul = ec_GF2m_simple_mul, .precompute_mult = ec_GF2m_precompute_mult, .have_precompute_mult = ec_GF2m_have_precompute_mult, @@ -123,31 +126,34 @@ EC_GF2m_simple_method(void) /* Initialize a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_new. */ -int ec_GF2m_simple_group_init(EC_GROUP *group) - { +int +ec_GF2m_simple_group_init(EC_GROUP * group) +{ BN_init(&group->field); BN_init(&group->a); BN_init(&group->b); return 1; - } +} /* Free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_free. */ -void ec_GF2m_simple_group_finish(EC_GROUP *group) - { +void +ec_GF2m_simple_group_finish(EC_GROUP * group) +{ BN_free(&group->field); BN_free(&group->a); BN_free(&group->b); - } +} /* Clear and free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_clear_free. */ -void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) - { +void +ec_GF2m_simple_group_clear_finish(EC_GROUP * group) +{ BN_clear_free(&group->field); BN_clear_free(&group->a); BN_clear_free(&group->b); @@ -157,127 +163,145 @@ void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) group->poly[3] = 0; group->poly[4] = 0; group->poly[5] = -1; - } +} /* Copy a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_copy. */ -int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +ec_GF2m_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ int i; - if (!BN_copy(&dest->field, &src->field)) return 0; - if (!BN_copy(&dest->a, &src->a)) return 0; - if (!BN_copy(&dest->b, &src->b)) return 0; + + if (!BN_copy(&dest->field, &src->field)) + return 0; + if (!BN_copy(&dest->a, &src->a)) + return 0; + if (!BN_copy(&dest->b, &src->b)) + return 0; dest->poly[0] = src->poly[0]; dest->poly[1] = src->poly[1]; dest->poly[2] = src->poly[2]; dest->poly[3] = src->poly[3]; dest->poly[4] = src->poly[4]; dest->poly[5] = src->poly[5]; - if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; - if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; - for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; - for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; + if (bn_wexpand(&dest->a, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + return 0; + if (bn_wexpand(&dest->b, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + return 0; + for (i = dest->a.top; i < dest->a.dmax; i++) + dest->a.d[i] = 0; + for (i = dest->b.top; i < dest->b.dmax; i++) + dest->b.d[i] = 0; return 1; - } +} /* Set the curve parameters of an EC_GROUP structure. */ -int ec_GF2m_simple_group_set_curve(EC_GROUP *group, - const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_set_curve(EC_GROUP * group, + const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0, i; /* group->field */ - if (!BN_copy(&group->field, p)) goto err; + if (!BN_copy(&group->field, p)) + goto err; i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; - if ((i != 5) && (i != 3)) - { + if ((i != 5) && (i != 3)) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); goto err; - } - + } /* group->a */ - if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; - if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; - for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; - + if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) + goto err; + if (bn_wexpand(&group->a, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + goto err; + for (i = group->a.top; i < group->a.dmax; i++) + group->a.d[i] = 0; + /* group->b */ - if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; - if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; - for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; - + if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) + goto err; + if (bn_wexpand(&group->b, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) + goto err; + for (i = group->b.top; i < group->b.dmax; i++) + group->b.d[i] = 0; + ret = 1; - err: +err: return ret; - } +} /* Get the curve parameters of an EC_GROUP structure. * If p, a, or b are NULL then there values will not be set but the method will return with success. */ -int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_get_curve(const EC_GROUP *group, + BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) +{ int ret = 0; - - if (p != NULL) - { - if (!BN_copy(p, &group->field)) return 0; - } - if (a != NULL) - { - if (!BN_copy(a, &group->a)) goto err; - } - - if (b != NULL) - { - if (!BN_copy(b, &group->b)) goto err; - } - + if (p != NULL) { + if (!BN_copy(p, &group->field)) + return 0; + } + if (a != NULL) { + if (!BN_copy(a, &group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, &group->b)) + goto err; + } ret = 1; - - err: + +err: return ret; - } +} /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ -int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) - { - return BN_num_bits(&group->field)-1; - } +int +ec_GF2m_simple_group_get_degree(const EC_GROUP * group) +{ + return BN_num_bits(&group->field) - 1; +} /* Checks the discriminant of the curve. - * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) + * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) */ -int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; BIGNUM *b; BN_CTX *new_ctx = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); b = BN_CTX_get(ctx); - if (b == NULL) goto err; + if (b == NULL) + goto err; + + if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) + goto err; - if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; - - /* check the discriminant: - * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) + /* + * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic + * curve <=> b != 0 (mod p) */ - if (BN_is_zero(b)) goto err; + if (BN_is_zero(b)) + goto err; ret = 1; @@ -287,151 +311,157 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Initializes an EC_POINT. */ -int ec_GF2m_simple_point_init(EC_POINT *point) - { +int +ec_GF2m_simple_point_init(EC_POINT * point) +{ BN_init(&point->X); BN_init(&point->Y); BN_init(&point->Z); return 1; - } +} /* Frees an EC_POINT. */ -void ec_GF2m_simple_point_finish(EC_POINT *point) - { +void +ec_GF2m_simple_point_finish(EC_POINT * point) +{ BN_free(&point->X); BN_free(&point->Y); BN_free(&point->Z); - } +} /* Clears and frees an EC_POINT. */ -void ec_GF2m_simple_point_clear_finish(EC_POINT *point) - { +void +ec_GF2m_simple_point_clear_finish(EC_POINT * point) +{ BN_clear_free(&point->X); BN_clear_free(&point->Y); BN_clear_free(&point->Z); point->Z_is_one = 0; - } +} /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ -int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) - { - if (!BN_copy(&dest->X, &src->X)) return 0; - if (!BN_copy(&dest->Y, &src->Y)) return 0; - if (!BN_copy(&dest->Z, &src->Z)) return 0; +int +ec_GF2m_simple_point_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (!BN_copy(&dest->X, &src->X)) + return 0; + if (!BN_copy(&dest->Y, &src->Y)) + return 0; + if (!BN_copy(&dest->Z, &src->Z)) + return 0; dest->Z_is_one = src->Z_is_one; return 1; - } +} -/* Set an EC_POINT to the point at infinity. +/* Set an EC_POINT to the point at infinity. * A point at infinity is represented by having Z=0. */ -int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { +int +ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ point->Z_is_one = 0; BN_zero(&point->Z); return 1; - } +} -/* Set the coordinates of an EC_POINT using affine coordinates. +/* Set the coordinates of an EC_POINT using affine coordinates. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - int ret = 0; - if (x == NULL || y == NULL) - { +int +ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) +{ + int ret = 0; + if (x == NULL || y == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if (!BN_copy(&point->X, x)) goto err; + } + if (!BN_copy(&point->X, x)) + goto err; BN_set_negative(&point->X, 0); - if (!BN_copy(&point->Y, y)) goto err; + if (!BN_copy(&point->Y, y)) + goto err; BN_set_negative(&point->Y, 0); - if (!BN_copy(&point->Z, BN_value_one())) goto err; + if (!BN_copy(&point->Z, BN_value_one())) + goto err; BN_set_negative(&point->Z, 0); point->Z_is_one = 1; ret = 1; - err: +err: return ret; - } +} -/* Gets the affine coordinates of an EC_POINT. +/* Gets the affine coordinates of an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ -int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ int ret = 0; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; - } - - if (BN_cmp(&point->Z, BN_value_one())) - { + } + if (BN_cmp(&point->Z, BN_value_one())) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; + } + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; BN_set_negative(x, 0); - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; BN_set_negative(y, 0); - } + } ret = 1; - - err: + +err: return ret; - } +} /* Computes a + b and stores the result in r. r could be a or b, a could be b. * Uses algorithm A.10.2 of IEEE P1363. */ -int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; int ret = 0; - - if (EC_POINT_is_at_infinity(group, a)) - { - if (!EC_POINT_copy(r, b)) return 0; - return 1; - } - if (EC_POINT_is_at_infinity(group, b)) - { - if (!EC_POINT_copy(r, a)) return 0; + if (EC_POINT_is_at_infinity(group, a)) { + if (!EC_POINT_copy(r, b)) + return 0; return 1; - } - - if (ctx == NULL) - { + } + if (EC_POINT_is_at_infinity(group, b)) { + if (!EC_POINT_copy(r, a)) + return 0; + return 1; + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x0 = BN_CTX_get(ctx); y0 = BN_CTX_get(ctx); @@ -441,149 +471,178 @@ int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, co y2 = BN_CTX_get(ctx); s = BN_CTX_get(ctx); t = BN_CTX_get(ctx); - if (t == NULL) goto err; + if (t == NULL) + goto err; - if (a->Z_is_one) - { - if (!BN_copy(x0, &a->X)) goto err; - if (!BN_copy(y0, &a->Y)) goto err; - } - else - { - if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; - } - if (b->Z_is_one) - { - if (!BN_copy(x1, &b->X)) goto err; - if (!BN_copy(y1, &b->Y)) goto err; - } - else - { - if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; - } + if (a->Z_is_one) { + if (!BN_copy(x0, &a->X)) + goto err; + if (!BN_copy(y0, &a->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) + goto err; + } + if (b->Z_is_one) { + if (!BN_copy(x1, &b->X)) + goto err; + if (!BN_copy(y1, &b->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) + goto err; + } - if (BN_GF2m_cmp(x0, x1)) - { - if (!BN_GF2m_add(t, x0, x1)) goto err; - if (!BN_GF2m_add(s, y0, y1)) goto err; - if (!group->meth->field_div(group, s, s, t, ctx)) goto err; - if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, &group->a)) goto err; - if (!BN_GF2m_add(x2, x2, s)) goto err; - if (!BN_GF2m_add(x2, x2, t)) goto err; - } - else - { - if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; + if (BN_GF2m_cmp(x0, x1)) { + if (!BN_GF2m_add(t, x0, x1)) + goto err; + if (!BN_GF2m_add(s, y0, y1)) + goto err; + if (!group->meth->field_div(group, s, s, t, ctx)) + goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->a)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, t)) + goto err; + } else { + if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; ret = 1; goto err; - } - if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; - if (!BN_GF2m_add(s, s, x1)) goto err; - - if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; - if (!BN_GF2m_add(x2, x2, s)) goto err; - if (!BN_GF2m_add(x2, x2, &group->a)) goto err; } + if (!group->meth->field_div(group, s, y1, x1, ctx)) + goto err; + if (!BN_GF2m_add(s, s, x1)) + goto err; - if (!BN_GF2m_add(y2, x1, x2)) goto err; - if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; - if (!BN_GF2m_add(y2, y2, x2)) goto err; - if (!BN_GF2m_add(y2, y2, y1)) goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, &group->a)) + goto err; + } - if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; + if (!BN_GF2m_add(y2, x1, x2)) + goto err; + if (!group->meth->field_mul(group, y2, y2, s, ctx)) + goto err; + if (!BN_GF2m_add(y2, y2, x2)) + goto err; + if (!BN_GF2m_add(y2, y2, y1)) + goto err; + + if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Computes 2 * a and stores the result in r. r could be a. * Uses algorithm A.10.2 of IEEE P1363. */ -int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { +int +ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ return ec_GF2m_simple_add(group, r, a, a, ctx); - } - +} -int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) /* point is its own inverse */ return 1; - - if (!EC_POINT_make_affine(group, point, ctx)) return 0; + + if (!EC_POINT_make_affine(group, point, ctx)) + return 0; return BN_GF2m_add(&point->Y, &point->X, &point->Y); - } +} /* Indicates whether the given point is the point at infinity. */ -int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { +int +ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ return BN_is_zero(&point->Z); - } +} /* Determines whether the given EC_POINT is an actual point on the curve defined * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: * y^2 + x*y = x^3 + a*x^2 + b. */ -int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) +{ int ret = -1; BN_CTX *new_ctx = NULL; BIGNUM *lh, *y2; - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); if (EC_POINT_is_at_infinity(group, point)) return 1; field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; + field_sqr = group->meth->field_sqr; /* only support affine coordinates */ - if (!point->Z_is_one) return -1; + if (!point->Z_is_one) + return -1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); y2 = BN_CTX_get(ctx); lh = BN_CTX_get(ctx); - if (lh == NULL) goto err; + if (lh == NULL) + goto err; - /* We have a curve defined by a Weierstrass equation - * y^2 + x*y = x^3 + a*x^2 + b. - * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 - * <=> ((x + a) * x + y ) * x + b + y^2 = 0 + /* + * We have a curve defined by a Weierstrass equation y^2 + x*y = x^3 + * + a*x^2 + b. <=> x^3 + a*x^2 + x*y + b + y^2 = 0 <=> ((x + a) * x + * + y ) * x + b + y^2 = 0 */ - if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; - if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; - if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, &group->b)) goto err; - if (!field_sqr(group, y2, &point->Y, ctx)) goto err; - if (!BN_GF2m_add(lh, lh, y2)) goto err; + if (!BN_GF2m_add(lh, &point->X, &group->a)) + goto err; + if (!field_mul(group, lh, lh, &point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, &point->Y)) + goto err; + if (!field_mul(group, lh, lh, &point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, &group->b)) + goto err; + if (!field_sqr(group, y2, &point->Y, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, y2)) + goto err; ret = BN_is_zero(lh); - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Indicates whether two points are equal. @@ -592,118 +651,132 @@ int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_ * 0 equal (in affine coordinates) * 1 not equal */ -int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ BIGNUM *aX, *aY, *bX, *bY; BN_CTX *new_ctx = NULL; int ret = -1; - if (EC_POINT_is_at_infinity(group, a)) - { + if (EC_POINT_is_at_infinity(group, a)) { return EC_POINT_is_at_infinity(group, b) ? 0 : 1; - } - + } if (EC_POINT_is_at_infinity(group, b)) return 1; - - if (a->Z_is_one && b->Z_is_one) - { - return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; - } - if (ctx == NULL) - { + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); aX = BN_CTX_get(ctx); aY = BN_CTX_get(ctx); bX = BN_CTX_get(ctx); bY = BN_CTX_get(ctx); - if (bY == NULL) goto err; + if (bY == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; - if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) + goto err; ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Forces the given EC_POINT to internally use affine coordinates. */ -int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GF2m_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; - - if (ctx == NULL) - { + + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - if (!BN_copy(&point->X, x)) goto err; - if (!BN_copy(&point->Y, y)) goto err; - if (!BN_one(&point->Z)) goto err; - - ret = 1; - - err: - if (ctx) BN_CTX_end(ctx); - if (new_ctx) BN_CTX_free(new_ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + if (!BN_copy(&point->X, x)) + goto err; + if (!BN_copy(&point->Y, y)) + goto err; + if (!BN_one(&point->Z)) + goto err; + + ret = 1; + +err: + if (ctx) + BN_CTX_end(ctx); + if (new_ctx) + BN_CTX_free(new_ctx); return ret; - } +} /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ -int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ size_t i; - for (i = 0; i < num; i++) - { - if (!group->meth->make_affine(group, points[i], ctx)) return 0; - } + for (i = 0; i < num; i++) { + if (!group->meth->make_affine(group, points[i], ctx)) + return 0; + } return 1; - } +} /* Wrapper to simple binary polynomial field multiplication implementation. */ -int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); - } +} /* Wrapper to simple binary polynomial field squaring implementation. */ -int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); - } +} /* Wrapper to simple binary polynomial field division implementation. */ -int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ return BN_GF2m_mod_div(r, a, b, &group->field, ctx); - } +} #endif diff --git a/lib/libssl/src/crypto/ec/ec_ameth.c b/lib/libssl/src/crypto/ec/ec_ameth.c index 0e6381f5439..9b52c3cbfc8 100644 --- a/lib/libssl/src/crypto/ec/ec_ameth.c +++ b/lib/libssl/src/crypto/ec/ec_ameth.c @@ -9,7 +9,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -65,54 +65,51 @@ #endif #include "asn1_locl.h" -static int eckey_param2type(int *pptype, void **ppval, EC_KEY *ec_key) - { - const EC_GROUP *group; +static int +eckey_param2type(int *pptype, void **ppval, EC_KEY * ec_key) +{ + const EC_GROUP *group; int nid; - if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) - { + if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) { ECerr(EC_F_ECKEY_PARAM2TYPE, EC_R_MISSING_PARAMETERS); return 0; } - if (EC_GROUP_get_asn1_flag(group) - && (nid = EC_GROUP_get_curve_name(group))) + if (EC_GROUP_get_asn1_flag(group) && + (nid = EC_GROUP_get_curve_name(group))) { /* we have a 'named curve' => just set the OID */ - { *ppval = OBJ_nid2obj(nid); *pptype = V_ASN1_OBJECT; - } - else /* explicit parameters */ - { + } else { + /* explicit parameters */ ASN1_STRING *pstr = NULL; pstr = ASN1_STRING_new(); if (!pstr) return 0; pstr->length = i2d_ECParameters(ec_key, &pstr->data); - if (pstr->length <= 0) - { + if (pstr->length <= 0) { ASN1_STRING_free(pstr); ECerr(EC_F_ECKEY_PARAM2TYPE, ERR_R_EC_LIB); return 0; - } + } *ppval = pstr; *pptype = V_ASN1_SEQUENCE; - } - return 1; } + return 1; +} -static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) - { +static int +eckey_pub_encode(X509_PUBKEY * pk, const EVP_PKEY * pkey) +{ EC_KEY *ec_key = pkey->pkey.ec; void *pval = NULL; int ptype; unsigned char *penc = NULL, *p; int penclen; - if (!eckey_param2type(&ptype, &pval, ec_key)) - { + if (!eckey_param2type(&ptype, &pval, ec_key)) { ECerr(EC_F_ECKEY_PUB_ENCODE, ERR_R_EC_LIB); return 0; - } + } penclen = i2o_ECPublicKey(ec_key, NULL); if (penclen <= 0) goto err; @@ -124,9 +121,9 @@ static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) if (penclen <= 0) goto err; if (X509_PUBKEY_set0_param(pk, OBJ_nid2obj(EVP_PKEY_EC), - ptype, pval, penc, penclen)) + ptype, pval, penc, penclen)) return 1; - err: +err: if (ptype == V_ASN1_OBJECT) ASN1_OBJECT_free(pval); else @@ -134,37 +131,36 @@ static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) if (penc) free(penc); return 0; - } +} -static EC_KEY *eckey_type2param(int ptype, void *pval) - { +static EC_KEY * +eckey_type2param(int ptype, void *pval) +{ EC_KEY *eckey = NULL; - if (ptype == V_ASN1_SEQUENCE) - { + + if (ptype == V_ASN1_SEQUENCE) { ASN1_STRING *pstr = pval; const unsigned char *pm = NULL; int pmlen; + pm = pstr->data; pmlen = pstr->length; - if (!(eckey = d2i_ECParameters(NULL, &pm, pmlen))) - { + if (!(eckey = d2i_ECParameters(NULL, &pm, pmlen))) { ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); goto ecerr; - } } - else if (ptype == V_ASN1_OBJECT) - { + } else if (ptype == V_ASN1_OBJECT) { ASN1_OBJECT *poid = pval; EC_GROUP *group; - /* type == V_ASN1_OBJECT => the parameters are given - * by an asn1 OID + /* + * type == V_ASN1_OBJECT => the parameters are given by an + * asn1 OID */ - if ((eckey = EC_KEY_new()) == NULL) - { + if ((eckey = EC_KEY_new()) == NULL) { ECerr(EC_F_ECKEY_TYPE2PARAM, ERR_R_MALLOC_FAILURE); goto ecerr; - } + } group = EC_GROUP_new_by_curve_name(OBJ_obj2nid(poid)); if (group == NULL) goto ecerr; @@ -172,23 +168,22 @@ static EC_KEY *eckey_type2param(int ptype, void *pval) if (EC_KEY_set_group(eckey, group) == 0) goto ecerr; EC_GROUP_free(group); - } - else - { + } else { ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); goto ecerr; - } + } return eckey; - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return NULL; - } +} -static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) - { +static int +eckey_pub_decode(EVP_PKEY * pkey, X509_PUBKEY * pubkey) +{ const unsigned char *p = NULL; void *pval; int ptype, pklen; @@ -201,44 +196,42 @@ static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) eckey = eckey_type2param(ptype, pval); - if (!eckey) - { + if (!eckey) { ECerr(EC_F_ECKEY_PUB_DECODE, ERR_R_EC_LIB); return 0; - } - + } /* We have parameters now set public key */ - if (!o2i_ECPublicKey(&eckey, &p, pklen)) - { + if (!o2i_ECPublicKey(&eckey, &p, pklen)) { ECerr(EC_F_ECKEY_PUB_DECODE, EC_R_DECODE_ERROR); goto ecerr; - } - + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return 0; - } +} -static int eckey_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b) - { - int r; +static int +eckey_pub_cmp(const EVP_PKEY * a, const EVP_PKEY * b) +{ + int r; const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec); - const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), - *pb = EC_KEY_get0_public_key(b->pkey.ec); + const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), *pb = EC_KEY_get0_public_key(b->pkey.ec); + r = EC_POINT_cmp(group, pa, pb, NULL); if (r == 0) return 1; if (r == 1) return 0; return -2; - } +} -static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8) - { +static int +eckey_priv_decode(EVP_PKEY * pkey, PKCS8_PRIV_KEY_INFO * p8) +{ const unsigned char *p = NULL; void *pval; int ptype, pklen; @@ -255,100 +248,92 @@ static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8) goto ecliberr; /* We have parameters now set private key */ - if (!d2i_ECPrivateKey(&eckey, &p, pklen)) - { + if (!d2i_ECPrivateKey(&eckey, &p, pklen)) { ECerr(EC_F_ECKEY_PRIV_DECODE, EC_R_DECODE_ERROR); goto ecerr; - } - + } /* calculate public key (if necessary) */ - if (EC_KEY_get0_public_key(eckey) == NULL) - { + if (EC_KEY_get0_public_key(eckey) == NULL) { const BIGNUM *priv_key; const EC_GROUP *group; EC_POINT *pub_key; - /* the public key was not included in the SEC1 private - * key => calculate the public key */ - group = EC_KEY_get0_group(eckey); + /* + * the public key was not included in the SEC1 private key => + * calculate the public key + */ + group = EC_KEY_get0_group(eckey); pub_key = EC_POINT_new(group); - if (pub_key == NULL) - { + if (pub_key == NULL) { ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group))) - { + } + if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group))) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } + } priv_key = EC_KEY_get0_private_key(eckey); - if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL)) - { + if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL)) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - if (EC_KEY_set_public_key(eckey, pub_key) == 0) - { + } + if (EC_KEY_set_public_key(eckey, pub_key) == 0) { EC_POINT_free(pub_key); ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); goto ecliberr; - } - EC_POINT_free(pub_key); } - + EC_POINT_free(pub_key); + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - ecliberr: +ecliberr: ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); - ecerr: +ecerr: if (eckey) EC_KEY_free(eckey); return 0; - } +} -static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) +static int +eckey_priv_encode(PKCS8_PRIV_KEY_INFO * p8, const EVP_PKEY * pkey) { - EC_KEY *ec_key; - unsigned char *ep, *p; - int eplen, ptype; - void *pval; - unsigned int tmp_flags, old_flags; + EC_KEY *ec_key; + unsigned char *ep, *p; + int eplen, ptype; + void *pval; + unsigned int tmp_flags, old_flags; ec_key = pkey->pkey.ec; - if (!eckey_param2type(&ptype, &pval, ec_key)) - { + if (!eckey_param2type(&ptype, &pval, ec_key)) { ECerr(EC_F_ECKEY_PRIV_ENCODE, EC_R_DECODE_ERROR); return 0; - } - + } /* set the private key */ - /* do not include the parameters in the SEC1 private key - * see PKCS#11 12.11 */ + /* + * do not include the parameters in the SEC1 private key see PKCS#11 + * 12.11 + */ old_flags = EC_KEY_get_enc_flags(ec_key); tmp_flags = old_flags | EC_PKEY_NO_PARAMETERS; EC_KEY_set_enc_flags(ec_key, tmp_flags); eplen = i2d_ECPrivateKey(ec_key, NULL); - if (!eplen) - { + if (!eplen) { EC_KEY_set_enc_flags(ec_key, old_flags); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); return 0; } ep = (unsigned char *) malloc(eplen); - if (!ep) - { + if (!ep) { EC_KEY_set_enc_flags(ec_key, old_flags); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); return 0; } p = ep; - if (!i2d_ECPrivateKey(ec_key, &p)) - { + if (!i2d_ECPrivateKey(ec_key, &p)) { EC_KEY_set_enc_flags(ec_key, old_flags); free(ep); ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); @@ -358,49 +343,50 @@ static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) EC_KEY_set_enc_flags(ec_key, old_flags); if (!PKCS8_pkey_set0(p8, OBJ_nid2obj(NID_X9_62_id_ecPublicKey), 0, - ptype, pval, ep, eplen)) + ptype, pval, ep, eplen)) return 0; return 1; } -static int int_ec_size(const EVP_PKEY *pkey) - { +static int +int_ec_size(const EVP_PKEY * pkey) +{ return ECDSA_size(pkey->pkey.ec); - } +} -static int ec_bits(const EVP_PKEY *pkey) - { +static int +ec_bits(const EVP_PKEY * pkey) +{ BIGNUM *order = BN_new(); const EC_GROUP *group; int ret; - if (!order) - { + if (!order) { ERR_clear_error(); return 0; - } + } group = EC_KEY_get0_group(pkey->pkey.ec); - if (!EC_GROUP_get_order(group, order, NULL)) - { + if (!EC_GROUP_get_order(group, order, NULL)) { ERR_clear_error(); return 0; - } - + } ret = BN_num_bits(order); BN_free(order); return ret; - } +} -static int ec_missing_parameters(const EVP_PKEY *pkey) - { +static int +ec_missing_parameters(const EVP_PKEY * pkey) +{ if (EC_KEY_get0_group(pkey->pkey.ec) == NULL) return 1; return 0; - } +} -static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) - { +static int +ec_copy_parameters(EVP_PKEY * to, const EVP_PKEY * from) +{ EC_GROUP *group = EC_GROUP_dup(EC_KEY_get0_group(from->pkey.ec)); if (group == NULL) return 0; @@ -408,79 +394,70 @@ static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) return 0; EC_GROUP_free(group); return 1; - } +} -static int ec_cmp_parameters(const EVP_PKEY *a, const EVP_PKEY *b) - { - const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), - *group_b = EC_KEY_get0_group(b->pkey.ec); +static int +ec_cmp_parameters(const EVP_PKEY * a, const EVP_PKEY * b) +{ + const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), *group_b = EC_KEY_get0_group(b->pkey.ec); if (EC_GROUP_cmp(group_a, group_b, NULL)) return 0; else return 1; - } +} -static void int_ec_free(EVP_PKEY *pkey) - { +static void +int_ec_free(EVP_PKEY * pkey) +{ EC_KEY_free(pkey->pkey.ec); - } +} -static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) - { - unsigned char *buffer=NULL; +static int +do_EC_KEY_print(BIO * bp, const EC_KEY * x, int off, int ktype) +{ + unsigned char *buffer = NULL; const char *ecstr; - size_t buf_len=0, i; - int ret=0, reason=ERR_R_BIO_LIB; - BIGNUM *pub_key=NULL, *order=NULL; - BN_CTX *ctx=NULL; + size_t buf_len = 0, i; + int ret = 0, reason = ERR_R_BIO_LIB; + BIGNUM *pub_key = NULL, *order = NULL; + BN_CTX *ctx = NULL; const EC_GROUP *group; const EC_POINT *public_key; const BIGNUM *priv_key; - - if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) - { + + if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) { reason = ERR_R_PASSED_NULL_PARAMETER; goto err; - } - + } ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - - if (ktype > 0) - { + } + if (ktype > 0) { public_key = EC_KEY_get0_public_key(x); if ((pub_key = EC_POINT_point2bn(group, public_key, - EC_KEY_get_conv_form(x), NULL, ctx)) == NULL) - { + EC_KEY_get_conv_form(x), NULL, ctx)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - if (pub_key) - buf_len = (size_t)BN_num_bytes(pub_key); } - - if (ktype == 2) - { + if (pub_key) + buf_len = (size_t) BN_num_bytes(pub_key); + } + if (ktype == 2) { priv_key = EC_KEY_get0_private_key(x); - if (priv_key && (i = (size_t)BN_num_bytes(priv_key)) > buf_len) + if (priv_key && (i = (size_t) BN_num_bytes(priv_key)) > buf_len) buf_len = i; - } - else + } else priv_key = NULL; - if (ktype > 0) - { + if (ktype > 0) { buf_len += 10; - if ((buffer = malloc(buf_len)) == NULL) - { + if ((buffer = malloc(buf_len)) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } } + } if (ktype == 2) ecstr = "Private-Key"; else if (ktype == 1) @@ -495,9 +472,10 @@ static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) if (!EC_GROUP_get_order(group, order, NULL)) goto err; if (BIO_printf(bp, "%s: (%d bit)\n", ecstr, - BN_num_bits(order)) <= 0) goto err; - - if ((priv_key != NULL) && !ASN1_bn_print(bp, "priv:", priv_key, + BN_num_bits(order)) <= 0) + goto err; + + if ((priv_key != NULL) && !ASN1_bn_print(bp, "priv:", priv_key, buffer, off)) goto err; if ((pub_key != NULL) && !ASN1_bn_print(bp, "pub: ", pub_key, @@ -505,11 +483,11 @@ static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) goto err; if (!ECPKParameters_print(bp, group, off)) goto err; - ret=1; + ret = 1; err: if (!ret) - ECerr(EC_F_DO_EC_KEY_PRINT, reason); - if (pub_key) + ECerr(EC_F_DO_EC_KEY_PRINT, reason); + if (pub_key) BN_free(pub_key); if (order) BN_free(order); @@ -517,71 +495,75 @@ err: BN_CTX_free(ctx); if (buffer != NULL) free(buffer); - return(ret); - } + return (ret); +} -static int eckey_param_decode(EVP_PKEY *pkey, - const unsigned char **pder, int derlen) - { +static int +eckey_param_decode(EVP_PKEY * pkey, + const unsigned char **pder, int derlen) +{ EC_KEY *eckey; - if (!(eckey = d2i_ECParameters(NULL, pder, derlen))) - { + if (!(eckey = d2i_ECParameters(NULL, pder, derlen))) { ECerr(EC_F_ECKEY_PARAM_DECODE, ERR_R_EC_LIB); return 0; - } + } EVP_PKEY_assign_EC_KEY(pkey, eckey); return 1; - } +} -static int eckey_param_encode(const EVP_PKEY *pkey, unsigned char **pder) - { +static int +eckey_param_encode(const EVP_PKEY * pkey, unsigned char **pder) +{ return i2d_ECParameters(pkey->pkey.ec, pder); - } +} -static int eckey_param_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_param_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 0); - } +} -static int eckey_pub_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_pub_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 1); - } +} -static int eckey_priv_print(BIO *bp, const EVP_PKEY *pkey, int indent, - ASN1_PCTX *ctx) - { +static int +eckey_priv_print(BIO * bp, const EVP_PKEY * pkey, int indent, + ASN1_PCTX * ctx) +{ return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 2); - } +} -static int old_ec_priv_decode(EVP_PKEY *pkey, - const unsigned char **pder, int derlen) - { +static int +old_ec_priv_decode(EVP_PKEY * pkey, + const unsigned char **pder, int derlen) +{ EC_KEY *ec; - if (!(ec = d2i_ECPrivateKey (NULL, pder, derlen))) - { + if (!(ec = d2i_ECPrivateKey(NULL, pder, derlen))) { ECerr(EC_F_OLD_EC_PRIV_DECODE, EC_R_DECODE_ERROR); return 0; - } + } EVP_PKEY_assign_EC_KEY(pkey, ec); return 1; - } +} -static int old_ec_priv_encode(const EVP_PKEY *pkey, unsigned char **pder) - { +static int +old_ec_priv_encode(const EVP_PKEY * pkey, unsigned char **pder) +{ return i2d_ECPrivateKey(pkey->pkey.ec, pder); - } +} -static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) - { - switch (op) - { - case ASN1_PKEY_CTRL_PKCS7_SIGN: - if (arg1 == 0) - { +static int +ec_pkey_ctrl(EVP_PKEY * pkey, int op, long arg1, void *arg2) +{ + switch (op) { + case ASN1_PKEY_CTRL_PKCS7_SIGN: + if (arg1 == 0) { int snid, hnid; X509_ALGOR *alg1, *alg2; PKCS7_SIGNER_INFO_get0_algs(arg2, NULL, &alg1, &alg2); @@ -591,41 +573,40 @@ static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) if (hnid == NID_undef) return -1; if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) - return -1; + return -1; X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); - } + } return 1; #ifndef OPENSSL_NO_CMS - case ASN1_PKEY_CTRL_CMS_SIGN: - if (arg1 == 0) - { + case ASN1_PKEY_CTRL_CMS_SIGN: + if (arg1 == 0) { int snid, hnid; X509_ALGOR *alg1, *alg2; CMS_SignerInfo_get0_algs(arg2, NULL, NULL, - &alg1, &alg2); + &alg1, &alg2); if (alg1 == NULL || alg1->algorithm == NULL) return -1; hnid = OBJ_obj2nid(alg1->algorithm); if (hnid == NID_undef) return -1; if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) - return -1; + return -1; X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); - } + } return 1; #endif - case ASN1_PKEY_CTRL_DEFAULT_MD_NID: - *(int *)arg2 = NID_sha1; + case ASN1_PKEY_CTRL_DEFAULT_MD_NID: + *(int *) arg2 = NID_sha1; return 2; - default: + default: return -2; - } - } +} + const EVP_PKEY_ASN1_METHOD eckey_asn1_meth = { .pkey_id = EVP_PKEY_EC, .pkey_base_id = EVP_PKEY_EC, diff --git a/lib/libssl/src/crypto/ec/ec_asn1.c b/lib/libssl/src/crypto/ec/ec_asn1.c index 2bde9a6a3c5..70670a4c750 100644 --- a/lib/libssl/src/crypto/ec/ec_asn1.c +++ b/lib/libssl/src/crypto/ec/ec_asn1.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -63,12 +63,13 @@ #include -int EC_GROUP_get_basis_type(const EC_GROUP *group) - { - int i=0; +int +EC_GROUP_get_basis_type(const EC_GROUP * group) +{ + int i = 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != - NID_X9_62_characteristic_two_field) + NID_X9_62_characteristic_two_field) /* everything else is currently not supported */ return 0; @@ -82,40 +83,38 @@ int EC_GROUP_get_basis_type(const EC_GROUP *group) else /* everything else is currently not supported */ return 0; - } +} #ifndef OPENSSL_NO_EC2M -int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) - { +int +EC_GROUP_get_trinomial_basis(const EC_GROUP * group, unsigned int *k) +{ if (group == NULL) return 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != NID_X9_62_characteristic_two_field - || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] == 0))) - { + || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] == 0))) { ECerr(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - + } if (k) *k = group->poly[1]; return 1; - } -int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, - unsigned int *k2, unsigned int *k3) - { +} +int +EC_GROUP_get_pentanomial_basis(const EC_GROUP * group, unsigned int *k1, + unsigned int *k2, unsigned int *k3) +{ if (group == NULL) return 0; if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != NID_X9_62_characteristic_two_field - || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] != 0) && (group->poly[3] != 0) && (group->poly[4] == 0))) - { + || !((group->poly[0] != 0) && (group->poly[1] != 0) && (group->poly[2] != 0) && (group->poly[3] != 0) && (group->poly[4] == 0))) { ECerr(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - + } if (k1) *k1 = group->poly[3]; if (k2) @@ -124,7 +123,7 @@ int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, *k3 = group->poly[1]; return 1; - } +} #endif @@ -133,27 +132,27 @@ typedef struct x9_62_pentanomial_st { long k1; long k2; long k3; - } X9_62_PENTANOMIAL; +} X9_62_PENTANOMIAL; typedef struct x9_62_characteristic_two_st { long m; - ASN1_OBJECT *type; - union { + ASN1_OBJECT *type; + union { char *ptr; /* NID_X9_62_onBasis */ - ASN1_NULL *onBasis; + ASN1_NULL *onBasis; /* NID_X9_62_tpBasis */ ASN1_INTEGER *tpBasis; /* NID_X9_62_ppBasis */ X9_62_PENTANOMIAL *ppBasis; /* anything else */ ASN1_TYPE *other; - } p; - } X9_62_CHARACTERISTIC_TWO; + } p; +} X9_62_CHARACTERISTIC_TWO; typedef struct x9_62_fieldid_st { - ASN1_OBJECT *fieldType; - union { + ASN1_OBJECT *fieldType; + union { char *ptr; /* NID_X9_62_prime_field */ ASN1_INTEGER *prime; @@ -161,40 +160,40 @@ typedef struct x9_62_fieldid_st { X9_62_CHARACTERISTIC_TWO *char_two; /* anything else */ ASN1_TYPE *other; - } p; - } X9_62_FIELDID; + } p; +} X9_62_FIELDID; typedef struct x9_62_curve_st { - ASN1_OCTET_STRING *a; - ASN1_OCTET_STRING *b; - ASN1_BIT_STRING *seed; - } X9_62_CURVE; + ASN1_OCTET_STRING *a; + ASN1_OCTET_STRING *b; + ASN1_BIT_STRING *seed; +} X9_62_CURVE; typedef struct ec_parameters_st { - long version; - X9_62_FIELDID *fieldID; - X9_62_CURVE *curve; - ASN1_OCTET_STRING *base; - ASN1_INTEGER *order; - ASN1_INTEGER *cofactor; - } ECPARAMETERS; + long version; + X9_62_FIELDID *fieldID; + X9_62_CURVE *curve; + ASN1_OCTET_STRING *base; + ASN1_INTEGER *order; + ASN1_INTEGER *cofactor; +} ECPARAMETERS; struct ecpk_parameters_st { - int type; + int type; union { - ASN1_OBJECT *named_curve; + ASN1_OBJECT *named_curve; ECPARAMETERS *parameters; - ASN1_NULL *implicitlyCA; + ASN1_NULL *implicitlyCA; } value; - }/* ECPKPARAMETERS */; +} /* ECPKPARAMETERS */ ; /* SEC1 ECPrivateKey */ typedef struct ec_privatekey_st { - long version; + long version; ASN1_OCTET_STRING *privateKey; - ECPKPARAMETERS *parameters; - ASN1_BIT_STRING *publicKey; - } EC_PRIVATEKEY; + ECPKPARAMETERS *parameters; + ASN1_BIT_STRING *publicKey; +} EC_PRIVATEKEY; /* the OpenSSL ASN.1 definitions */ ASN1_SEQUENCE(X9_62_PENTANOMIAL) = { @@ -219,10 +218,8 @@ ASN1_SEQUENCE(X9_62_CHARACTERISTIC_TWO) = { ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, type, ASN1_OBJECT), ASN1_ADB_OBJECT(X9_62_CHARACTERISTIC_TWO) } ASN1_SEQUENCE_END(X9_62_CHARACTERISTIC_TWO) - DECLARE_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) IMPLEMENT_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) - ASN1_ADB_TEMPLATE(fieldID_def) = ASN1_SIMPLE(X9_62_FIELDID, p.other, ASN1_ANY); ASN1_ADB(X9_62_FIELDID) = { @@ -249,7 +246,6 @@ ASN1_SEQUENCE(ECPARAMETERS) = { ASN1_SIMPLE(ECPARAMETERS, order, ASN1_INTEGER), ASN1_OPT(ECPARAMETERS, cofactor, ASN1_INTEGER) } ASN1_SEQUENCE_END(ECPARAMETERS) - DECLARE_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) IMPLEMENT_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) @@ -258,7 +254,6 @@ ASN1_CHOICE(ECPKPARAMETERS) = { ASN1_SIMPLE(ECPKPARAMETERS, value.parameters, ECPARAMETERS), ASN1_SIMPLE(ECPKPARAMETERS, value.implicitlyCA, ASN1_NULL) } ASN1_CHOICE_END(ECPKPARAMETERS) - DECLARE_ASN1_FUNCTIONS_const(ECPKPARAMETERS) DECLARE_ASN1_ENCODE_FUNCTIONS_const(ECPKPARAMETERS, ECPKPARAMETERS) IMPLEMENT_ASN1_FUNCTIONS_const(ECPKPARAMETERS) @@ -269,39 +264,38 @@ ASN1_SEQUENCE(EC_PRIVATEKEY) = { ASN1_EXP_OPT(EC_PRIVATEKEY, parameters, ECPKPARAMETERS, 0), ASN1_EXP_OPT(EC_PRIVATEKEY, publicKey, ASN1_BIT_STRING, 1) } ASN1_SEQUENCE_END(EC_PRIVATEKEY) - DECLARE_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) DECLARE_ASN1_ENCODE_FUNCTIONS_const(EC_PRIVATEKEY, EC_PRIVATEKEY) IMPLEMENT_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) - /* some declarations of internal function */ -/* ec_asn1_group2field() sets the values in a X9_62_FIELDID object */ +/* ec_asn1_group2field() sets the values in a X9_62_FIELDID object */ static int ec_asn1_group2fieldid(const EC_GROUP *, X9_62_FIELDID *); -/* ec_asn1_group2curve() sets the values in a X9_62_CURVE object */ +/* ec_asn1_group2curve() sets the values in a X9_62_CURVE object */ static int ec_asn1_group2curve(const EC_GROUP *, X9_62_CURVE *); /* ec_asn1_parameters2group() creates a EC_GROUP object from a * ECPARAMETERS object */ -static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *); -/* ec_asn1_group2parameters() creates a ECPARAMETERS object from a +static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *); +/* ec_asn1_group2parameters() creates a ECPARAMETERS object from a * EC_GROUP object */ -static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *,ECPARAMETERS *); +static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *, ECPARAMETERS *); /* ec_asn1_pkparameters2group() creates a EC_GROUP object from a * ECPKPARAMETERS object */ -static EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *); -/* ec_asn1_group2pkparameters() creates a ECPKPARAMETERS object from a +static EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *); +/* ec_asn1_group2pkparameters() creates a ECPKPARAMETERS object from a * EC_GROUP object */ -static ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *, - ECPKPARAMETERS *); +static ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *, + ECPKPARAMETERS *); /* the function definitions */ -static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) - { - int ok=0, nid; - BIGNUM *tmp = NULL; - +static int +ec_asn1_group2fieldid(const EC_GROUP * group, X9_62_FIELDID * field) +{ + int ok = 0, nid; + BIGNUM *tmp = NULL; + if (group == NULL || field == NULL) return 0; @@ -313,248 +307,203 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); /* set OID for the field */ - if ((field->fieldType = OBJ_nid2obj(nid)) == NULL) - { + if ((field->fieldType = OBJ_nid2obj(nid)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); goto err; - } - - if (nid == NID_X9_62_prime_field) - { - if ((tmp = BN_new()) == NULL) - { + } + if (nid == NID_X9_62_prime_field) { + if ((tmp = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } + } /* the parameters are specified by the prime number p */ - if (!EC_GROUP_get_curve_GFp(group, tmp, NULL, NULL, NULL)) - { + if (!EC_GROUP_get_curve_GFp(group, tmp, NULL, NULL, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); goto err; - } + } /* set the prime number */ - field->p.prime = BN_to_ASN1_INTEGER(tmp,NULL); - if (field->p.prime == NULL) - { + field->p.prime = BN_to_ASN1_INTEGER(tmp, NULL); + if (field->p.prime == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_ASN1_LIB); goto err; - } } - else /* nid == NID_X9_62_characteristic_two_field */ + } else /* nid == NID_X9_62_characteristic_two_field */ #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_GF2M_NOT_SUPPORTED); goto err; - } + } #else - { - int field_type; + { + int field_type; X9_62_CHARACTERISTIC_TWO *char_two; field->p.char_two = X9_62_CHARACTERISTIC_TWO_new(); char_two = field->p.char_two; - if (char_two == NULL) - { + if (char_two == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - - char_two->m = (long)EC_GROUP_get_degree(group); + } + char_two->m = (long) EC_GROUP_get_degree(group); field_type = EC_GROUP_get_basis_type(group); - if (field_type == 0) - { + if (field_type == 0) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); goto err; - } + } /* set base type OID */ - if ((char_two->type = OBJ_nid2obj(field_type)) == NULL) - { + if ((char_two->type = OBJ_nid2obj(field_type)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); goto err; - } - - if (field_type == NID_X9_62_tpBasis) - { + } + if (field_type == NID_X9_62_tpBasis) { unsigned int k; if (!EC_GROUP_get_trinomial_basis(group, &k)) goto err; char_two->p.tpBasis = ASN1_INTEGER_new(); - if (!char_two->p.tpBasis) - { + if (!char_two->p.tpBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - if (!ASN1_INTEGER_set(char_two->p.tpBasis, (long)k)) - { + } + if (!ASN1_INTEGER_set(char_two->p.tpBasis, (long) k)) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, - ERR_R_ASN1_LIB); + ERR_R_ASN1_LIB); goto err; - } } - else if (field_type == NID_X9_62_ppBasis) - { + } else if (field_type == NID_X9_62_ppBasis) { unsigned int k1, k2, k3; if (!EC_GROUP_get_pentanomial_basis(group, &k1, &k2, &k3)) goto err; char_two->p.ppBasis = X9_62_PENTANOMIAL_new(); - if (!char_two->p.ppBasis) - { + if (!char_two->p.ppBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } - - /* set k? values */ - char_two->p.ppBasis->k1 = (long)k1; - char_two->p.ppBasis->k2 = (long)k2; - char_two->p.ppBasis->k3 = (long)k3; } - else /* field_type == NID_X9_62_onBasis */ - { + /* set k? values */ + char_two->p.ppBasis->k1 = (long) k1; + char_two->p.ppBasis->k2 = (long) k2; + char_two->p.ppBasis->k3 = (long) k3; + } else { /* field_type == NID_X9_62_onBasis */ /* for ONB the parameters are (asn1) NULL */ char_two->p.onBasis = ASN1_NULL_new(); - if (!char_two->p.onBasis) - { + if (!char_two->p.onBasis) { ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); goto err; - } } } + } #endif ok = 1; -err : if (tmp) +err: if (tmp) BN_free(tmp); - return(ok); + return (ok); } -static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) - { - int ok=0, nid; - BIGNUM *tmp_1=NULL, *tmp_2=NULL; - unsigned char *buffer_1=NULL, *buffer_2=NULL, - *a_buf=NULL, *b_buf=NULL; - size_t len_1, len_2; +static int +ec_asn1_group2curve(const EC_GROUP * group, X9_62_CURVE * curve) +{ + int ok = 0, nid; + BIGNUM *tmp_1 = NULL, *tmp_2 = NULL; + unsigned char *buffer_1 = NULL, *buffer_2 = NULL, *a_buf = NULL, + *b_buf = NULL; + size_t len_1, len_2; unsigned char char_zero = 0; if (!group || !curve || !curve->a || !curve->b) return 0; - if ((tmp_1 = BN_new()) == NULL || (tmp_2 = BN_new()) == NULL) - { + if ((tmp_1 = BN_new()) == NULL || (tmp_2 = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); goto err; - } - + } nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); /* get a and b */ - if (nid == NID_X9_62_prime_field) - { - if (!EC_GROUP_get_curve_GFp(group, NULL, tmp_1, tmp_2, NULL)) - { + if (nid == NID_X9_62_prime_field) { + if (!EC_GROUP_get_curve_GFp(group, NULL, tmp_1, tmp_2, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); goto err; - } } + } #ifndef OPENSSL_NO_EC2M - else /* nid == NID_X9_62_characteristic_two_field */ - { - if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) - { + else { /* nid == NID_X9_62_characteristic_two_field */ + if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); goto err; - } } + } #endif - len_1 = (size_t)BN_num_bytes(tmp_1); - len_2 = (size_t)BN_num_bytes(tmp_2); + len_1 = (size_t) BN_num_bytes(tmp_1); + len_2 = (size_t) BN_num_bytes(tmp_2); - if (len_1 == 0) - { + if (len_1 == 0) { /* len_1 == 0 => a == 0 */ a_buf = &char_zero; len_1 = 1; - } - else - { - if ((buffer_1 = malloc(len_1)) == NULL) - { + } else { + if ((buffer_1 = malloc(len_1)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - if ( (len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) - { + } + if ((len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); goto err; - } - a_buf = buffer_1; } + a_buf = buffer_1; + } - if (len_2 == 0) - { + if (len_2 == 0) { /* len_2 == 0 => b == 0 */ b_buf = &char_zero; len_2 = 1; - } - else - { - if ((buffer_2 = malloc(len_2)) == NULL) - { + } else { + if ((buffer_2 = malloc(len_2)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - if ( (len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) - { + } + if ((len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); goto err; - } - b_buf = buffer_2; } - + b_buf = buffer_2; + } + /* set a and b */ if (!M_ASN1_OCTET_STRING_set(curve->a, a_buf, len_1) || - !M_ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) - { + !M_ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); goto err; - } - + } /* set the seed (optional) */ - if (group->seed) - { + if (group->seed) { if (!curve->seed) - if ((curve->seed = ASN1_BIT_STRING_new()) == NULL) - { + if ((curve->seed = ASN1_BIT_STRING_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); goto err; - } - curve->seed->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT|0x07); + } + curve->seed->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); curve->seed->flags |= ASN1_STRING_FLAG_BITS_LEFT; - if (!ASN1_BIT_STRING_set(curve->seed, group->seed, - (int)group->seed_len)) - { + if (!ASN1_BIT_STRING_set(curve->seed, group->seed, + (int) group->seed_len)) { ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); goto err; - } } - else - { - if (curve->seed) - { + } else { + if (curve->seed) { ASN1_BIT_STRING_free(curve->seed); curve->seed = NULL; - } } + } ok = 1; @@ -566,880 +515,729 @@ err: if (buffer_1) BN_free(tmp_1); if (tmp_2) BN_free(tmp_2); - return(ok); - } + return (ok); +} -static ECPARAMETERS *ec_asn1_group2parameters(const EC_GROUP *group, - ECPARAMETERS *param) - { - int ok=0; - size_t len=0; - ECPARAMETERS *ret=NULL; - BIGNUM *tmp=NULL; - unsigned char *buffer=NULL; - const EC_POINT *point=NULL; +static ECPARAMETERS * +ec_asn1_group2parameters(const EC_GROUP * group, ECPARAMETERS * param) +{ + int ok = 0; + size_t len = 0; + ECPARAMETERS *ret = NULL; + BIGNUM *tmp = NULL; + unsigned char *buffer = NULL; + const EC_POINT *point = NULL; point_conversion_form_t form; - if ((tmp = BN_new()) == NULL) - { + if ((tmp = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - - if (param == NULL) - { - if ((ret = ECPARAMETERS_new()) == NULL) - { - ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, - ERR_R_MALLOC_FAILURE); - goto err; - } } - else + if (param == NULL) { + if ((ret = ECPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, + ERR_R_MALLOC_FAILURE); + goto err; + } + } else ret = param; /* set the version (always one) */ - ret->version = (long)0x1; + ret->version = (long) 0x1; /* set the fieldID */ - if (!ec_asn1_group2fieldid(group, ret->fieldID)) - { + if (!ec_asn1_group2fieldid(group, ret->fieldID)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - + } /* set the curve */ - if (!ec_asn1_group2curve(group, ret->curve)) - { + if (!ec_asn1_group2curve(group, ret->curve)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - + } /* set the base point */ - if ((point = EC_GROUP_get0_generator(group)) == NULL) - { + if ((point = EC_GROUP_get0_generator(group)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, EC_R_UNDEFINED_GENERATOR); goto err; - } - + } form = EC_GROUP_get_point_conversion_form(group); len = EC_POINT_point2oct(group, point, form, NULL, len, NULL); - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - if ((buffer = malloc(len)) == NULL) - { + } + if ((buffer = malloc(len)) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - if (!EC_POINT_point2oct(group, point, form, buffer, len, NULL)) - { + } + if (!EC_POINT_point2oct(group, point, form, buffer, len, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } - if (ret->base == NULL && (ret->base = ASN1_OCTET_STRING_new()) == NULL) - { + } + if (ret->base == NULL && (ret->base = ASN1_OCTET_STRING_new()) == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_MALLOC_FAILURE); goto err; - } - if (!ASN1_OCTET_STRING_set(ret->base, buffer, len)) - { + } + if (!ASN1_OCTET_STRING_set(ret->base, buffer, len)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } - + } /* set the order */ - if (!EC_GROUP_get_order(group, tmp, NULL)) - { + if (!EC_GROUP_get_order(group, tmp, NULL)) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_EC_LIB); goto err; - } + } ret->order = BN_to_ASN1_INTEGER(tmp, ret->order); - if (ret->order == NULL) - { + if (ret->order == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } - + } /* set the cofactor (optional) */ - if (EC_GROUP_get_cofactor(group, tmp, NULL)) - { + if (EC_GROUP_get_cofactor(group, tmp, NULL)) { ret->cofactor = BN_to_ASN1_INTEGER(tmp, ret->cofactor); - if (ret->cofactor == NULL) - { + if (ret->cofactor == NULL) { ECerr(EC_F_EC_ASN1_GROUP2PARAMETERS, ERR_R_ASN1_LIB); goto err; - } } - + } ok = 1; -err : if(!ok) - { +err: if (!ok) { if (ret && !param) ECPARAMETERS_free(ret); ret = NULL; - } + } if (tmp) BN_free(tmp); if (buffer) free(buffer); - return(ret); - } + return (ret); +} -ECPKPARAMETERS *ec_asn1_group2pkparameters(const EC_GROUP *group, - ECPKPARAMETERS *params) - { - int ok = 1, tmp; +ECPKPARAMETERS * +ec_asn1_group2pkparameters(const EC_GROUP * group, ECPKPARAMETERS * params) +{ + int ok = 1, tmp; ECPKPARAMETERS *ret = params; - if (ret == NULL) - { - if ((ret = ECPKPARAMETERS_new()) == NULL) - { - ECerr(EC_F_EC_ASN1_GROUP2PKPARAMETERS, - ERR_R_MALLOC_FAILURE); + if (ret == NULL) { + if ((ret = ECPKPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2PKPARAMETERS, + ERR_R_MALLOC_FAILURE); return NULL; - } } - else - { + } else { if (ret->type == 0 && ret->value.named_curve) ASN1_OBJECT_free(ret->value.named_curve); else if (ret->type == 1 && ret->value.parameters) ECPARAMETERS_free(ret->value.parameters); - } + } - if (EC_GROUP_get_asn1_flag(group)) - { - /* use the asn1 OID to describe the - * the elliptic curve parameters + if (EC_GROUP_get_asn1_flag(group)) { + /* + * use the asn1 OID to describe the the elliptic curve + * parameters */ tmp = EC_GROUP_get_curve_name(group); - if (tmp) - { + if (tmp) { ret->type = 0; if ((ret->value.named_curve = OBJ_nid2obj(tmp)) == NULL) ok = 0; - } - else + } else /* we don't kmow the nid => ERROR */ ok = 0; - } - else - { + } else { /* use the ECPARAMETERS structure */ ret->type = 1; if ((ret->value.parameters = ec_asn1_group2parameters( - group, NULL)) == NULL) + group, NULL)) == NULL) ok = 0; - } + } - if (!ok) - { + if (!ok) { ECPKPARAMETERS_free(ret); return NULL; - } - return ret; } + return ret; +} -static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) - { - int ok = 0, tmp; - EC_GROUP *ret = NULL; - BIGNUM *p = NULL, *a = NULL, *b = NULL; - EC_POINT *point=NULL; - long field_bits; - - if (!params->fieldID || !params->fieldID->fieldType || - !params->fieldID->p.ptr) - { +static EC_GROUP * +ec_asn1_parameters2group(const ECPARAMETERS * params) +{ + int ok = 0, tmp; + EC_GROUP *ret = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL; + EC_POINT *point = NULL; + long field_bits; + + if (!params->fieldID || !params->fieldID->fieldType || + !params->fieldID->p.ptr) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - + } /* now extract the curve parameters a and b */ - if (!params->curve || !params->curve->a || + if (!params->curve || !params->curve->a || !params->curve->a->data || !params->curve->b || - !params->curve->b->data) - { + !params->curve->b->data) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } a = BN_bin2bn(params->curve->a->data, params->curve->a->length, NULL); - if (a == NULL) - { + if (a == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_BN_LIB); goto err; - } + } b = BN_bin2bn(params->curve->b->data, params->curve->b->length, NULL); - if (b == NULL) - { + if (b == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_BN_LIB); goto err; - } - + } /* get the field parameters */ tmp = OBJ_obj2nid(params->fieldID->fieldType); if (tmp == NID_X9_62_characteristic_two_field) #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_GF2M_NOT_SUPPORTED); goto err; - } + } #else - { + { X9_62_CHARACTERISTIC_TWO *char_two; char_two = params->fieldID->p.char_two; field_bits = char_two->m; - if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) - { + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_FIELD_TOO_LARGE); goto err; - } - - if ((p = BN_new()) == NULL) - { + } + if ((p = BN_new()) == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_MALLOC_FAILURE); goto err; - } - + } /* get the base type */ tmp = OBJ_obj2nid(char_two->type); - if (tmp == NID_X9_62_tpBasis) - { + if (tmp == NID_X9_62_tpBasis) { long tmp_long; - if (!char_two->p.tpBasis) - { + if (!char_two->p.tpBasis) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - + } tmp_long = ASN1_INTEGER_get(char_two->p.tpBasis); - if (!(char_two->m > tmp_long && tmp_long > 0)) - { + if (!(char_two->m > tmp_long && tmp_long > 0)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_TRINOMIAL_BASIS); goto err; - } - + } /* create the polynomial */ - if (!BN_set_bit(p, (int)char_two->m)) + if (!BN_set_bit(p, (int) char_two->m)) goto err; - if (!BN_set_bit(p, (int)tmp_long)) + if (!BN_set_bit(p, (int) tmp_long)) goto err; if (!BN_set_bit(p, 0)) goto err; - } - else if (tmp == NID_X9_62_ppBasis) - { + } else if (tmp == NID_X9_62_ppBasis) { X9_62_PENTANOMIAL *penta; penta = char_two->p.ppBasis; - if (!penta) - { + if (!penta) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - - if (!(char_two->m > penta->k3 && penta->k3 > penta->k2 && penta->k2 > penta->k1 && penta->k1 > 0)) - { + } + if (!(char_two->m > penta->k3 && penta->k3 > penta->k2 && penta->k2 > penta->k1 && penta->k1 > 0)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_PENTANOMIAL_BASIS); goto err; - } - - /* create the polynomial */ - if (!BN_set_bit(p, (int)char_two->m)) goto err; - if (!BN_set_bit(p, (int)penta->k1)) goto err; - if (!BN_set_bit(p, (int)penta->k2)) goto err; - if (!BN_set_bit(p, (int)penta->k3)) goto err; - if (!BN_set_bit(p, 0)) goto err; } - else if (tmp == NID_X9_62_onBasis) - { + /* create the polynomial */ + if (!BN_set_bit(p, (int) char_two->m)) + goto err; + if (!BN_set_bit(p, (int) penta->k1)) + goto err; + if (!BN_set_bit(p, (int) penta->k2)) + goto err; + if (!BN_set_bit(p, (int) penta->k3)) + goto err; + if (!BN_set_bit(p, 0)) + goto err; + } else if (tmp == NID_X9_62_onBasis) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_NOT_IMPLEMENTED); goto err; - } - else /* error */ - { + } else { /* error */ ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GF2m(p, a, b, NULL); - } + } #endif - else if (tmp == NID_X9_62_prime_field) - { + else if (tmp == NID_X9_62_prime_field) { /* we have a curve over a prime field */ /* extract the prime number */ - if (!params->fieldID->p.prime) - { + if (!params->fieldID->p.prime) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } + } p = ASN1_INTEGER_to_BN(params->fieldID->p.prime, NULL); - if (p == NULL) - { + if (p == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); goto err; - } - - if (BN_is_negative(p) || BN_is_zero(p)) - { + } + if (BN_is_negative(p) || BN_is_zero(p)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_FIELD); goto err; - } - + } field_bits = BN_num_bits(p); - if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) - { + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_FIELD_TOO_LARGE); goto err; - } - + } /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GFp(p, a, b, NULL); - } - else - { + } else { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_FIELD); goto err; - } + } - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } /* extract seed (optional) */ - if (params->curve->seed != NULL) - { + if (params->curve->seed != NULL) { if (ret->seed != NULL) free(ret->seed); - if (!(ret->seed = malloc(params->curve->seed->length))) - { - ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, - ERR_R_MALLOC_FAILURE); + if (!(ret->seed = malloc(params->curve->seed->length))) { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, + ERR_R_MALLOC_FAILURE); goto err; - } - memcpy(ret->seed, params->curve->seed->data, - params->curve->seed->length); - ret->seed_len = params->curve->seed->length; } - - if (!params->order || !params->base || !params->base->data) - { + memcpy(ret->seed, params->curve->seed->data, + params->curve->seed->length); + ret->seed_len = params->curve->seed->length; + } + if (!params->order || !params->base || !params->base->data) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_ASN1_ERROR); goto err; - } - - if ((point = EC_POINT_new(ret)) == NULL) goto err; + } + if ((point = EC_POINT_new(ret)) == NULL) + goto err; /* set the point conversion form */ EC_GROUP_set_point_conversion_form(ret, (point_conversion_form_t) - (params->base->data[0] & ~0x01)); + (params->base->data[0] & ~0x01)); /* extract the ec point */ - if (!EC_POINT_oct2point(ret, point, params->base->data, - params->base->length, NULL)) - { + if (!EC_POINT_oct2point(ret, point, params->base->data, + params->base->length, NULL)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } /* extract the order */ - if ((a = ASN1_INTEGER_to_BN(params->order, a)) == NULL) - { + if ((a = ASN1_INTEGER_to_BN(params->order, a)) == NULL) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); goto err; - } - if (BN_is_negative(a) || BN_is_zero(a)) - { + } + if (BN_is_negative(a) || BN_is_zero(a)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_GROUP_ORDER); goto err; - } - if (BN_num_bits(a) > (int)field_bits + 1) /* Hasse bound */ - { + } + if (BN_num_bits(a) > (int) field_bits + 1) { /* Hasse bound */ ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_INVALID_GROUP_ORDER); goto err; - } - + } /* extract the cofactor (optional) */ - if (params->cofactor == NULL) - { - if (b) - { + if (params->cofactor == NULL) { + if (b) { BN_free(b); b = NULL; - } } - else - if ((b = ASN1_INTEGER_to_BN(params->cofactor, b)) == NULL) - { - ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); - goto err; - } + } else if ((b = ASN1_INTEGER_to_BN(params->cofactor, b)) == NULL) { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_ASN1_LIB); + goto err; + } /* set the generator, order and cofactor (if present) */ - if (!EC_GROUP_set_generator(ret, point, a, b)) - { + if (!EC_GROUP_set_generator(ret, point, a, b)) { ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, ERR_R_EC_LIB); goto err; - } - + } ok = 1; -err: if (!ok) - { - if (ret) +err: if (!ok) { + if (ret) EC_GROUP_clear_free(ret); ret = NULL; - } - - if (p) + } + if (p) BN_free(p); - if (a) + if (a) BN_free(a); - if (b) + if (b) BN_free(b); - if (point) + if (point) EC_POINT_free(point); - return(ret); + return (ret); } -EC_GROUP *ec_asn1_pkparameters2group(const ECPKPARAMETERS *params) - { - EC_GROUP *ret=NULL; - int tmp=0; +EC_GROUP * +ec_asn1_pkparameters2group(const ECPKPARAMETERS * params) +{ + EC_GROUP *ret = NULL; + int tmp = 0; - if (params == NULL) - { - ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, - EC_R_MISSING_PARAMETERS); + if (params == NULL) { + ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, + EC_R_MISSING_PARAMETERS); return NULL; - } - - if (params->type == 0) - { /* the curve is given by an OID */ + } + if (params->type == 0) {/* the curve is given by an OID */ tmp = OBJ_obj2nid(params->value.named_curve); - if ((ret = EC_GROUP_new_by_curve_name(tmp)) == NULL) - { - ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, - EC_R_EC_GROUP_NEW_BY_NAME_FAILURE); + if ((ret = EC_GROUP_new_by_curve_name(tmp)) == NULL) { + ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, + EC_R_EC_GROUP_NEW_BY_NAME_FAILURE); return NULL; - } - EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_NAMED_CURVE); } - else if (params->type == 1) - { /* the parameters are given by a ECPARAMETERS - * structure */ + EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_NAMED_CURVE); + } else if (params->type == 1) { /* the parameters are given by a + * ECPARAMETERS structure */ ret = ec_asn1_parameters2group(params->value.parameters); - if (!ret) - { + if (!ret) { ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, ERR_R_EC_LIB); return NULL; - } - EC_GROUP_set_asn1_flag(ret, 0x0); } - else if (params->type == 2) - { /* implicitlyCA */ + EC_GROUP_set_asn1_flag(ret, 0x0); + } else if (params->type == 2) { /* implicitlyCA */ return NULL; - } - else - { + } else { ECerr(EC_F_EC_ASN1_PKPARAMETERS2GROUP, EC_R_ASN1_ERROR); return NULL; - } + } return ret; - } +} /* EC_GROUP <-> DER encoding of ECPKPARAMETERS */ -EC_GROUP *d2i_ECPKParameters(EC_GROUP **a, const unsigned char **in, long len) - { - EC_GROUP *group = NULL; - ECPKPARAMETERS *params = NULL; +EC_GROUP * +d2i_ECPKParameters(EC_GROUP ** a, const unsigned char **in, long len) +{ + EC_GROUP *group = NULL; + ECPKPARAMETERS *params = NULL; - if ((params = d2i_ECPKPARAMETERS(NULL, in, len)) == NULL) - { + if ((params = d2i_ECPKPARAMETERS(NULL, in, len)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_D2I_ECPKPARAMETERS_FAILURE); ECPKPARAMETERS_free(params); return NULL; - } - - if ((group = ec_asn1_pkparameters2group(params)) == NULL) - { + } + if ((group = ec_asn1_pkparameters2group(params)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_PKPARAMETERS2GROUP_FAILURE); ECPKPARAMETERS_free(params); - return NULL; - } - - + return NULL; + } if (a && *a) EC_GROUP_clear_free(*a); if (a) *a = group; ECPKPARAMETERS_free(params); - return(group); - } + return (group); +} -int i2d_ECPKParameters(const EC_GROUP *a, unsigned char **out) - { - int ret=0; - ECPKPARAMETERS *tmp = ec_asn1_group2pkparameters(a, NULL); - if (tmp == NULL) - { +int +i2d_ECPKParameters(const EC_GROUP * a, unsigned char **out) +{ + int ret = 0; + ECPKPARAMETERS *tmp = ec_asn1_group2pkparameters(a, NULL); + if (tmp == NULL) { ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_GROUP2PKPARAMETERS_FAILURE); return 0; - } - if ((ret = i2d_ECPKPARAMETERS(tmp, out)) == 0) - { + } + if ((ret = i2d_ECPKPARAMETERS(tmp, out)) == 0) { ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_I2D_ECPKPARAMETERS_FAILURE); ECPKPARAMETERS_free(tmp); return 0; - } - ECPKPARAMETERS_free(tmp); - return(ret); } + ECPKPARAMETERS_free(tmp); + return (ret); +} /* some EC_KEY functions */ -EC_KEY *d2i_ECPrivateKey(EC_KEY **a, const unsigned char **in, long len) - { - int ok=0; - EC_KEY *ret=NULL; - EC_PRIVATEKEY *priv_key=NULL; +EC_KEY * +d2i_ECPrivateKey(EC_KEY ** a, const unsigned char **in, long len) +{ + int ok = 0; + EC_KEY *ret = NULL; + EC_PRIVATEKEY *priv_key = NULL; - if ((priv_key = EC_PRIVATEKEY_new()) == NULL) - { + if ((priv_key = EC_PRIVATEKEY_new()) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); return NULL; - } - - if ((priv_key = d2i_EC_PRIVATEKEY(&priv_key, in, len)) == NULL) - { + } + if ((priv_key = d2i_EC_PRIVATEKEY(&priv_key, in, len)) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); EC_PRIVATEKEY_free(priv_key); return NULL; - } - - if (a == NULL || *a == NULL) - { - if ((ret = EC_KEY_new()) == NULL) - { + } + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } + } if (a) *a = ret; - } - else + } else ret = *a; - if (priv_key->parameters) - { + if (priv_key->parameters) { if (ret->group) EC_GROUP_clear_free(ret->group); ret->group = ec_asn1_pkparameters2group(priv_key->parameters); - } - - if (ret->group == NULL) - { + } + if (ret->group == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - + } ret->version = priv_key->version; - if (priv_key->privateKey) - { + if (priv_key->privateKey) { ret->priv_key = BN_bin2bn( - M_ASN1_STRING_data(priv_key->privateKey), - M_ASN1_STRING_length(priv_key->privateKey), - ret->priv_key); - if (ret->priv_key == NULL) - { + M_ASN1_STRING_data(priv_key->privateKey), + M_ASN1_STRING_length(priv_key->privateKey), + ret->priv_key); + if (ret->priv_key == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, - ERR_R_BN_LIB); + ERR_R_BN_LIB); goto err; - } } - else - { - ECerr(EC_F_D2I_ECPRIVATEKEY, - EC_R_MISSING_PRIVATE_KEY); + } else { + ECerr(EC_F_D2I_ECPRIVATEKEY, + EC_R_MISSING_PRIVATE_KEY); goto err; - } + } - if (priv_key->publicKey) - { + if (priv_key->publicKey) { const unsigned char *pub_oct; size_t pub_oct_len; if (ret->pub_key) EC_POINT_clear_free(ret->pub_key); ret->pub_key = EC_POINT_new(ret->group); - if (ret->pub_key == NULL) - { + if (ret->pub_key == NULL) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - pub_oct = M_ASN1_STRING_data(priv_key->publicKey); + } + pub_oct = M_ASN1_STRING_data(priv_key->publicKey); pub_oct_len = M_ASN1_STRING_length(priv_key->publicKey); /* save the point conversion form */ - ret->conv_form = (point_conversion_form_t)(pub_oct[0] & ~0x01); + ret->conv_form = (point_conversion_form_t) (pub_oct[0] & ~0x01); if (!EC_POINT_oct2point(ret->group, ret->pub_key, - pub_oct, pub_oct_len, NULL)) - { + pub_oct, pub_oct_len, NULL)) { ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } } - + } ok = 1; err: - if (!ok) - { + if (!ok) { if (ret) EC_KEY_free(ret); ret = NULL; - } - + } if (priv_key) EC_PRIVATEKEY_free(priv_key); - return(ret); - } + return (ret); +} -int i2d_ECPrivateKey(EC_KEY *a, unsigned char **out) - { - int ret=0, ok=0; - unsigned char *buffer=NULL; - size_t buf_len=0, tmp_len; - EC_PRIVATEKEY *priv_key=NULL; +int +i2d_ECPrivateKey(EC_KEY * a, unsigned char **out) +{ + int ret = 0, ok = 0; + unsigned char *buffer = NULL; + size_t buf_len = 0, tmp_len; + EC_PRIVATEKEY *priv_key = NULL; - if (a == NULL || a->group == NULL || a->priv_key == NULL) - { + if (a == NULL || a->group == NULL || a->priv_key == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_PASSED_NULL_PARAMETER); + ERR_R_PASSED_NULL_PARAMETER); goto err; - } - - if ((priv_key = EC_PRIVATEKEY_new()) == NULL) - { + } + if ((priv_key = EC_PRIVATEKEY_new()) == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - + } priv_key->version = a->version; - buf_len = (size_t)BN_num_bytes(a->priv_key); + buf_len = (size_t) BN_num_bytes(a->priv_key); buffer = malloc(buf_len); - if (buffer == NULL) - { + if (buffer == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - - if (!BN_bn2bin(a->priv_key, buffer)) - { + } + if (!BN_bn2bin(a->priv_key, buffer)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_BN_LIB); goto err; - } - - if (!M_ASN1_OCTET_STRING_set(priv_key->privateKey, buffer, buf_len)) - { + } + if (!M_ASN1_OCTET_STRING_set(priv_key->privateKey, buffer, buf_len)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_ASN1_LIB); goto err; - } - - if (!(a->enc_flag & EC_PKEY_NO_PARAMETERS)) - { + } + if (!(a->enc_flag & EC_PKEY_NO_PARAMETERS)) { if ((priv_key->parameters = ec_asn1_group2pkparameters( - a->group, priv_key->parameters)) == NULL) - { + a->group, priv_key->parameters)) == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } } - - if (!(a->enc_flag & EC_PKEY_NO_PUBKEY)) - { + } + if (!(a->enc_flag & EC_PKEY_NO_PUBKEY)) { priv_key->publicKey = M_ASN1_BIT_STRING_new(); - if (priv_key->publicKey == NULL) - { + if (priv_key->publicKey == NULL) { ECerr(EC_F_I2D_ECPRIVATEKEY, - ERR_R_MALLOC_FAILURE); + ERR_R_MALLOC_FAILURE); goto err; - } - - tmp_len = EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, NULL, 0, NULL); + } + tmp_len = EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, NULL, 0, NULL); - if (tmp_len > buf_len) - { + if (tmp_len > buf_len) { unsigned char *tmp_buffer = realloc(buffer, tmp_len); - if (!tmp_buffer) - { + if (!tmp_buffer) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); goto err; - } + } buffer = tmp_buffer; buf_len = tmp_len; - } - - if (!EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, buffer, buf_len, NULL)) - { + } + if (!EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, buffer, buf_len, NULL)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - - priv_key->publicKey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT|0x07); + } + priv_key->publicKey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); priv_key->publicKey->flags |= ASN1_STRING_FLAG_BITS_LEFT; - if (!M_ASN1_BIT_STRING_set(priv_key->publicKey, buffer, - buf_len)) - { + if (!M_ASN1_BIT_STRING_set(priv_key->publicKey, buffer, + buf_len)) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_ASN1_LIB); goto err; - } } - - if ((ret = i2d_EC_PRIVATEKEY(priv_key, out)) == 0) - { + } + if ((ret = i2d_EC_PRIVATEKEY(priv_key, out)) == 0) { ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); goto err; - } - ok=1; + } + ok = 1; err: if (buffer) free(buffer); if (priv_key) EC_PRIVATEKEY_free(priv_key); - return(ok?ret:0); - } + return (ok ? ret : 0); +} -int i2d_ECParameters(EC_KEY *a, unsigned char **out) - { - if (a == NULL) - { +int +i2d_ECParameters(EC_KEY * a, unsigned char **out) +{ + if (a == NULL) { ECerr(EC_F_I2D_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - return i2d_ECPKParameters(a->group, out); } + return i2d_ECPKParameters(a->group, out); +} -EC_KEY *d2i_ECParameters(EC_KEY **a, const unsigned char **in, long len) - { - EC_KEY *ret; +EC_KEY * +d2i_ECParameters(EC_KEY ** a, const unsigned char **in, long len) +{ + EC_KEY *ret; - if (in == NULL || *in == NULL) - { + if (in == NULL || *in == NULL) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } - - if (a == NULL || *a == NULL) - { - if ((ret = EC_KEY_new()) == NULL) - { + } + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_MALLOC_FAILURE); return NULL; - } + } if (a) *a = ret; - } - else + } else ret = *a; - if (!d2i_ECPKParameters(&ret->group, in, len)) - { + if (!d2i_ECPKParameters(&ret->group, in, len)) { ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_EC_LIB); return NULL; - } - - return ret; } + return ret; +} -EC_KEY *o2i_ECPublicKey(EC_KEY **a, const unsigned char **in, long len) - { - EC_KEY *ret=NULL; +EC_KEY * +o2i_ECPublicKey(EC_KEY ** a, const unsigned char **in, long len) +{ + EC_KEY *ret = NULL; - if (a == NULL || (*a) == NULL || (*a)->group == NULL) - { - /* sorry, but a EC_GROUP-structur is necessary - * to set the public key */ + if (a == NULL || (*a) == NULL || (*a)->group == NULL) { + /* + * sorry, but a EC_GROUP-structur is necessary to set the + * public key + */ ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } + } ret = *a; - if (ret->pub_key == NULL && - (ret->pub_key = EC_POINT_new(ret->group)) == NULL) - { + if (ret->pub_key == NULL && + (ret->pub_key = EC_POINT_new(ret->group)) == NULL) { ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_MALLOC_FAILURE); return 0; - } - if (!EC_POINT_oct2point(ret->group, ret->pub_key, *in, len, NULL)) - { + } + if (!EC_POINT_oct2point(ret->group, ret->pub_key, *in, len, NULL)) { ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_EC_LIB); return 0; - } + } /* save the point conversion form */ - ret->conv_form = (point_conversion_form_t)(*in[0] & ~0x01); + ret->conv_form = (point_conversion_form_t) (*in[0] & ~0x01); *in += len; return ret; - } +} -int i2o_ECPublicKey(EC_KEY *a, unsigned char **out) - { - size_t buf_len=0; +int +i2o_ECPublicKey(EC_KEY * a, unsigned char **out) +{ + size_t buf_len = 0; int new_buffer = 0; - if (a == NULL) - { + if (a == NULL) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - buf_len = EC_POINT_point2oct(a->group, a->pub_key, - a->conv_form, NULL, 0, NULL); + } + buf_len = EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, NULL, 0, NULL); if (out == NULL || buf_len == 0) - /* out == NULL => just return the length of the octet string */ + /* out == NULL => just return the length of the octet string */ return buf_len; - if (*out == NULL) - { - if ((*out = malloc(buf_len)) == NULL) - { + if (*out == NULL) { + if ((*out = malloc(buf_len)) == NULL) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_MALLOC_FAILURE); return 0; - } - new_buffer = 1; } - if (!EC_POINT_point2oct(a->group, a->pub_key, a->conv_form, - *out, buf_len, NULL)) - { + new_buffer = 1; + } + if (!EC_POINT_point2oct(a->group, a->pub_key, a->conv_form, + *out, buf_len, NULL)) { ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_EC_LIB); free(*out); *out = NULL; return 0; - } + } if (!new_buffer) *out += buf_len; return buf_len; - } +} diff --git a/lib/libssl/src/crypto/ec/ec_check.c b/lib/libssl/src/crypto/ec/ec_check.c index 0e316b4b3ff..8f533d5ff8a 100644 --- a/lib/libssl/src/crypto/ec/ec_check.c +++ b/lib/libssl/src/crypto/ec/ec_check.c @@ -7,7 +7,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -56,60 +56,54 @@ #include "ec_lcl.h" #include -int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx) - { +int +EC_GROUP_check(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; BIGNUM *order; BN_CTX *new_ctx = NULL; EC_POINT *point = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GROUP_CHECK, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); - if ((order = BN_CTX_get(ctx)) == NULL) goto err; + if ((order = BN_CTX_get(ctx)) == NULL) + goto err; /* check the discriminant */ - if (!EC_GROUP_check_discriminant(group, ctx)) - { + if (!EC_GROUP_check_discriminant(group, ctx)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_DISCRIMINANT_IS_ZERO); goto err; - } - + } /* check the generator */ - if (group->generator == NULL) - { + if (group->generator == NULL) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_GENERATOR); goto err; - } - if (!EC_POINT_is_on_curve(group, group->generator, ctx)) - { + } + if (!EC_POINT_is_on_curve(group, group->generator, ctx)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } /* check the order of the generator */ - if ((point = EC_POINT_new(group)) == NULL) goto err; - if (!EC_GROUP_get_order(group, order, ctx)) goto err; - if (BN_is_zero(order)) - { + if ((point = EC_POINT_new(group)) == NULL) + goto err; + if (!EC_GROUP_get_order(group, order, ctx)) + goto err; + if (BN_is_zero(order)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_ORDER); goto err; - } - - if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx)) goto err; - if (!EC_POINT_is_at_infinity(group, point)) - { + } + if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx)) + goto err; + if (!EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GROUP_CHECK, EC_R_INVALID_GROUP_ORDER); goto err; - } - + } ret = 1; err: @@ -120,4 +114,4 @@ err: if (point) EC_POINT_free(point); return ret; - } +} diff --git a/lib/libssl/src/crypto/ec/ec_curve.c b/lib/libssl/src/crypto/ec/ec_curve.c index 23bc3ab94e1..daaa8edd7eb 100644 --- a/lib/libssl/src/crypto/ec/ec_curve.c +++ b/lib/libssl/src/crypto/ec/ec_curve.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -58,13 +58,13 @@ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * - * Portions of the attached software ("Contribution") are developed by + * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the OpenSSL open source * license provided above. * - * The elliptic curve binary polynomial software is originally written by + * The elliptic curve binary polynomial software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. * */ @@ -75,1692 +75,2075 @@ #include typedef struct { - int field_type, /* either NID_X9_62_prime_field or + int field_type, /* either NID_X9_62_prime_field or * NID_X9_62_characteristic_two_field */ - seed_len, - param_len; + seed_len, param_len; unsigned int cofactor; /* promoted to BN_ULONG */ } EC_CURVE_DATA; /* the nist prime curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_NIST_PRIME_192 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0x30,0x45,0xAE,0x6F,0xC8,0x42,0x2F,0x64,0xED,0x57, /* seed */ - 0x95,0x28,0xD3,0x81,0x20,0xEA,0xE1,0x21,0x96,0xD5, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0x64,0x21,0x05,0x19,0xE5,0x9C,0x80,0xE7,0x0F,0xA7, /* b */ - 0xE9,0xAB,0x72,0x24,0x30,0x49,0xFE,0xB8,0xDE,0xEC, - 0xC1,0x46,0xB9,0xB1, - 0x18,0x8D,0xA8,0x0E,0xB0,0x30,0x90,0xF6,0x7C,0xBF, /* x */ - 0x20,0xEB,0x43,0xA1,0x88,0x00,0xF4,0xFF,0x0A,0xFD, - 0x82,0xFF,0x10,0x12, - 0x07,0x19,0x2b,0x95,0xff,0xc8,0xda,0x78,0x63,0x10, /* y */ - 0x11,0xed,0x6b,0x24,0xcd,0xd5,0x73,0xf9,0x77,0xa1, - 0x1e,0x79,0x48,0x11, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x99,0xDE,0xF8,0x36,0x14,0x6B,0xC9,0xB1, - 0xB4,0xD2,0x28,0x31 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+28*6]; } - _EC_NIST_PRIME_224 = { - { NID_X9_62_prime_field,20,28,1 }, - { 0xBD,0x71,0x34,0x47,0x99,0xD5,0xC7,0xFC,0xDC,0x45, /* seed */ - 0xB5,0x9F,0xA3,0xB9,0xAB,0x8F,0x6A,0x94,0x8B,0xC5, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, - 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, - 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, - 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+48*6]; } - _EC_NIST_PRIME_384 = { - { NID_X9_62_prime_field,20,48,1 }, - { 0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00, /* seed */ - 0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFC, - 0xB3,0x31,0x2F,0xA7,0xE2,0x3E,0xE7,0xE4,0x98,0x8E, /* b */ - 0x05,0x6B,0xE3,0xF8,0x2D,0x19,0x18,0x1D,0x9C,0x6E, - 0xFE,0x81,0x41,0x12,0x03,0x14,0x08,0x8F,0x50,0x13, - 0x87,0x5A,0xC6,0x56,0x39,0x8D,0x8A,0x2E,0xD1,0x9D, - 0x2A,0x85,0xC8,0xED,0xD3,0xEC,0x2A,0xEF, - 0xAA,0x87,0xCA,0x22,0xBE,0x8B,0x05,0x37,0x8E,0xB1, /* x */ - 0xC7,0x1E,0xF3,0x20,0xAD,0x74,0x6E,0x1D,0x3B,0x62, - 0x8B,0xA7,0x9B,0x98,0x59,0xF7,0x41,0xE0,0x82,0x54, - 0x2A,0x38,0x55,0x02,0xF2,0x5D,0xBF,0x55,0x29,0x6C, - 0x3A,0x54,0x5E,0x38,0x72,0x76,0x0A,0xB7, - 0x36,0x17,0xde,0x4a,0x96,0x26,0x2c,0x6f,0x5d,0x9e, /* y */ - 0x98,0xbf,0x92,0x92,0xdc,0x29,0xf8,0xf4,0x1d,0xbd, - 0x28,0x9a,0x14,0x7c,0xe9,0xda,0x31,0x13,0xb5,0xf0, - 0xb8,0xc0,0x0a,0x60,0xb1,0xce,0x1d,0x7e,0x81,0x9d, - 0x7a,0x43,0x1d,0x7c,0x90,0xea,0x0e,0x5f, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xC7,0x63,0x4D,0x81,0xF4,0x37, - 0x2D,0xDF,0x58,0x1A,0x0D,0xB2,0x48,0xB0,0xA7,0x7A, - 0xEC,0xEC,0x19,0x6A,0xCC,0xC5,0x29,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+66*6]; } - _EC_NIST_PRIME_521 = { - { NID_X9_62_prime_field,20,66,1 }, - { 0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC, /* seed */ - 0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA, - - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, - 0x00,0x51,0x95,0x3E,0xB9,0x61,0x8E,0x1C,0x9A,0x1F, /* b */ - 0x92,0x9A,0x21,0xA0,0xB6,0x85,0x40,0xEE,0xA2,0xDA, - 0x72,0x5B,0x99,0xB3,0x15,0xF3,0xB8,0xB4,0x89,0x91, - 0x8E,0xF1,0x09,0xE1,0x56,0x19,0x39,0x51,0xEC,0x7E, - 0x93,0x7B,0x16,0x52,0xC0,0xBD,0x3B,0xB1,0xBF,0x07, - 0x35,0x73,0xDF,0x88,0x3D,0x2C,0x34,0xF1,0xEF,0x45, - 0x1F,0xD4,0x6B,0x50,0x3F,0x00, - 0x00,0xC6,0x85,0x8E,0x06,0xB7,0x04,0x04,0xE9,0xCD, /* x */ - 0x9E,0x3E,0xCB,0x66,0x23,0x95,0xB4,0x42,0x9C,0x64, - 0x81,0x39,0x05,0x3F,0xB5,0x21,0xF8,0x28,0xAF,0x60, - 0x6B,0x4D,0x3D,0xBA,0xA1,0x4B,0x5E,0x77,0xEF,0xE7, - 0x59,0x28,0xFE,0x1D,0xC1,0x27,0xA2,0xFF,0xA8,0xDE, - 0x33,0x48,0xB3,0xC1,0x85,0x6A,0x42,0x9B,0xF9,0x7E, - 0x7E,0x31,0xC2,0xE5,0xBD,0x66, - 0x01,0x18,0x39,0x29,0x6a,0x78,0x9a,0x3b,0xc0,0x04, /* y */ - 0x5c,0x8a,0x5f,0xb4,0x2c,0x7d,0x1b,0xd9,0x98,0xf5, - 0x44,0x49,0x57,0x9b,0x44,0x68,0x17,0xaf,0xbd,0x17, - 0x27,0x3e,0x66,0x2c,0x97,0xee,0x72,0x99,0x5e,0xf4, - 0x26,0x40,0xc5,0x50,0xb9,0x01,0x3f,0xad,0x07,0x61, - 0x35,0x3c,0x70,0x86,0xa2,0x72,0xc2,0x40,0x88,0xbe, - 0x94,0x76,0x9f,0xd1,0x66,0x50, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFA,0x51,0x86,0x87,0x83,0xBF,0x2F, - 0x96,0x6B,0x7F,0xCC,0x01,0x48,0xF7,0x09,0xA5,0xD0, - 0x3B,0xB5,0xC9,0xB8,0x89,0x9C,0x47,0xAE,0xBB,0x6F, - 0xB7,0x1E,0x91,0x38,0x64,0x09 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_NIST_PRIME_192 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0x30, 0x45, 0xAE, 0x6F, 0xC8, 0x42, 0x2F, 0x64, 0xED, 0x57, /* seed */ + 0x95, 0x28, 0xD3, 0x81, 0x20, 0xEA, 0xE1, 0x21, 0x96, 0xD5, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0x64, 0x21, 0x05, 0x19, 0xE5, 0x9C, 0x80, 0xE7, 0x0F, 0xA7, /* b */ + 0xE9, 0xAB, 0x72, 0x24, 0x30, 0x49, 0xFE, 0xB8, 0xDE, 0xEC, + 0xC1, 0x46, 0xB9, 0xB1, + 0x18, 0x8D, 0xA8, 0x0E, 0xB0, 0x30, 0x90, 0xF6, 0x7C, 0xBF, /* x */ + 0x20, 0xEB, 0x43, 0xA1, 0x88, 0x00, 0xF4, 0xFF, 0x0A, 0xFD, + 0x82, 0xFF, 0x10, 0x12, + 0x07, 0x19, 0x2b, 0x95, 0xff, 0xc8, 0xda, 0x78, 0x63, 0x10, /* y */ + 0x11, 0xed, 0x6b, 0x24, 0xcd, 0xd5, 0x73, 0xf9, 0x77, 0xa1, + 0x1e, 0x79, 0x48, 0x11, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x99, 0xDE, 0xF8, 0x36, 0x14, 0x6B, 0xC9, 0xB1, + 0xB4, 0xD2, 0x28, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 28 * 6]; +} + _EC_NIST_PRIME_224 = { + { + NID_X9_62_prime_field, 20, 28, 1 + }, + { + 0xBD, 0x71, 0x34, 0x47, 0x99, 0xD5, 0xC7, 0xFC, 0xDC, 0x45, /* seed */ + 0xB5, 0x9F, 0xA3, 0xB9, 0xAB, 0x8F, 0x6A, 0x94, 0x8B, 0xC5, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4, + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21, + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, + 0x13, 0xDD, 0x29, 0x45, 0x5C, 0x5C, 0x2A, 0x3D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 48 * 6]; +} + _EC_NIST_PRIME_384 = { + { + NID_X9_62_prime_field, 20, 48, 1 + }, + { + 0xA3, 0x35, 0x92, 0x6A, 0xA3, 0x19, 0xA2, 0x7A, 0x1D, 0x00, /* seed */ + 0x89, 0x6A, 0x67, 0x73, 0xA4, 0x82, 0x7A, 0xCD, 0xAC, 0x73, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC, + 0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, /* b */ + 0x05, 0x6B, 0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, + 0xFE, 0x81, 0x41, 0x12, 0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, + 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D, 0x8A, 0x2E, 0xD1, 0x9D, + 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF, + 0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, /* x */ + 0xC7, 0x1E, 0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, + 0x8B, 0xA7, 0x9B, 0x98, 0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, + 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D, 0xBF, 0x55, 0x29, 0x6C, + 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7, + 0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, /* y */ + 0x98, 0xbf, 0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, + 0x28, 0x9a, 0x14, 0x7c, 0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, + 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce, 0x1d, 0x7e, 0x81, 0x9d, + 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, + 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2, 0x48, 0xB0, 0xA7, 0x7A, + 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 66 * 6]; +} + _EC_NIST_PRIME_521 = { + { + NID_X9_62_prime_field, 20, 66, 1 + }, + { + 0xD0, 0x9E, 0x88, 0x00, 0x29, 0x1C, 0xB8, 0x53, 0x96, 0xCC, /* seed */ + 0x67, 0x17, 0x39, 0x32, 0x84, 0xAA, 0xA0, 0xDA, 0x64, 0xBA, + + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + 0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, /* b */ + 0x92, 0x9A, 0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, + 0x72, 0x5B, 0x99, 0xB3, 0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, + 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19, 0x39, 0x51, 0xEC, 0x7E, + 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1, 0xBF, 0x07, + 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45, + 0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00, + 0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, /* x */ + 0x9E, 0x3E, 0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, + 0x81, 0x39, 0x05, 0x3F, 0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, + 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B, 0x5E, 0x77, 0xEF, 0xE7, + 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF, 0xA8, 0xDE, + 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E, + 0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66, + 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x04, /* y */ + 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, + 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, + 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, + 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, + 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, + 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86, 0x87, 0x83, 0xBF, 0x2F, + 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09, 0xA5, 0xD0, + 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F, + 0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09 + } +}; /* the x9.62 prime curves (minus the nist prime curves) */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_PRIME_192V2 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0x31,0xA9,0x2E,0xE2,0x02,0x9F,0xD1,0x0D,0x90,0x1B, /* seed */ - 0x11,0x3E,0x99,0x07,0x10,0xF0,0xD2,0x1A,0xC6,0xB6, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0xCC,0x22,0xD6,0xDF,0xB9,0x5C,0x6B,0x25,0xE4,0x9C, /* b */ - 0x0D,0x63,0x64,0xA4,0xE5,0x98,0x0C,0x39,0x3A,0xA2, - 0x16,0x68,0xD9,0x53, - 0xEE,0xA2,0xBA,0xE7,0xE1,0x49,0x78,0x42,0xF2,0xDE, /* x */ - 0x77,0x69,0xCF,0xE9,0xC9,0x89,0xC0,0x72,0xAD,0x69, - 0x6F,0x48,0x03,0x4A, - 0x65,0x74,0xd1,0x1d,0x69,0xb6,0xec,0x7a,0x67,0x2b, /* y */ - 0xb8,0x2a,0x08,0x3d,0xf2,0xf2,0xb0,0x84,0x7d,0xe9, - 0x70,0xb2,0xde,0x15, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFE,0x5F,0xB1,0xA7,0x24,0xDC,0x80,0x41,0x86, - 0x48,0xD8,0xDD,0x31 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_PRIME_192V3 = { - { NID_X9_62_prime_field,20,24,1 }, - { 0xC4,0x69,0x68,0x44,0x35,0xDE,0xB3,0x78,0xC4,0xB6, /* seed */ - 0x5C,0xA9,0x59,0x1E,0x2A,0x57,0x63,0x05,0x9A,0x2E, - - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFC, - 0x22,0x12,0x3D,0xC2,0x39,0x5A,0x05,0xCA,0xA7,0x42, /* b */ - 0x3D,0xAE,0xCC,0xC9,0x47,0x60,0xA7,0xD4,0x62,0x25, - 0x6B,0xD5,0x69,0x16, - 0x7D,0x29,0x77,0x81,0x00,0xC6,0x5A,0x1D,0xA1,0x78, /* x */ - 0x37,0x16,0x58,0x8D,0xCE,0x2B,0x8B,0x4A,0xEE,0x8E, - 0x22,0x8F,0x18,0x96, - 0x38,0xa9,0x0f,0x22,0x63,0x73,0x37,0x33,0x4b,0x49, /* y */ - 0xdc,0xb6,0x6a,0x6d,0xc8,0xf9,0x97,0x8a,0xca,0x76, - 0x48,0xa9,0x43,0xb0, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7A,0x62,0xD0,0x31,0xC8,0x3F,0x42,0x94, - 0xF6,0x40,0xEC,0x13 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V1 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0xE4,0x3B,0xB4,0x60,0xF0,0xB8,0x0C,0xC0,0xC0,0xB0, /* seed */ - 0x75,0x79,0x8E,0x94,0x80,0x60,0xF8,0x32,0x1B,0x7D, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x6B,0x01,0x6C,0x3B,0xDC,0xF1,0x89,0x41,0xD0,0xD6, /* b */ - 0x54,0x92,0x14,0x75,0xCA,0x71,0xA9,0xDB,0x2F,0xB2, - 0x7D,0x1D,0x37,0x79,0x61,0x85,0xC2,0x94,0x2C,0x0A, - - 0x0F,0xFA,0x96,0x3C,0xDC,0xA8,0x81,0x6C,0xCC,0x33, /* x */ - 0xB8,0x64,0x2B,0xED,0xF9,0x05,0xC3,0xD3,0x58,0x57, - 0x3D,0x3F,0x27,0xFB,0xBD,0x3B,0x3C,0xB9,0xAA,0xAF, - - 0x7d,0xeb,0xe8,0xe4,0xe9,0x0a,0x5d,0xae,0x6e,0x40, /* y */ - 0x54,0xca,0x53,0x0b,0xa0,0x46,0x54,0xb3,0x68,0x18, - 0xce,0x22,0x6b,0x39,0xfc,0xcb,0x7b,0x02,0xf1,0xae, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0x9E,0x5E,0x9A,0x9F,0x5D, - 0x90,0x71,0xFB,0xD1,0x52,0x26,0x88,0x90,0x9D,0x0B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V2 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0xE8,0xB4,0x01,0x16,0x04,0x09,0x53,0x03,0xCA,0x3B, /* seed */ - 0x80,0x99,0x98,0x2B,0xE0,0x9F,0xCB,0x9A,0xE6,0x16, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x61,0x7F,0xAB,0x68,0x32,0x57,0x6C,0xBB,0xFE,0xD5, /* b */ - 0x0D,0x99,0xF0,0x24,0x9C,0x3F,0xEE,0x58,0xB9,0x4B, - 0xA0,0x03,0x8C,0x7A,0xE8,0x4C,0x8C,0x83,0x2F,0x2C, - - 0x38,0xAF,0x09,0xD9,0x87,0x27,0x70,0x51,0x20,0xC9, /* x */ - 0x21,0xBB,0x5E,0x9E,0x26,0x29,0x6A,0x3C,0xDC,0xF2, - 0xF3,0x57,0x57,0xA0,0xEA,0xFD,0x87,0xB8,0x30,0xE7, - - 0x5b,0x01,0x25,0xe4,0xdb,0xea,0x0e,0xc7,0x20,0x6d, /* y */ - 0xa0,0xfc,0x01,0xd9,0xb0,0x81,0x32,0x9f,0xb5,0x55, - 0xde,0x6e,0xf4,0x60,0x23,0x7d,0xff,0x8b,0xe4,0xba, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x80,0x00,0x00,0xCF,0xA7,0xE8,0x59,0x43, - 0x77,0xD4,0x14,0xC0,0x38,0x21,0xBC,0x58,0x20,0x63 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_PRIME_239V3 = { - { NID_X9_62_prime_field,20,30,1 }, - { 0x7D,0x73,0x74,0x16,0x8F,0xFE,0x34,0x71,0xB6,0x0A, /* seed */ - 0x85,0x76,0x86,0xA1,0x94,0x75,0xD3,0xBF,0xA2,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, - 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, - - 0x25,0x57,0x05,0xFA,0x2A,0x30,0x66,0x54,0xB1,0xF4, /* b */ - 0xCB,0x03,0xD6,0xA7,0x50,0xA3,0x0C,0x25,0x01,0x02, - 0xD4,0x98,0x87,0x17,0xD9,0xBA,0x15,0xAB,0x6D,0x3E, - - 0x67,0x68,0xAE,0x8E,0x18,0xBB,0x92,0xCF,0xCF,0x00, /* x */ - 0x5C,0x94,0x9A,0xA2,0xC6,0xD9,0x48,0x53,0xD0,0xE6, - 0x60,0xBB,0xF8,0x54,0xB1,0xC9,0x50,0x5F,0xE9,0x5A, - - 0x16,0x07,0xe6,0x89,0x8f,0x39,0x0c,0x06,0xbc,0x1d, /* y */ - 0x55,0x2b,0xad,0x22,0x6f,0x3b,0x6f,0xcf,0xe4,0x8b, - 0x6e,0x81,0x84,0x99,0xaf,0x18,0xe3,0xed,0x6c,0xf3, - - 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0x7F,0xFF,0xFF,0x97,0x5D,0xEB,0x41,0xB3, - 0xA6,0x05,0x7C,0x3C,0x43,0x21,0x46,0x52,0x65,0x51 } - }; - - -static const struct { EC_CURVE_DATA h; unsigned char data[20+32*6]; } - _EC_X9_62_PRIME_256V1 = { - { NID_X9_62_prime_field,20,32,1 }, - { 0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66, /* seed */ - 0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90, - - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFC, - 0x5A,0xC6,0x35,0xD8,0xAA,0x3A,0x93,0xE7,0xB3,0xEB, /* b */ - 0xBD,0x55,0x76,0x98,0x86,0xBC,0x65,0x1D,0x06,0xB0, - 0xCC,0x53,0xB0,0xF6,0x3B,0xCE,0x3C,0x3E,0x27,0xD2, - 0x60,0x4B, - 0x6B,0x17,0xD1,0xF2,0xE1,0x2C,0x42,0x47,0xF8,0xBC, /* x */ - 0xE6,0xE5,0x63,0xA4,0x40,0xF2,0x77,0x03,0x7D,0x81, - 0x2D,0xEB,0x33,0xA0,0xF4,0xA1,0x39,0x45,0xD8,0x98, - 0xC2,0x96, - 0x4f,0xe3,0x42,0xe2,0xfe,0x1a,0x7f,0x9b,0x8e,0xe7, /* y */ - 0xeb,0x4a,0x7c,0x0f,0x9e,0x16,0x2b,0xce,0x33,0x57, - 0x6b,0x31,0x5e,0xce,0xcb,0xb6,0x40,0x68,0x37,0xbf, - 0x51,0xf5, - 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xBC,0xE6,0xFA,0xAD, - 0xA7,0x17,0x9E,0x84,0xF3,0xB9,0xCA,0xC2,0xFC,0x63, - 0x25,0x51 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_PRIME_192V2 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0x31, 0xA9, 0x2E, 0xE2, 0x02, 0x9F, 0xD1, 0x0D, 0x90, 0x1B, /* seed */ + 0x11, 0x3E, 0x99, 0x07, 0x10, 0xF0, 0xD2, 0x1A, 0xC6, 0xB6, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0xCC, 0x22, 0xD6, 0xDF, 0xB9, 0x5C, 0x6B, 0x25, 0xE4, 0x9C, /* b */ + 0x0D, 0x63, 0x64, 0xA4, 0xE5, 0x98, 0x0C, 0x39, 0x3A, 0xA2, + 0x16, 0x68, 0xD9, 0x53, + 0xEE, 0xA2, 0xBA, 0xE7, 0xE1, 0x49, 0x78, 0x42, 0xF2, 0xDE, /* x */ + 0x77, 0x69, 0xCF, 0xE9, 0xC9, 0x89, 0xC0, 0x72, 0xAD, 0x69, + 0x6F, 0x48, 0x03, 0x4A, + 0x65, 0x74, 0xd1, 0x1d, 0x69, 0xb6, 0xec, 0x7a, 0x67, 0x2b, /* y */ + 0xb8, 0x2a, 0x08, 0x3d, 0xf2, 0xf2, 0xb0, 0x84, 0x7d, 0xe9, + 0x70, 0xb2, 0xde, 0x15, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFE, 0x5F, 0xB1, 0xA7, 0x24, 0xDC, 0x80, 0x41, 0x86, + 0x48, 0xD8, 0xDD, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_PRIME_192V3 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + 0xC4, 0x69, 0x68, 0x44, 0x35, 0xDE, 0xB3, 0x78, 0xC4, 0xB6, /* seed */ + 0x5C, 0xA9, 0x59, 0x1E, 0x2A, 0x57, 0x63, 0x05, 0x9A, 0x2E, + + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + 0x22, 0x12, 0x3D, 0xC2, 0x39, 0x5A, 0x05, 0xCA, 0xA7, 0x42, /* b */ + 0x3D, 0xAE, 0xCC, 0xC9, 0x47, 0x60, 0xA7, 0xD4, 0x62, 0x25, + 0x6B, 0xD5, 0x69, 0x16, + 0x7D, 0x29, 0x77, 0x81, 0x00, 0xC6, 0x5A, 0x1D, 0xA1, 0x78, /* x */ + 0x37, 0x16, 0x58, 0x8D, 0xCE, 0x2B, 0x8B, 0x4A, 0xEE, 0x8E, + 0x22, 0x8F, 0x18, 0x96, + 0x38, 0xa9, 0x0f, 0x22, 0x63, 0x73, 0x37, 0x33, 0x4b, 0x49, /* y */ + 0xdc, 0xb6, 0x6a, 0x6d, 0xc8, 0xf9, 0x97, 0x8a, 0xca, 0x76, + 0x48, 0xa9, 0x43, 0xb0, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7A, 0x62, 0xD0, 0x31, 0xC8, 0x3F, 0x42, 0x94, + 0xF6, 0x40, 0xEC, 0x13 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V1 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0xE4, 0x3B, 0xB4, 0x60, 0xF0, 0xB8, 0x0C, 0xC0, 0xC0, 0xB0, /* seed */ + 0x75, 0x79, 0x8E, 0x94, 0x80, 0x60, 0xF8, 0x32, 0x1B, 0x7D, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x6B, 0x01, 0x6C, 0x3B, 0xDC, 0xF1, 0x89, 0x41, 0xD0, 0xD6, /* b */ + 0x54, 0x92, 0x14, 0x75, 0xCA, 0x71, 0xA9, 0xDB, 0x2F, 0xB2, + 0x7D, 0x1D, 0x37, 0x79, 0x61, 0x85, 0xC2, 0x94, 0x2C, 0x0A, + + 0x0F, 0xFA, 0x96, 0x3C, 0xDC, 0xA8, 0x81, 0x6C, 0xCC, 0x33, /* x */ + 0xB8, 0x64, 0x2B, 0xED, 0xF9, 0x05, 0xC3, 0xD3, 0x58, 0x57, + 0x3D, 0x3F, 0x27, 0xFB, 0xBD, 0x3B, 0x3C, 0xB9, 0xAA, 0xAF, + + 0x7d, 0xeb, 0xe8, 0xe4, 0xe9, 0x0a, 0x5d, 0xae, 0x6e, 0x40, /* y */ + 0x54, 0xca, 0x53, 0x0b, 0xa0, 0x46, 0x54, 0xb3, 0x68, 0x18, + 0xce, 0x22, 0x6b, 0x39, 0xfc, 0xcb, 0x7b, 0x02, 0xf1, 0xae, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0x9E, 0x5E, 0x9A, 0x9F, 0x5D, + 0x90, 0x71, 0xFB, 0xD1, 0x52, 0x26, 0x88, 0x90, 0x9D, 0x0B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V2 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0xE8, 0xB4, 0x01, 0x16, 0x04, 0x09, 0x53, 0x03, 0xCA, 0x3B, /* seed */ + 0x80, 0x99, 0x98, 0x2B, 0xE0, 0x9F, 0xCB, 0x9A, 0xE6, 0x16, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x61, 0x7F, 0xAB, 0x68, 0x32, 0x57, 0x6C, 0xBB, 0xFE, 0xD5, /* b */ + 0x0D, 0x99, 0xF0, 0x24, 0x9C, 0x3F, 0xEE, 0x58, 0xB9, 0x4B, + 0xA0, 0x03, 0x8C, 0x7A, 0xE8, 0x4C, 0x8C, 0x83, 0x2F, 0x2C, + + 0x38, 0xAF, 0x09, 0xD9, 0x87, 0x27, 0x70, 0x51, 0x20, 0xC9, /* x */ + 0x21, 0xBB, 0x5E, 0x9E, 0x26, 0x29, 0x6A, 0x3C, 0xDC, 0xF2, + 0xF3, 0x57, 0x57, 0xA0, 0xEA, 0xFD, 0x87, 0xB8, 0x30, 0xE7, + + 0x5b, 0x01, 0x25, 0xe4, 0xdb, 0xea, 0x0e, 0xc7, 0x20, 0x6d, /* y */ + 0xa0, 0xfc, 0x01, 0xd9, 0xb0, 0x81, 0x32, 0x9f, 0xb5, 0x55, + 0xde, 0x6e, 0xf4, 0x60, 0x23, 0x7d, 0xff, 0x8b, 0xe4, 0xba, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x80, 0x00, 0x00, 0xCF, 0xA7, 0xE8, 0x59, 0x43, + 0x77, 0xD4, 0x14, 0xC0, 0x38, 0x21, 0xBC, 0x58, 0x20, 0x63 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_PRIME_239V3 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + 0x7D, 0x73, 0x74, 0x16, 0x8F, 0xFE, 0x34, 0x71, 0xB6, 0x0A, /* seed */ + 0x85, 0x76, 0x86, 0xA1, 0x94, 0x75, 0xD3, 0xBF, 0xA2, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + + 0x25, 0x57, 0x05, 0xFA, 0x2A, 0x30, 0x66, 0x54, 0xB1, 0xF4, /* b */ + 0xCB, 0x03, 0xD6, 0xA7, 0x50, 0xA3, 0x0C, 0x25, 0x01, 0x02, + 0xD4, 0x98, 0x87, 0x17, 0xD9, 0xBA, 0x15, 0xAB, 0x6D, 0x3E, + + 0x67, 0x68, 0xAE, 0x8E, 0x18, 0xBB, 0x92, 0xCF, 0xCF, 0x00, /* x */ + 0x5C, 0x94, 0x9A, 0xA2, 0xC6, 0xD9, 0x48, 0x53, 0xD0, 0xE6, + 0x60, 0xBB, 0xF8, 0x54, 0xB1, 0xC9, 0x50, 0x5F, 0xE9, 0x5A, + + 0x16, 0x07, 0xe6, 0x89, 0x8f, 0x39, 0x0c, 0x06, 0xbc, 0x1d, /* y */ + 0x55, 0x2b, 0xad, 0x22, 0x6f, 0x3b, 0x6f, 0xcf, 0xe4, 0x8b, + 0x6e, 0x81, 0x84, 0x99, 0xaf, 0x18, 0xe3, 0xed, 0x6c, 0xf3, + + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0x97, 0x5D, 0xEB, 0x41, 0xB3, + 0xA6, 0x05, 0x7C, 0x3C, 0x43, 0x21, 0x46, 0x52, 0x65, 0x51 + } +}; + + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 32 * 6]; +} + _EC_X9_62_PRIME_256V1 = { + { + NID_X9_62_prime_field, 20, 32, 1 + }, + { + 0xC4, 0x9D, 0x36, 0x08, 0x86, 0xE7, 0x04, 0x93, 0x6A, 0x66, /* seed */ + 0x78, 0xE1, 0x13, 0x9D, 0x26, 0xB7, 0x81, 0x9F, 0x7E, 0x90, + + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFC, + 0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, /* b */ + 0xBD, 0x55, 0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, + 0xCC, 0x53, 0xB0, 0xF6, 0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, + 0x60, 0x4B, + 0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, /* x */ + 0xE6, 0xE5, 0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, + 0x2D, 0xEB, 0x33, 0xA0, 0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, + 0xC2, 0x96, + 0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, 0x8e, 0xe7, /* y */ + 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, 0x2b, 0xce, 0x33, 0x57, + 0x6b, 0x31, 0x5e, 0xce, 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, + 0x51, 0xf5, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, + 0xA7, 0x17, 0x9E, 0x84, 0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, + 0x25, 0x51 + } +}; /* the secg prime curves (minus the nist and x9.62 prime curves) */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } - _EC_SECG_PRIME_112R1 = { - { NID_X9_62_prime_field,20,14,1 }, - { 0x00,0xF5,0x0B,0x02,0x8E,0x4D,0x69,0x6E,0x67,0x68, /* seed */ - 0x75,0x61,0x51,0x75,0x29,0x04,0x72,0x78,0x3F,0xB1, - - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ - 0xBE,0xAD,0x20,0x8B, - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* a */ - 0xBE,0xAD,0x20,0x88, - 0x65,0x9E,0xF8,0xBA,0x04,0x39,0x16,0xEE,0xDE,0x89, /* b */ - 0x11,0x70,0x2B,0x22, - 0x09,0x48,0x72,0x39,0x99,0x5A,0x5E,0xE7,0x6B,0x55, /* x */ - 0xF9,0xC2,0xF0,0x98, - 0xa8,0x9c,0xe5,0xaf,0x87,0x24,0xc0,0xa2,0x3e,0x0e, /* y */ - 0x0f,0xf7,0x75,0x00, - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x76,0x28,0xDF, /* order */ - 0xAC,0x65,0x61,0xC5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } - _EC_SECG_PRIME_112R2 = { - { NID_X9_62_prime_field,20,14,4 }, - { 0x00,0x27,0x57,0xA1,0x11,0x4D,0x69,0x6E,0x67,0x68, /* seed */ - 0x75,0x61,0x51,0x75,0x53,0x16,0xC0,0x5E,0x0B,0xD4, - - 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ - 0xBE,0xAD,0x20,0x8B, - 0x61,0x27,0xC2,0x4C,0x05,0xF3,0x8A,0x0A,0xAA,0xF6, /* a */ - 0x5C,0x0E,0xF0,0x2C, - 0x51,0xDE,0xF1,0x81,0x5D,0xB5,0xED,0x74,0xFC,0xC3, /* b */ - 0x4C,0x85,0xD7,0x09, - 0x4B,0xA3,0x0A,0xB5,0xE8,0x92,0xB4,0xE1,0x64,0x9D, /* x */ - 0xD0,0x92,0x86,0x43, - 0xad,0xcd,0x46,0xf5,0x88,0x2e,0x37,0x47,0xde,0xf3, /* y */ - 0x6e,0x95,0x6e,0x97, - 0x36,0xDF,0x0A,0xAF,0xD8,0xB8,0xD7,0x59,0x7C,0xA1, /* order */ - 0x05,0x20,0xD0,0x4B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } - _EC_SECG_PRIME_128R1 = { - { NID_X9_62_prime_field,20,16,1 }, - { 0x00,0x0E,0x0D,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0x0C,0xC0,0x3A,0x44,0x73,0xD0,0x36,0x79, - - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, - 0xE8,0x75,0x79,0xC1,0x10,0x79,0xF4,0x3D,0xD8,0x24, /* b */ - 0x99,0x3C,0x2C,0xEE,0x5E,0xD3, - 0x16,0x1F,0xF7,0x52,0x8B,0x89,0x9B,0x2D,0x0C,0x28, /* x */ - 0x60,0x7C,0xA5,0x2C,0x5B,0x86, - 0xcf,0x5a,0xc8,0x39,0x5b,0xaf,0xeb,0x13,0xc0,0x2d, /* y */ - 0xa2,0x92,0xdd,0xed,0x7a,0x83, - 0xFF,0xFF,0xFF,0xFE,0x00,0x00,0x00,0x00,0x75,0xA3, /* order */ - 0x0D,0x1B,0x90,0x38,0xA1,0x15 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } - _EC_SECG_PRIME_128R2 = { - { NID_X9_62_prime_field,20,16,4 }, - { 0x00,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75, /* seed */ - 0x12,0xD8,0xF0,0x34,0x31,0xFC,0xE6,0x3B,0x88,0xF4, - - 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xD6,0x03,0x19,0x98,0xD1,0xB3,0xBB,0xFE,0xBF,0x59, /* a */ - 0xCC,0x9B,0xBF,0xF9,0xAE,0xE1, - 0x5E,0xEE,0xFC,0xA3,0x80,0xD0,0x29,0x19,0xDC,0x2C, /* b */ - 0x65,0x58,0xBB,0x6D,0x8A,0x5D, - 0x7B,0x6A,0xA5,0xD8,0x5E,0x57,0x29,0x83,0xE6,0xFB, /* x */ - 0x32,0xA7,0xCD,0xEB,0xC1,0x40, - 0x27,0xb6,0x91,0x6a,0x89,0x4d,0x3a,0xee,0x71,0x06, /* y */ - 0xfe,0x80,0x5f,0xc3,0x4b,0x44, - 0x3F,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xBE,0x00, /* order */ - 0x24,0x72,0x06,0x13,0xB5,0xA3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_SECG_PRIME_160K1 = { - { NID_X9_62_prime_field,0,21,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x73, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x07, - 0x00,0x3B,0x4C,0x38,0x2C,0xE3,0x7A,0xA1,0x92,0xA4, /* x */ - 0x01,0x9E,0x76,0x30,0x36,0xF4,0xF5,0xDD,0x4D,0x7E, - 0xBB, - 0x00,0x93,0x8c,0xf9,0x35,0x31,0x8f,0xdc,0xed,0x6b, /* y */ - 0xc2,0x82,0x86,0x53,0x17,0x33,0xc3,0xf0,0x3c,0x4f, - 0xee, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xB8,0xFA,0x16,0xDF,0xAB,0x9A,0xCA,0x16,0xB6, - 0xB3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_SECG_PRIME_160R1 = { - { NID_X9_62_prime_field,20,21,1 }, - { 0x10,0x53,0xCD,0xE4,0x2C,0x14,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x53,0x3B,0xF3,0xF8,0x33,0x45, - - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, - 0xFF, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, - 0xFC, - 0x00,0x1C,0x97,0xBE,0xFC,0x54,0xBD,0x7A,0x8B,0x65, /* b */ - 0xAC,0xF8,0x9F,0x81,0xD4,0xD4,0xAD,0xC5,0x65,0xFA, - 0x45, - 0x00,0x4A,0x96,0xB5,0x68,0x8E,0xF5,0x73,0x28,0x46, /* x */ - 0x64,0x69,0x89,0x68,0xC3,0x8B,0xB9,0x13,0xCB,0xFC, - 0x82, - 0x00,0x23,0xa6,0x28,0x55,0x31,0x68,0x94,0x7d,0x59, /* y */ - 0xdc,0xc9,0x12,0x04,0x23,0x51,0x37,0x7a,0xc5,0xfb, - 0x32, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xF4,0xC8,0xF9,0x27,0xAE,0xD3,0xCA,0x75,0x22, - 0x57 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_SECG_PRIME_160R2 = { - { NID_X9_62_prime_field,20,21,1 }, - { 0xB9,0x9B,0x99,0xB0,0x99,0xB3,0x23,0xE0,0x27,0x09, /* seed */ - 0xA4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x51, - - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x73, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, - 0x70, - 0x00,0xB4,0xE1,0x34,0xD3,0xFB,0x59,0xEB,0x8B,0xAB, /* b */ - 0x57,0x27,0x49,0x04,0x66,0x4D,0x5A,0xF5,0x03,0x88, - 0xBA, - 0x00,0x52,0xDC,0xB0,0x34,0x29,0x3A,0x11,0x7E,0x1F, /* x */ - 0x4F,0xF1,0x1B,0x30,0xF7,0x19,0x9D,0x31,0x44,0xCE, - 0x6D, - 0x00,0xfe,0xaf,0xfe,0xf2,0xe3,0x31,0xf2,0x96,0xe0, /* y */ - 0x71,0xfa,0x0d,0xf9,0x98,0x2c,0xfe,0xa7,0xd4,0x3f, - 0x2e, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x35,0x1E,0xE7,0x86,0xA8,0x18,0xF3,0xA1,0xA1, - 0x6B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_SECG_PRIME_192K1 = { - { NID_X9_62_prime_field,0,24,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xFF,0xFF,0xEE,0x37, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x03, - 0xDB,0x4F,0xF1,0x0E,0xC0,0x57,0xE9,0xAE,0x26,0xB0, /* x */ - 0x7D,0x02,0x80,0xB7,0xF4,0x34,0x1D,0xA5,0xD1,0xB1, - 0xEA,0xE0,0x6C,0x7D, - 0x9b,0x2f,0x2f,0x6d,0x9c,0x56,0x28,0xa7,0x84,0x41, /* y */ - 0x63,0xd0,0x15,0xbe,0x86,0x34,0x40,0x82,0xaa,0x88, - 0xd9,0x5e,0x2f,0x9d, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFE,0x26,0xF2,0xFC,0x17,0x0F,0x69,0x46,0x6A, - 0x74,0xDE,0xFD,0x8D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+29*6]; } - _EC_SECG_PRIME_224K1 = { - { NID_X9_62_prime_field,0,29,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xE5,0x6D, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x05, - 0x00,0xA1,0x45,0x5B,0x33,0x4D,0xF0,0x99,0xDF,0x30, /* x */ - 0xFC,0x28,0xA1,0x69,0xA4,0x67,0xE9,0xE4,0x70,0x75, - 0xA9,0x0F,0x7E,0x65,0x0E,0xB6,0xB7,0xA4,0x5C, - 0x00,0x7e,0x08,0x9f,0xed,0x7f,0xba,0x34,0x42,0x82, /* y */ - 0xca,0xfb,0xd6,0xf7,0xe3,0x19,0xf7,0xc0,0xb0,0xbd, - 0x59,0xe2,0xca,0x4b,0xdb,0x55,0x6d,0x61,0xa5, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x01,0xDC,0xE8,0xD2,0xEC,0x61, - 0x84,0xCA,0xF0,0xA9,0x71,0x76,0x9F,0xB1,0xF7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_SECG_PRIME_256K1 = { - { NID_X9_62_prime_field,0,32,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF, - 0xFC,0x2F, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x07, - 0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0, /* x */ - 0x62,0x95,0xCE,0x87,0x0B,0x07,0x02,0x9B,0xFC,0xDB, - 0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, - 0x17,0x98, - 0x48,0x3a,0xda,0x77,0x26,0xa3,0xc4,0x65,0x5d,0xa4, /* y */ - 0xfb,0xfc,0x0e,0x11,0x08,0xa8,0xfd,0x17,0xb4,0x48, - 0xa6,0x85,0x54,0x19,0x9c,0x47,0xd0,0x8f,0xfb,0x10, - 0xd4,0xb8, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6, - 0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,0x8C,0xD0,0x36, - 0x41,0x41 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} + _EC_SECG_PRIME_112R1 = { + { + NID_X9_62_prime_field, 20, 14, 1 + }, + { + 0x00, 0xF5, 0x0B, 0x02, 0x8E, 0x4D, 0x69, 0x6E, 0x67, 0x68, /* seed */ + 0x75, 0x61, 0x51, 0x75, 0x29, 0x04, 0x72, 0x78, 0x3F, 0xB1, + + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* p */ + 0xBE, 0xAD, 0x20, 0x8B, + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* a */ + 0xBE, 0xAD, 0x20, 0x88, + 0x65, 0x9E, 0xF8, 0xBA, 0x04, 0x39, 0x16, 0xEE, 0xDE, 0x89, /* b */ + 0x11, 0x70, 0x2B, 0x22, + 0x09, 0x48, 0x72, 0x39, 0x99, 0x5A, 0x5E, 0xE7, 0x6B, 0x55, /* x */ + 0xF9, 0xC2, 0xF0, 0x98, + 0xa8, 0x9c, 0xe5, 0xaf, 0x87, 0x24, 0xc0, 0xa2, 0x3e, 0x0e, /* y */ + 0x0f, 0xf7, 0x75, 0x00, + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x76, 0x28, 0xDF, /* order */ + 0xAC, 0x65, 0x61, 0xC5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} + _EC_SECG_PRIME_112R2 = { + { + NID_X9_62_prime_field, 20, 14, 4 + }, + { + 0x00, 0x27, 0x57, 0xA1, 0x11, 0x4D, 0x69, 0x6E, 0x67, 0x68, /* seed */ + 0x75, 0x61, 0x51, 0x75, 0x53, 0x16, 0xC0, 0x5E, 0x0B, 0xD4, + + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, /* p */ + 0xBE, 0xAD, 0x20, 0x8B, + 0x61, 0x27, 0xC2, 0x4C, 0x05, 0xF3, 0x8A, 0x0A, 0xAA, 0xF6, /* a */ + 0x5C, 0x0E, 0xF0, 0x2C, + 0x51, 0xDE, 0xF1, 0x81, 0x5D, 0xB5, 0xED, 0x74, 0xFC, 0xC3, /* b */ + 0x4C, 0x85, 0xD7, 0x09, + 0x4B, 0xA3, 0x0A, 0xB5, 0xE8, 0x92, 0xB4, 0xE1, 0x64, 0x9D, /* x */ + 0xD0, 0x92, 0x86, 0x43, + 0xad, 0xcd, 0x46, 0xf5, 0x88, 0x2e, 0x37, 0x47, 0xde, 0xf3, /* y */ + 0x6e, 0x95, 0x6e, 0x97, + 0x36, 0xDF, 0x0A, 0xAF, 0xD8, 0xB8, 0xD7, 0x59, 0x7C, 0xA1, /* order */ + 0x05, 0x20, 0xD0, 0x4B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} + _EC_SECG_PRIME_128R1 = { + { + NID_X9_62_prime_field, 20, 16, 1 + }, + { + 0x00, 0x0E, 0x0D, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0x0C, 0xC0, 0x3A, 0x44, 0x73, 0xD0, 0x36, 0x79, + + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + 0xE8, 0x75, 0x79, 0xC1, 0x10, 0x79, 0xF4, 0x3D, 0xD8, 0x24, /* b */ + 0x99, 0x3C, 0x2C, 0xEE, 0x5E, 0xD3, + 0x16, 0x1F, 0xF7, 0x52, 0x8B, 0x89, 0x9B, 0x2D, 0x0C, 0x28, /* x */ + 0x60, 0x7C, 0xA5, 0x2C, 0x5B, 0x86, + 0xcf, 0x5a, 0xc8, 0x39, 0x5b, 0xaf, 0xeb, 0x13, 0xc0, 0x2d, /* y */ + 0xa2, 0x92, 0xdd, 0xed, 0x7a, 0x83, + 0xFF, 0xFF, 0xFF, 0xFE, 0x00, 0x00, 0x00, 0x00, 0x75, 0xA3, /* order */ + 0x0D, 0x1B, 0x90, 0x38, 0xA1, 0x15 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} + _EC_SECG_PRIME_128R2 = { + { + NID_X9_62_prime_field, 20, 16, 4 + }, + { + 0x00, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, /* seed */ + 0x12, 0xD8, 0xF0, 0x34, 0x31, 0xFC, 0xE6, 0x3B, 0x88, 0xF4, + + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xD6, 0x03, 0x19, 0x98, 0xD1, 0xB3, 0xBB, 0xFE, 0xBF, 0x59, /* a */ + 0xCC, 0x9B, 0xBF, 0xF9, 0xAE, 0xE1, + 0x5E, 0xEE, 0xFC, 0xA3, 0x80, 0xD0, 0x29, 0x19, 0xDC, 0x2C, /* b */ + 0x65, 0x58, 0xBB, 0x6D, 0x8A, 0x5D, + 0x7B, 0x6A, 0xA5, 0xD8, 0x5E, 0x57, 0x29, 0x83, 0xE6, 0xFB, /* x */ + 0x32, 0xA7, 0xCD, 0xEB, 0xC1, 0x40, + 0x27, 0xb6, 0x91, 0x6a, 0x89, 0x4d, 0x3a, 0xee, 0x71, 0x06, /* y */ + 0xfe, 0x80, 0x5f, 0xc3, 0x4b, 0x44, + 0x3F, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xBE, 0x00, /* order */ + 0x24, 0x72, 0x06, 0x13, 0xB5, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_SECG_PRIME_160K1 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x73, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x07, + 0x00, 0x3B, 0x4C, 0x38, 0x2C, 0xE3, 0x7A, 0xA1, 0x92, 0xA4, /* x */ + 0x01, 0x9E, 0x76, 0x30, 0x36, 0xF4, 0xF5, 0xDD, 0x4D, 0x7E, + 0xBB, + 0x00, 0x93, 0x8c, 0xf9, 0x35, 0x31, 0x8f, 0xdc, 0xed, 0x6b, /* y */ + 0xc2, 0x82, 0x86, 0x53, 0x17, 0x33, 0xc3, 0xf0, 0x3c, 0x4f, + 0xee, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xB8, 0xFA, 0x16, 0xDF, 0xAB, 0x9A, 0xCA, 0x16, 0xB6, + 0xB3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_SECG_PRIME_160R1 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + 0x10, 0x53, 0xCD, 0xE4, 0x2C, 0x14, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x53, 0x3B, 0xF3, 0xF8, 0x33, 0x45, + + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, + 0xFF, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, + 0xFC, + 0x00, 0x1C, 0x97, 0xBE, 0xFC, 0x54, 0xBD, 0x7A, 0x8B, 0x65, /* b */ + 0xAC, 0xF8, 0x9F, 0x81, 0xD4, 0xD4, 0xAD, 0xC5, 0x65, 0xFA, + 0x45, + 0x00, 0x4A, 0x96, 0xB5, 0x68, 0x8E, 0xF5, 0x73, 0x28, 0x46, /* x */ + 0x64, 0x69, 0x89, 0x68, 0xC3, 0x8B, 0xB9, 0x13, 0xCB, 0xFC, + 0x82, + 0x00, 0x23, 0xa6, 0x28, 0x55, 0x31, 0x68, 0x94, 0x7d, 0x59, /* y */ + 0xdc, 0xc9, 0x12, 0x04, 0x23, 0x51, 0x37, 0x7a, 0xc5, 0xfb, + 0x32, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xF4, 0xC8, 0xF9, 0x27, 0xAE, 0xD3, 0xCA, 0x75, 0x22, + 0x57 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_SECG_PRIME_160R2 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + 0xB9, 0x9B, 0x99, 0xB0, 0x99, 0xB3, 0x23, 0xE0, 0x27, 0x09, /* seed */ + 0xA4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x51, + + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x73, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, + 0x70, + 0x00, 0xB4, 0xE1, 0x34, 0xD3, 0xFB, 0x59, 0xEB, 0x8B, 0xAB, /* b */ + 0x57, 0x27, 0x49, 0x04, 0x66, 0x4D, 0x5A, 0xF5, 0x03, 0x88, + 0xBA, + 0x00, 0x52, 0xDC, 0xB0, 0x34, 0x29, 0x3A, 0x11, 0x7E, 0x1F, /* x */ + 0x4F, 0xF1, 0x1B, 0x30, 0xF7, 0x19, 0x9D, 0x31, 0x44, 0xCE, + 0x6D, + 0x00, 0xfe, 0xaf, 0xfe, 0xf2, 0xe3, 0x31, 0xf2, 0x96, 0xe0, /* y */ + 0x71, 0xfa, 0x0d, 0xf9, 0x98, 0x2c, 0xfe, 0xa7, 0xd4, 0x3f, + 0x2e, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x35, 0x1E, 0xE7, 0x86, 0xA8, 0x18, 0xF3, 0xA1, 0xA1, + 0x6B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_SECG_PRIME_192K1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xFF, 0xFF, 0xEE, 0x37, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x03, + 0xDB, 0x4F, 0xF1, 0x0E, 0xC0, 0x57, 0xE9, 0xAE, 0x26, 0xB0, /* x */ + 0x7D, 0x02, 0x80, 0xB7, 0xF4, 0x34, 0x1D, 0xA5, 0xD1, 0xB1, + 0xEA, 0xE0, 0x6C, 0x7D, + 0x9b, 0x2f, 0x2f, 0x6d, 0x9c, 0x56, 0x28, 0xa7, 0x84, 0x41, /* y */ + 0x63, 0xd0, 0x15, 0xbe, 0x86, 0x34, 0x40, 0x82, 0xaa, 0x88, + 0xd9, 0x5e, 0x2f, 0x9d, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFE, 0x26, 0xF2, 0xFC, 0x17, 0x0F, 0x69, 0x46, 0x6A, + 0x74, 0xDE, 0xFD, 0x8D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 29 * 6]; +} + _EC_SECG_PRIME_224K1 = { + { + NID_X9_62_prime_field, 0, 29, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xE5, 0x6D, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x05, + 0x00, 0xA1, 0x45, 0x5B, 0x33, 0x4D, 0xF0, 0x99, 0xDF, 0x30, /* x */ + 0xFC, 0x28, 0xA1, 0x69, 0xA4, 0x67, 0xE9, 0xE4, 0x70, 0x75, + 0xA9, 0x0F, 0x7E, 0x65, 0x0E, 0xB6, 0xB7, 0xA4, 0x5C, + 0x00, 0x7e, 0x08, 0x9f, 0xed, 0x7f, 0xba, 0x34, 0x42, 0x82, /* y */ + 0xca, 0xfb, 0xd6, 0xf7, 0xe3, 0x19, 0xf7, 0xc0, 0xb0, 0xbd, + 0x59, 0xe2, 0xca, 0x4b, 0xdb, 0x55, 0x6d, 0x61, 0xa5, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x01, 0xDC, 0xE8, 0xD2, 0xEC, 0x61, + 0x84, 0xCA, 0xF0, 0xA9, 0x71, 0x76, 0x9F, 0xB1, 0xF7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_SECG_PRIME_256K1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, + 0xFC, 0x2F, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x07, + 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, /* x */ + 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, + 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, + 0x17, 0x98, + 0x48, 0x3a, 0xda, 0x77, 0x26, 0xa3, 0xc4, 0x65, 0x5d, 0xa4, /* y */ + 0xfb, 0xfc, 0x0e, 0x11, 0x08, 0xa8, 0xfd, 0x17, 0xb4, 0x48, + 0xa6, 0x85, 0x54, 0x19, 0x9c, 0x47, 0xd0, 0x8f, 0xfb, 0x10, + 0xd4, 0xb8, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, + 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, + 0x41, 0x41 + } +}; /* some wap/wtls curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } - _EC_WTLS_8 = { - { NID_X9_62_prime_field,0,15,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFD,0xE7, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x03, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x02, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xEC,0xEA, /* order */ - 0x55,0x1A,0xD8,0x37,0xE9 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_WTLS_9 = { - { NID_X9_62_prime_field,0,21,1 }, - { /* no seed */ - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFC,0x80, - 0x8F, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x03, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x02, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xCD,0xC9,0x8A,0xE0,0xE2,0xDE,0x57,0x4A,0xBF, - 0x33 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_WTLS_12 = { - { NID_X9_62_prime_field,0,28,1 }, - { /* no seed */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, - 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, - 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, - 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, - 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} + _EC_WTLS_8 = { + { + NID_X9_62_prime_field, 0, 15, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFD, 0xE7, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x02, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xEC, 0xEA, /* order */ + 0x55, 0x1A, 0xD8, 0x37, 0xE9 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_WTLS_9 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { /* no seed */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, 0x80, + 0x8F, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x02, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xCD, 0xC9, 0x8A, 0xE0, 0xE2, 0xDE, 0x57, 0x4A, 0xBF, + 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_WTLS_12 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4, + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21, + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, + 0x13, 0xDD, 0x29, 0x45, 0x5C, 0x5C, 0x2A, 0x3D + } +}; #ifndef OPENSSL_NO_EC2M /* characteristic two curves */ -static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } - _EC_SECG_CHAR2_113R1 = { - { NID_X9_62_characteristic_two_field,20,15,2 }, - { 0x10,0xE7,0x23,0xAB,0x14,0xD6,0x96,0xE6,0x76,0x87, /* seed */ - 0x56,0x15,0x17,0x56,0xFE,0xBF,0x8F,0xCB,0x49,0xA9, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x30,0x88,0x25,0x0C,0xA6,0xE7,0xC7,0xFE,0x64, /* a */ - 0x9C,0xE8,0x58,0x20,0xF7, - 0x00,0xE8,0xBE,0xE4,0xD3,0xE2,0x26,0x07,0x44,0x18, /* b */ - 0x8B,0xE0,0xE9,0xC7,0x23, - 0x00,0x9D,0x73,0x61,0x6F,0x35,0xF4,0xAB,0x14,0x07, /* x */ - 0xD7,0x35,0x62,0xC1,0x0F, - 0x00,0xA5,0x28,0x30,0x27,0x79,0x58,0xEE,0x84,0xD1, /* y */ - 0x31,0x5E,0xD3,0x18,0x86, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0xD9,0xCC, /* order */ - 0xEC,0x8A,0x39,0xE5,0x6F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } - _EC_SECG_CHAR2_113R2 = { - { NID_X9_62_characteristic_two_field,20,15,2 }, - { 0x10,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, /* seed */ - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x5D, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x68,0x99,0x18,0xDB,0xEC,0x7E,0x5A,0x0D,0xD6, /* a */ - 0xDF,0xC0,0xAA,0x55,0xC7, - 0x00,0x95,0xE9,0xA9,0xEC,0x9B,0x29,0x7B,0xD4,0xBF, /* b */ - 0x36,0xE0,0x59,0x18,0x4F, - 0x01,0xA5,0x7A,0x6A,0x7B,0x26,0xCA,0x5E,0xF5,0x2F, /* x */ - 0xCD,0xB8,0x16,0x47,0x97, - 0x00,0xB3,0xAD,0xC9,0x4E,0xD1,0xFE,0x67,0x4C,0x06, /* y */ - 0xE6,0x95,0xBA,0xBA,0x1D, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x08,0x78, /* order */ - 0x9B,0x24,0x96,0xAF,0x93 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } - _EC_SECG_CHAR2_131R1 = { - { NID_X9_62_characteristic_two_field,20,17,2 }, - { 0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,0x98, /* seed */ - 0x5B,0xD3,0xAD,0xBA,0xDA,0x21,0xB4,0x3A,0x97,0xE2, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, - 0x07,0xA1,0x1B,0x09,0xA7,0x6B,0x56,0x21,0x44,0x41, /* a */ - 0x8F,0xF3,0xFF,0x8C,0x25,0x70,0xB8, - 0x02,0x17,0xC0,0x56,0x10,0x88,0x4B,0x63,0xB9,0xC6, /* b */ - 0xC7,0x29,0x16,0x78,0xF9,0xD3,0x41, - 0x00,0x81,0xBA,0xF9,0x1F,0xDF,0x98,0x33,0xC4,0x0F, /* x */ - 0x9C,0x18,0x13,0x43,0x63,0x83,0x99, - 0x07,0x8C,0x6E,0x7E,0xA3,0x8C,0x00,0x1F,0x73,0xC8, /* y */ - 0x13,0x4B,0x1B,0x4E,0xF9,0xE1,0x50, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x02,0x31, /* order */ - 0x23,0x95,0x3A,0x94,0x64,0xB5,0x4D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } - _EC_SECG_CHAR2_131R2 = { - { NID_X9_62_characteristic_two_field,20,17,2 }, - { 0x98,0x5B,0xD3,0xAD,0xBA,0xD4,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x5A,0x21,0xB4,0x3A,0x97,0xE3, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, - 0x03,0xE5,0xA8,0x89,0x19,0xD7,0xCA,0xFC,0xBF,0x41, /* a */ - 0x5F,0x07,0xC2,0x17,0x65,0x73,0xB2, - 0x04,0xB8,0x26,0x6A,0x46,0xC5,0x56,0x57,0xAC,0x73, /* b */ - 0x4C,0xE3,0x8F,0x01,0x8F,0x21,0x92, - 0x03,0x56,0xDC,0xD8,0xF2,0xF9,0x50,0x31,0xAD,0x65, /* x */ - 0x2D,0x23,0x95,0x1B,0xB3,0x66,0xA8, - 0x06,0x48,0xF0,0x6D,0x86,0x79,0x40,0xA5,0x36,0x6D, /* y */ - 0x9E,0x26,0x5D,0xE9,0xEB,0x24,0x0F, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x69, /* order */ - 0x54,0xA2,0x33,0x04,0x9B,0xA9,0x8F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_NIST_CHAR2_163K = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x02,0xFE,0x13,0xC0,0x53,0x7B,0xBC,0x11,0xAC,0xAA, /* x */ - 0x07,0xD7,0x93,0xDE,0x4E,0x6D,0x5E,0x5C,0x94,0xEE, - 0xE8, - 0x02,0x89,0x07,0x0F,0xB0,0x5D,0x38,0xFF,0x58,0x32, /* y */ - 0x1F,0x2E,0x80,0x05,0x36,0xD5,0x38,0xCC,0xDA,0xA3, - 0xD9, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x02,0x01,0x08,0xA2,0xE0,0xCC,0x0D,0x99,0xF8,0xA5, - 0xEF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_SECG_CHAR2_163R1 = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} + _EC_SECG_CHAR2_113R1 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + 0x10, 0xE7, 0x23, 0xAB, 0x14, 0xD6, 0x96, 0xE6, 0x76, 0x87, /* seed */ + 0x56, 0x15, 0x17, 0x56, 0xFE, 0xBF, 0x8F, 0xCB, 0x49, 0xA9, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x30, 0x88, 0x25, 0x0C, 0xA6, 0xE7, 0xC7, 0xFE, 0x64, /* a */ + 0x9C, 0xE8, 0x58, 0x20, 0xF7, + 0x00, 0xE8, 0xBE, 0xE4, 0xD3, 0xE2, 0x26, 0x07, 0x44, 0x18, /* b */ + 0x8B, 0xE0, 0xE9, 0xC7, 0x23, + 0x00, 0x9D, 0x73, 0x61, 0x6F, 0x35, 0xF4, 0xAB, 0x14, 0x07, /* x */ + 0xD7, 0x35, 0x62, 0xC1, 0x0F, + 0x00, 0xA5, 0x28, 0x30, 0x27, 0x79, 0x58, 0xEE, 0x84, 0xD1, /* y */ + 0x31, 0x5E, 0xD3, 0x18, 0x86, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xD9, 0xCC, /* order */ + 0xEC, 0x8A, 0x39, 0xE5, 0x6F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} + _EC_SECG_CHAR2_113R2 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + 0x10, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, /* seed */ + 0xF4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x5D, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x68, 0x99, 0x18, 0xDB, 0xEC, 0x7E, 0x5A, 0x0D, 0xD6, /* a */ + 0xDF, 0xC0, 0xAA, 0x55, 0xC7, + 0x00, 0x95, 0xE9, 0xA9, 0xEC, 0x9B, 0x29, 0x7B, 0xD4, 0xBF, /* b */ + 0x36, 0xE0, 0x59, 0x18, 0x4F, + 0x01, 0xA5, 0x7A, 0x6A, 0x7B, 0x26, 0xCA, 0x5E, 0xF5, 0x2F, /* x */ + 0xCD, 0xB8, 0x16, 0x47, 0x97, + 0x00, 0xB3, 0xAD, 0xC9, 0x4E, 0xD1, 0xFE, 0x67, 0x4C, 0x06, /* y */ + 0xE6, 0x95, 0xBA, 0xBA, 0x1D, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x08, 0x78, /* order */ + 0x9B, 0x24, 0x96, 0xAF, 0x93 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} + _EC_SECG_CHAR2_131R1 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, 0x98, /* seed */ + 0x5B, 0xD3, 0xAD, 0xBA, 0xDA, 0x21, 0xB4, 0x3A, 0x97, 0xE2, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x0D, + 0x07, 0xA1, 0x1B, 0x09, 0xA7, 0x6B, 0x56, 0x21, 0x44, 0x41, /* a */ + 0x8F, 0xF3, 0xFF, 0x8C, 0x25, 0x70, 0xB8, + 0x02, 0x17, 0xC0, 0x56, 0x10, 0x88, 0x4B, 0x63, 0xB9, 0xC6, /* b */ + 0xC7, 0x29, 0x16, 0x78, 0xF9, 0xD3, 0x41, + 0x00, 0x81, 0xBA, 0xF9, 0x1F, 0xDF, 0x98, 0x33, 0xC4, 0x0F, /* x */ + 0x9C, 0x18, 0x13, 0x43, 0x63, 0x83, 0x99, + 0x07, 0x8C, 0x6E, 0x7E, 0xA3, 0x8C, 0x00, 0x1F, 0x73, 0xC8, /* y */ + 0x13, 0x4B, 0x1B, 0x4E, 0xF9, 0xE1, 0x50, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x31, /* order */ + 0x23, 0x95, 0x3A, 0x94, 0x64, 0xB5, 0x4D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} + _EC_SECG_CHAR2_131R2 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + 0x98, 0x5B, 0xD3, 0xAD, 0xBA, 0xD4, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x5A, 0x21, 0xB4, 0x3A, 0x97, 0xE3, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x0D, + 0x03, 0xE5, 0xA8, 0x89, 0x19, 0xD7, 0xCA, 0xFC, 0xBF, 0x41, /* a */ + 0x5F, 0x07, 0xC2, 0x17, 0x65, 0x73, 0xB2, + 0x04, 0xB8, 0x26, 0x6A, 0x46, 0xC5, 0x56, 0x57, 0xAC, 0x73, /* b */ + 0x4C, 0xE3, 0x8F, 0x01, 0x8F, 0x21, 0x92, + 0x03, 0x56, 0xDC, 0xD8, 0xF2, 0xF9, 0x50, 0x31, 0xAD, 0x65, /* x */ + 0x2D, 0x23, 0x95, 0x1B, 0xB3, 0x66, 0xA8, + 0x06, 0x48, 0xF0, 0x6D, 0x86, 0x79, 0x40, 0xA5, 0x36, 0x6D, /* y */ + 0x9E, 0x26, 0x5D, 0xE9, 0xEB, 0x24, 0x0F, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x69, /* order */ + 0x54, 0xA2, 0x33, 0x04, 0x9B, 0xA9, 0x8F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_NIST_CHAR2_163K = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x02, 0xFE, 0x13, 0xC0, 0x53, 0x7B, 0xBC, 0x11, 0xAC, 0xAA, /* x */ + 0x07, 0xD7, 0x93, 0xDE, 0x4E, 0x6D, 0x5E, 0x5C, 0x94, 0xEE, + 0xE8, + 0x02, 0x89, 0x07, 0x0F, 0xB0, 0x5D, 0x38, 0xFF, 0x58, 0x32, /* y */ + 0x1F, 0x2E, 0x80, 0x05, 0x36, 0xD5, 0x38, 0xCC, 0xDA, 0xA3, + 0xD9, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x02, 0x01, 0x08, 0xA2, 0xE0, 0xCC, 0x0D, 0x99, 0xF8, 0xA5, + 0xEF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_SECG_CHAR2_163R1 = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ #if 0 /* The algorithm used to derive the curve parameters from * the seed used here is slightly different than the * algorithm described in X9.62 . */ - 0x24,0xB7,0xB1,0x37,0xC8,0xA1,0x4D,0x69,0x6E,0x67, - 0x68,0x75,0x61,0x51,0x75,0x6F,0xD0,0xDA,0x2E,0x5C, + 0x24, 0xB7, 0xB1, 0x37, 0xC8, 0xA1, 0x4D, 0x69, 0x6E, 0x67, + 0x68, 0x75, 0x61, 0x51, 0x75, 0x6F, 0xD0, 0xDA, 0x2E, 0x5C, #endif - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x07,0xB6,0x88,0x2C,0xAA,0xEF,0xA8,0x4F,0x95,0x54, /* a */ - 0xFF,0x84,0x28,0xBD,0x88,0xE2,0x46,0xD2,0x78,0x2A, - 0xE2, - 0x07,0x13,0x61,0x2D,0xCD,0xDC,0xB4,0x0A,0xAB,0x94, /* b */ - 0x6B,0xDA,0x29,0xCA,0x91,0xF7,0x3A,0xF9,0x58,0xAF, - 0xD9, - 0x03,0x69,0x97,0x96,0x97,0xAB,0x43,0x89,0x77,0x89, /* x */ - 0x56,0x67,0x89,0x56,0x7F,0x78,0x7A,0x78,0x76,0xA6, - 0x54, - 0x00,0x43,0x5E,0xDB,0x42,0xEF,0xAF,0xB2,0x98,0x9D, /* y */ - 0x51,0xFE,0xFC,0xE3,0xC8,0x09,0x88,0xF4,0x1F,0xF8, - 0x83, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0x48,0xAA,0xB6,0x89,0xC2,0x9C,0xA7,0x10,0x27, - 0x9B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } - _EC_NIST_CHAR2_163B = { - { NID_X9_62_characteristic_two_field,0,21,2 }, - { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x07, 0xB6, 0x88, 0x2C, 0xAA, 0xEF, 0xA8, 0x4F, 0x95, 0x54, /* a */ + 0xFF, 0x84, 0x28, 0xBD, 0x88, 0xE2, 0x46, 0xD2, 0x78, 0x2A, + 0xE2, + 0x07, 0x13, 0x61, 0x2D, 0xCD, 0xDC, 0xB4, 0x0A, 0xAB, 0x94, /* b */ + 0x6B, 0xDA, 0x29, 0xCA, 0x91, 0xF7, 0x3A, 0xF9, 0x58, 0xAF, + 0xD9, + 0x03, 0x69, 0x97, 0x96, 0x97, 0xAB, 0x43, 0x89, 0x77, 0x89, /* x */ + 0x56, 0x67, 0x89, 0x56, 0x7F, 0x78, 0x7A, 0x78, 0x76, 0xA6, + 0x54, + 0x00, 0x43, 0x5E, 0xDB, 0x42, 0xEF, 0xAF, 0xB2, 0x98, 0x9D, /* y */ + 0x51, 0xFE, 0xFC, 0xE3, 0xC8, 0x09, 0x88, 0xF4, 0x1F, 0xF8, + 0x83, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0x48, 0xAA, 0xB6, 0x89, 0xC2, 0x9C, 0xA7, 0x10, 0x27, + 0x9B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} + _EC_NIST_CHAR2_163B = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { /* no seed */ #if 0 /* The seed here was used to created the curve parameters in normal * basis representation (and not the polynomial representation used here) */ - 0x85,0xE2,0x5B,0xFE,0x5C,0x86,0x22,0x6C,0xDB,0x12, - 0x01,0x6F,0x75,0x53,0xF9,0xD0,0xE6,0x93,0xA2,0x68, + 0x85, 0xE2, 0x5B, 0xFE, 0x5C, 0x86, 0x22, 0x6C, 0xDB, 0x12, + 0x01, 0x6F, 0x75, 0x53, 0xF9, 0xD0, 0xE6, 0x93, 0xA2, 0x68, #endif - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0xC9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x01, - 0x02,0x0A,0x60,0x19,0x07,0xB8,0xC9,0x53,0xCA,0x14, /* b */ - 0x81,0xEB,0x10,0x51,0x2F,0x78,0x74,0x4A,0x32,0x05, - 0xFD, - 0x03,0xF0,0xEB,0xA1,0x62,0x86,0xA2,0xD5,0x7E,0xA0, /* x */ - 0x99,0x11,0x68,0xD4,0x99,0x46,0x37,0xE8,0x34,0x3E, - 0x36, - 0x00,0xD5,0x1F,0xBC,0x6C,0x71,0xA0,0x09,0x4F,0xA2, /* y */ - 0xCD,0xD5,0x45,0xB1,0x1C,0x5C,0x0C,0x79,0x73,0x24, - 0xF1, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x02,0x92,0xFE,0x77,0xE7,0x0C,0x12,0xA4,0x23,0x4C, - 0x33 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } - _EC_SECG_CHAR2_193R1 = { - { NID_X9_62_characteristic_two_field,20,25,2 }, - { 0x10,0x3F,0xAE,0xC7,0x4D,0x69,0x6E,0x67,0x68,0x75, /* seed */ - 0x61,0x51,0x75,0x77,0x7F,0xC5,0xB1,0x91,0xEF,0x30, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x80,0x01, - 0x00,0x17,0x85,0x8F,0xEB,0x7A,0x98,0x97,0x51,0x69, /* a */ - 0xE1,0x71,0xF7,0x7B,0x40,0x87,0xDE,0x09,0x8A,0xC8, - 0xA9,0x11,0xDF,0x7B,0x01, - 0x00,0xFD,0xFB,0x49,0xBF,0xE6,0xC3,0xA8,0x9F,0xAC, /* b */ - 0xAD,0xAA,0x7A,0x1E,0x5B,0xBC,0x7C,0xC1,0xC2,0xE5, - 0xD8,0x31,0x47,0x88,0x14, - 0x01,0xF4,0x81,0xBC,0x5F,0x0F,0xF8,0x4A,0x74,0xAD, /* x */ - 0x6C,0xDF,0x6F,0xDE,0xF4,0xBF,0x61,0x79,0x62,0x53, - 0x72,0xD8,0xC0,0xC5,0xE1, - 0x00,0x25,0xE3,0x99,0xF2,0x90,0x37,0x12,0xCC,0xF3, /* y */ - 0xEA,0x9E,0x3A,0x1A,0xD1,0x7F,0xB0,0xB3,0x20,0x1B, - 0x6A,0xF7,0xCE,0x1B,0x05, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0xC7,0xF3,0x4A,0x77,0x8F,0x44,0x3A, - 0xCC,0x92,0x0E,0xBA,0x49 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } - _EC_SECG_CHAR2_193R2 = { - { NID_X9_62_characteristic_two_field,20,25,2 }, - { 0x10,0xB7,0xB4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15, /* seed */ - 0x17,0x51,0x37,0xC8,0xA1,0x6F,0xD0,0xDA,0x22,0x11, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x80,0x01, - 0x01,0x63,0xF3,0x5A,0x51,0x37,0xC2,0xCE,0x3E,0xA6, /* a */ - 0xED,0x86,0x67,0x19,0x0B,0x0B,0xC4,0x3E,0xCD,0x69, - 0x97,0x77,0x02,0x70,0x9B, - 0x00,0xC9,0xBB,0x9E,0x89,0x27,0xD4,0xD6,0x4C,0x37, /* b */ - 0x7E,0x2A,0xB2,0x85,0x6A,0x5B,0x16,0xE3,0xEF,0xB7, - 0xF6,0x1D,0x43,0x16,0xAE, - 0x00,0xD9,0xB6,0x7D,0x19,0x2E,0x03,0x67,0xC8,0x03, /* x */ - 0xF3,0x9E,0x1A,0x7E,0x82,0xCA,0x14,0xA6,0x51,0x35, - 0x0A,0xAE,0x61,0x7E,0x8F, - 0x01,0xCE,0x94,0x33,0x56,0x07,0xC3,0x04,0xAC,0x29, /* y */ - 0xE7,0xDE,0xFB,0xD9,0xCA,0x01,0xF5,0x96,0xF9,0x27, - 0x22,0x4C,0xDE,0xCF,0x6C, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x01,0x5A,0xAB,0x56,0x1B,0x00,0x54,0x13, - 0xCC,0xD4,0xEE,0x99,0xD5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } - _EC_NIST_CHAR2_233K = { - { NID_X9_62_characteristic_two_field,0,30,4 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x01,0x72,0x32,0xBA,0x85,0x3A,0x7E,0x73,0x1A,0xF1, /* x */ - 0x29,0xF2,0x2F,0xF4,0x14,0x95,0x63,0xA4,0x19,0xC2, - 0x6B,0xF5,0x0A,0x4C,0x9D,0x6E,0xEF,0xAD,0x61,0x26, - - 0x01,0xDB,0x53,0x7D,0xEC,0xE8,0x19,0xB7,0xF7,0x0F, /* y */ - 0x55,0x5A,0x67,0xC4,0x27,0xA8,0xCD,0x9B,0xF1,0x8A, - 0xEB,0x9B,0x56,0xE0,0xC1,0x10,0x56,0xFA,0xE6,0xA3, - - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x06,0x9D,0x5B,0xB9,0x15, - 0xBC,0xD4,0x6E,0xFB,0x1A,0xD5,0xF1,0x73,0xAB,0xDF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_NIST_CHAR2_233B = { - { NID_X9_62_characteristic_two_field,20,30,2 }, - { 0x74,0xD5,0x9F,0xF0,0x7F,0x6B,0x41,0x3D,0x0E,0xA1, /* seed */ - 0x4B,0x34,0x4B,0x20,0xA2,0xDB,0x04,0x9B,0x50,0xC3, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x66,0x64,0x7E,0xDE,0x6C,0x33,0x2C,0x7F,0x8C, /* b */ - 0x09,0x23,0xBB,0x58,0x21,0x3B,0x33,0x3B,0x20,0xE9, - 0xCE,0x42,0x81,0xFE,0x11,0x5F,0x7D,0x8F,0x90,0xAD, - - 0x00,0xFA,0xC9,0xDF,0xCB,0xAC,0x83,0x13,0xBB,0x21, /* x */ - 0x39,0xF1,0xBB,0x75,0x5F,0xEF,0x65,0xBC,0x39,0x1F, - 0x8B,0x36,0xF8,0xF8,0xEB,0x73,0x71,0xFD,0x55,0x8B, - - 0x01,0x00,0x6A,0x08,0xA4,0x19,0x03,0x35,0x06,0x78, /* y */ - 0xE5,0x85,0x28,0xBE,0xBF,0x8A,0x0B,0xEF,0xF8,0x67, - 0xA7,0xCA,0x36,0x71,0x6F,0x7E,0x01,0xF8,0x10,0x52, - - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x13,0xE9,0x74,0xE7,0x2F, - 0x8A,0x69,0x22,0x03,0x1D,0x26,0x03,0xCF,0xE0,0xD7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } - _EC_SECG_CHAR2_239K1 = { - { NID_X9_62_characteristic_two_field,0,30,4 }, - { /* no seed */ - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - - 0x29,0xA0,0xB6,0xA8,0x87,0xA9,0x83,0xE9,0x73,0x09, /* x */ - 0x88,0xA6,0x87,0x27,0xA8,0xB2,0xD1,0x26,0xC4,0x4C, - 0xC2,0xCC,0x7B,0x2A,0x65,0x55,0x19,0x30,0x35,0xDC, - - 0x76,0x31,0x08,0x04,0xF1,0x2E,0x54,0x9B,0xDB,0x01, /* y */ - 0x1C,0x10,0x30,0x89,0xE7,0x35,0x10,0xAC,0xB2,0x75, - 0xFC,0x31,0x2A,0x5D,0xC6,0xB7,0x65,0x53,0xF0,0xCA, - - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x5A,0x79,0xFE,0xC6,0x7C, - 0xB6,0xE9,0x1F,0x1C,0x1D,0xA8,0x00,0xE4,0x78,0xA5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+36*6]; } - _EC_NIST_CHAR2_283K = { - { NID_X9_62_characteristic_two_field,0,36,4 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x10,0xA1, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x01, - 0x05,0x03,0x21,0x3F,0x78,0xCA,0x44,0x88,0x3F,0x1A, /* x */ - 0x3B,0x81,0x62,0xF1,0x88,0xE5,0x53,0xCD,0x26,0x5F, - 0x23,0xC1,0x56,0x7A,0x16,0x87,0x69,0x13,0xB0,0xC2, - 0xAC,0x24,0x58,0x49,0x28,0x36, - 0x01,0xCC,0xDA,0x38,0x0F,0x1C,0x9E,0x31,0x8D,0x90, /* y */ - 0xF9,0x5D,0x07,0xE5,0x42,0x6F,0xE8,0x7E,0x45,0xC0, - 0xE8,0x18,0x46,0x98,0xE4,0x59,0x62,0x36,0x4E,0x34, - 0x11,0x61,0x77,0xDD,0x22,0x59, - 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE9,0xAE, - 0x2E,0xD0,0x75,0x77,0x26,0x5D,0xFF,0x7F,0x94,0x45, - 0x1E,0x06,0x1E,0x16,0x3C,0x61 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+36*6]; } - _EC_NIST_CHAR2_283B = { - { NID_X9_62_characteristic_two_field,20,36,2 }, - { 0x77,0xE2,0xB0,0x73,0x70,0xEB,0x0F,0x83,0x2A,0x6D, /* no seed */ - 0xD5,0xB6,0x2D,0xFC,0x88,0xCD,0x06,0xBB,0x84,0xBE, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x10,0xA1, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x01, - 0x02,0x7B,0x68,0x0A,0xC8,0xB8,0x59,0x6D,0xA5,0xA4, /* b */ - 0xAF,0x8A,0x19,0xA0,0x30,0x3F,0xCA,0x97,0xFD,0x76, - 0x45,0x30,0x9F,0xA2,0xA5,0x81,0x48,0x5A,0xF6,0x26, - 0x3E,0x31,0x3B,0x79,0xA2,0xF5, - 0x05,0xF9,0x39,0x25,0x8D,0xB7,0xDD,0x90,0xE1,0x93, /* x */ - 0x4F,0x8C,0x70,0xB0,0xDF,0xEC,0x2E,0xED,0x25,0xB8, - 0x55,0x7E,0xAC,0x9C,0x80,0xE2,0xE1,0x98,0xF8,0xCD, - 0xBE,0xCD,0x86,0xB1,0x20,0x53, - 0x03,0x67,0x68,0x54,0xFE,0x24,0x14,0x1C,0xB9,0x8F, /* y */ - 0xE6,0xD4,0xB2,0x0D,0x02,0xB4,0x51,0x6F,0xF7,0x02, - 0x35,0x0E,0xDD,0xB0,0x82,0x67,0x79,0xC8,0x13,0xF0, - 0xDF,0x45,0xBE,0x81,0x12,0xF4, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xEF,0x90, - 0x39,0x96,0x60,0xFC,0x93,0x8A,0x90,0x16,0x5B,0x04, - 0x2A,0x7C,0xEF,0xAD,0xB3,0x07 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+52*6]; } - _EC_NIST_CHAR2_409K = { - { NID_X9_62_characteristic_two_field,0,52,4 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x60,0xF0,0x5F,0x65,0x8F,0x49,0xC1,0xAD,0x3A, /* x */ - 0xB1,0x89,0x0F,0x71,0x84,0x21,0x0E,0xFD,0x09,0x87, - 0xE3,0x07,0xC8,0x4C,0x27,0xAC,0xCF,0xB8,0xF9,0xF6, - 0x7C,0xC2,0xC4,0x60,0x18,0x9E,0xB5,0xAA,0xAA,0x62, - 0xEE,0x22,0x2E,0xB1,0xB3,0x55,0x40,0xCF,0xE9,0x02, - 0x37,0x46, - 0x01,0xE3,0x69,0x05,0x0B,0x7C,0x4E,0x42,0xAC,0xBA, /* y */ - 0x1D,0xAC,0xBF,0x04,0x29,0x9C,0x34,0x60,0x78,0x2F, - 0x91,0x8E,0xA4,0x27,0xE6,0x32,0x51,0x65,0xE9,0xEA, - 0x10,0xE3,0xDA,0x5F,0x6C,0x42,0xE9,0xC5,0x52,0x15, - 0xAA,0x9C,0xA2,0x7A,0x58,0x63,0xEC,0x48,0xD8,0xE0, - 0x28,0x6B, - 0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0x5F,0x83,0xB2, - 0xD4,0xEA,0x20,0x40,0x0E,0xC4,0x55,0x7D,0x5E,0xD3, - 0xE3,0xE7,0xCA,0x5B,0x4B,0x5C,0x83,0xB8,0xE0,0x1E, - 0x5F,0xCF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+52*6]; } - _EC_NIST_CHAR2_409B = { - { NID_X9_62_characteristic_two_field,20,52,2 }, - { 0x40,0x99,0xB5,0xA4,0x57,0xF9,0xD6,0x9F,0x79,0x21, /* seed */ - 0x3D,0x09,0x4C,0x4B,0xCD,0x4D,0x42,0x62,0x21,0x0B, - - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x00,0x21,0xA5,0xC2,0xC8,0xEE,0x9F,0xEB,0x5C,0x4B, /* b */ - 0x9A,0x75,0x3B,0x7B,0x47,0x6B,0x7F,0xD6,0x42,0x2E, - 0xF1,0xF3,0xDD,0x67,0x47,0x61,0xFA,0x99,0xD6,0xAC, - 0x27,0xC8,0xA9,0xA1,0x97,0xB2,0x72,0x82,0x2F,0x6C, - 0xD5,0x7A,0x55,0xAA,0x4F,0x50,0xAE,0x31,0x7B,0x13, - 0x54,0x5F, - 0x01,0x5D,0x48,0x60,0xD0,0x88,0xDD,0xB3,0x49,0x6B, /* x */ - 0x0C,0x60,0x64,0x75,0x62,0x60,0x44,0x1C,0xDE,0x4A, - 0xF1,0x77,0x1D,0x4D,0xB0,0x1F,0xFE,0x5B,0x34,0xE5, - 0x97,0x03,0xDC,0x25,0x5A,0x86,0x8A,0x11,0x80,0x51, - 0x56,0x03,0xAE,0xAB,0x60,0x79,0x4E,0x54,0xBB,0x79, - 0x96,0xA7, - 0x00,0x61,0xB1,0xCF,0xAB,0x6B,0xE5,0xF3,0x2B,0xBF, /* y */ - 0xA7,0x83,0x24,0xED,0x10,0x6A,0x76,0x36,0xB9,0xC5, - 0xA7,0xBD,0x19,0x8D,0x01,0x58,0xAA,0x4F,0x54,0x88, - 0xD0,0x8F,0x38,0x51,0x4F,0x1F,0xDF,0x4B,0x4F,0x40, - 0xD2,0x18,0x1B,0x36,0x81,0xC3,0x64,0xBA,0x02,0x73, - 0xC7,0x06, - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xE2,0xAA,0xD6, - 0xA6,0x12,0xF3,0x33,0x07,0xBE,0x5F,0xA4,0x7C,0x3C, - 0x9E,0x05,0x2F,0x83,0x81,0x64,0xCD,0x37,0xD9,0xA2, - 0x11,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+72*6]; } - _EC_NIST_CHAR2_571K = { - { NID_X9_62_characteristic_two_field,0,72,4 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x25, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x02,0x6E,0xB7,0xA8,0x59,0x92,0x3F,0xBC,0x82,0x18, /* x */ - 0x96,0x31,0xF8,0x10,0x3F,0xE4,0xAC,0x9C,0xA2,0x97, - 0x00,0x12,0xD5,0xD4,0x60,0x24,0x80,0x48,0x01,0x84, - 0x1C,0xA4,0x43,0x70,0x95,0x84,0x93,0xB2,0x05,0xE6, - 0x47,0xDA,0x30,0x4D,0xB4,0xCE,0xB0,0x8C,0xBB,0xD1, - 0xBA,0x39,0x49,0x47,0x76,0xFB,0x98,0x8B,0x47,0x17, - 0x4D,0xCA,0x88,0xC7,0xE2,0x94,0x52,0x83,0xA0,0x1C, - 0x89,0x72, - 0x03,0x49,0xDC,0x80,0x7F,0x4F,0xBF,0x37,0x4F,0x4A, /* y */ - 0xEA,0xDE,0x3B,0xCA,0x95,0x31,0x4D,0xD5,0x8C,0xEC, - 0x9F,0x30,0x7A,0x54,0xFF,0xC6,0x1E,0xFC,0x00,0x6D, - 0x8A,0x2C,0x9D,0x49,0x79,0xC0,0xAC,0x44,0xAE,0xA7, - 0x4F,0xBE,0xBB,0xB9,0xF7,0x72,0xAE,0xDC,0xB6,0x20, - 0xB0,0x1A,0x7B,0xA7,0xAF,0x1B,0x32,0x04,0x30,0xC8, - 0x59,0x19,0x84,0xF6,0x01,0xCD,0x4C,0x14,0x3E,0xF1, - 0xC7,0xA3, - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x13,0x18,0x50,0xE1, - 0xF1,0x9A,0x63,0xE4,0xB3,0x91,0xA8,0xDB,0x91,0x7F, - 0x41,0x38,0xB6,0x30,0xD8,0x4B,0xE5,0xD6,0x39,0x38, - 0x1E,0x91,0xDE,0xB4,0x5C,0xFE,0x77,0x8F,0x63,0x7C, - 0x10,0x01 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+72*6]; } - _EC_NIST_CHAR2_571B = { - { NID_X9_62_characteristic_two_field,20,72,2 }, - { 0x2A,0xA0,0x58,0xF7,0x3A,0x0E,0x33,0xAB,0x48,0x6B, /* seed */ - 0x0F,0x61,0x04,0x10,0xC5,0x3A,0x7F,0x13,0x23,0x10, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x04,0x25, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x01, - 0x02,0xF4,0x0E,0x7E,0x22,0x21,0xF2,0x95,0xDE,0x29, /* b */ - 0x71,0x17,0xB7,0xF3,0xD6,0x2F,0x5C,0x6A,0x97,0xFF, - 0xCB,0x8C,0xEF,0xF1,0xCD,0x6B,0xA8,0xCE,0x4A,0x9A, - 0x18,0xAD,0x84,0xFF,0xAB,0xBD,0x8E,0xFA,0x59,0x33, - 0x2B,0xE7,0xAD,0x67,0x56,0xA6,0x6E,0x29,0x4A,0xFD, - 0x18,0x5A,0x78,0xFF,0x12,0xAA,0x52,0x0E,0x4D,0xE7, - 0x39,0xBA,0xCA,0x0C,0x7F,0xFE,0xFF,0x7F,0x29,0x55, - 0x72,0x7A, - 0x03,0x03,0x00,0x1D,0x34,0xB8,0x56,0x29,0x6C,0x16, /* x */ - 0xC0,0xD4,0x0D,0x3C,0xD7,0x75,0x0A,0x93,0xD1,0xD2, - 0x95,0x5F,0xA8,0x0A,0xA5,0xF4,0x0F,0xC8,0xDB,0x7B, - 0x2A,0xBD,0xBD,0xE5,0x39,0x50,0xF4,0xC0,0xD2,0x93, - 0xCD,0xD7,0x11,0xA3,0x5B,0x67,0xFB,0x14,0x99,0xAE, - 0x60,0x03,0x86,0x14,0xF1,0x39,0x4A,0xBF,0xA3,0xB4, - 0xC8,0x50,0xD9,0x27,0xE1,0xE7,0x76,0x9C,0x8E,0xEC, - 0x2D,0x19, - 0x03,0x7B,0xF2,0x73,0x42,0xDA,0x63,0x9B,0x6D,0xCC, /* y */ - 0xFF,0xFE,0xB7,0x3D,0x69,0xD7,0x8C,0x6C,0x27,0xA6, - 0x00,0x9C,0xBB,0xCA,0x19,0x80,0xF8,0x53,0x39,0x21, - 0xE8,0xA6,0x84,0x42,0x3E,0x43,0xBA,0xB0,0x8A,0x57, - 0x62,0x91,0xAF,0x8F,0x46,0x1B,0xB2,0xA8,0xB3,0x53, - 0x1D,0x2F,0x04,0x85,0xC1,0x9B,0x16,0xE2,0xF1,0x51, - 0x6E,0x23,0xDD,0x3C,0x1A,0x48,0x27,0xAF,0x1B,0x8A, - 0xC1,0x5B, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE6,0x61,0xCE,0x18, - 0xFF,0x55,0x98,0x73,0x08,0x05,0x9B,0x18,0x68,0x23, - 0x85,0x1E,0xC7,0xDD,0x9C,0xA1,0x16,0x1D,0xE9,0x3D, - 0x51,0x74,0xD6,0x6E,0x83,0x82,0xE9,0xBB,0x2F,0xE8, - 0x4E,0x47 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V1 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0xD2,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x54, /* seed */ - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x07,0x25,0x46,0xB5,0x43,0x52,0x34,0xA4,0x22,0xE0, /* a */ - 0x78,0x96,0x75,0xF4,0x32,0xC8,0x94,0x35,0xDE,0x52, - 0x42, - 0x00,0xC9,0x51,0x7D,0x06,0xD5,0x24,0x0D,0x3C,0xFF, /* b */ - 0x38,0xC7,0x4B,0x20,0xB6,0xCD,0x4D,0x6F,0x9D,0xD4, - 0xD9, - 0x07,0xAF,0x69,0x98,0x95,0x46,0x10,0x3D,0x79,0x32, /* x */ - 0x9F,0xCC,0x3D,0x74,0x88,0x0F,0x33,0xBB,0xE8,0x03, - 0xCB, - 0x01,0xEC,0x23,0x21,0x1B,0x59,0x66,0xAD,0xEA,0x1D, /* y */ - 0x3F,0x87,0xF7,0xEA,0x58,0x48,0xAE,0xF0,0xB7,0xCA, - 0x9F, - 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x01,0xE6,0x0F,0xC8,0x82,0x1C,0xC7,0x4D,0xAE,0xAF, - 0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V2 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x01,0x08,0xB3,0x9E,0x77,0xC4,0xB1,0x08,0xBE,0xD9, /* a */ - 0x81,0xED,0x0E,0x89,0x0E,0x11,0x7C,0x51,0x1C,0xF0, - 0x72, - 0x06,0x67,0xAC,0xEB,0x38,0xAF,0x4E,0x48,0x8C,0x40, /* b */ - 0x74,0x33,0xFF,0xAE,0x4F,0x1C,0x81,0x16,0x38,0xDF, - 0x20, - 0x00,0x24,0x26,0x6E,0x4E,0xB5,0x10,0x6D,0x0A,0x96, /* x */ - 0x4D,0x92,0xC4,0x86,0x0E,0x26,0x71,0xDB,0x9B,0x6C, - 0xC5, - 0x07,0x9F,0x68,0x4D,0xDF,0x66,0x84,0xC5,0xCD,0x25, /* y */ - 0x8B,0x38,0x90,0x02,0x1B,0x23,0x86,0xDF,0xD1,0x9F, - 0xC5, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFD,0xF6,0x4D,0xE1,0x15,0x1A,0xDB,0xB7,0x8F,0x10, - 0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } - _EC_X9_62_CHAR2_163V3 = { - { NID_X9_62_characteristic_two_field,20,21,2 }, - { 0x50,0xCB,0xF1,0xD9,0x5C,0xA9,0x4D,0x69,0x6E,0x67, /* seed */ - 0x68,0x75,0x61,0x51,0x75,0xF1,0x6A,0x36,0xA3,0xB8, - - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, - 0x07, - 0x07,0xA5,0x26,0xC6,0x3D,0x3E,0x25,0xA2,0x56,0xA0, /* a */ - 0x07,0x69,0x9F,0x54,0x47,0xE3,0x2A,0xE4,0x56,0xB5, - 0x0E, - 0x03,0xF7,0x06,0x17,0x98,0xEB,0x99,0xE2,0x38,0xFD, /* b */ - 0x6F,0x1B,0xF9,0x5B,0x48,0xFE,0xEB,0x48,0x54,0x25, - 0x2B, - 0x02,0xF9,0xF8,0x7B,0x7C,0x57,0x4D,0x0B,0xDE,0xCF, /* x */ - 0x8A,0x22,0xE6,0x52,0x47,0x75,0xF9,0x8C,0xDE,0xBD, - 0xCB, - 0x05,0xB9,0x35,0x59,0x0C,0x15,0x5E,0x17,0xEA,0x48, /* y */ - 0xEB,0x3F,0xF3,0x71,0x8B,0x89,0x3D,0xF5,0x9A,0x05, - 0xD0, - 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFE,0x1A,0xEE,0x14,0x0F,0x11,0x0A,0xFF,0x96,0x13, - 0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+23*6]; } - _EC_X9_62_CHAR2_176V1 = { - { NID_X9_62_characteristic_two_field,0,23,0xFF6E }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00, - 0x00,0x00,0x07, - 0x00,0xE4,0xE6,0xDB,0x29,0x95,0x06,0x5C,0x40,0x7D, /* a */ - 0x9D,0x39,0xB8,0xD0,0x96,0x7B,0x96,0x70,0x4B,0xA8, - 0xE9,0xC9,0x0B, - 0x00,0x5D,0xDA,0x47,0x0A,0xBE,0x64,0x14,0xDE,0x8E, /* b */ - 0xC1,0x33,0xAE,0x28,0xE9,0xBB,0xD7,0xFC,0xEC,0x0A, - 0xE0,0xFF,0xF2, - 0x00,0x8D,0x16,0xC2,0x86,0x67,0x98,0xB6,0x00,0xF9, /* x */ - 0xF0,0x8B,0xB4,0xA8,0xE8,0x60,0xF3,0x29,0x8C,0xE0, - 0x4A,0x57,0x98, - 0x00,0x6F,0xA4,0x53,0x9C,0x2D,0xAD,0xDD,0xD6,0xBA, /* y */ - 0xB5,0x16,0x7D,0x61,0xB4,0x36,0xE1,0xD9,0x2B,0xB1, - 0x6A,0x56,0x2C, - 0x00,0x00,0x01,0x00,0x92,0x53,0x73,0x97,0xEC,0xA4, /* order */ - 0xF6,0x14,0x57,0x99,0xD6,0x2B,0x0A,0x19,0xCE,0x06, - 0xFE,0x26,0xAD } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V1 = { - { NID_X9_62_characteristic_two_field,20,24,2 }, - { 0x4E,0x13,0xCA,0x54,0x27,0x44,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x55,0x2F,0x27,0x9A,0x8C,0x84, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x28,0x66,0x53,0x7B,0x67,0x67,0x52,0x63,0x6A,0x68, /* a */ - 0xF5,0x65,0x54,0xE1,0x26,0x40,0x27,0x6B,0x64,0x9E, - 0xF7,0x52,0x62,0x67, - 0x2E,0x45,0xEF,0x57,0x1F,0x00,0x78,0x6F,0x67,0xB0, /* b */ - 0x08,0x1B,0x94,0x95,0xA3,0xD9,0x54,0x62,0xF5,0xDE, - 0x0A,0xA1,0x85,0xEC, - 0x36,0xB3,0xDA,0xF8,0xA2,0x32,0x06,0xF9,0xC4,0xF2, /* x */ - 0x99,0xD7,0xB2,0x1A,0x9C,0x36,0x91,0x37,0xF2,0xC8, - 0x4A,0xE1,0xAA,0x0D, - 0x76,0x5B,0xE7,0x34,0x33,0xB3,0xF9,0x5E,0x33,0x29, /* y */ - 0x32,0xE7,0x0E,0xA2,0x45,0xCA,0x24,0x18,0xEA,0x0E, - 0xF9,0x80,0x18,0xFB, - 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x04,0xA2,0x0E,0x90,0xC3,0x90,0x67,0xC8, - 0x93,0xBB,0xB9,0xA5 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V2 = { - { NID_X9_62_characteristic_two_field,20,24,4 }, - { 0x08,0x71,0xEF,0x2F,0xEF,0x24,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0xBE,0xE0,0xD9,0x5C,0x15, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x40,0x10,0x28,0x77,0x4D,0x77,0x77,0xC7,0xB7,0x66, /* a */ - 0x6D,0x13,0x66,0xEA,0x43,0x20,0x71,0x27,0x4F,0x89, - 0xFF,0x01,0xE7,0x18, - 0x06,0x20,0x04,0x8D,0x28,0xBC,0xBD,0x03,0xB6,0x24, /* b */ - 0x9C,0x99,0x18,0x2B,0x7C,0x8C,0xD1,0x97,0x00,0xC3, - 0x62,0xC4,0x6A,0x01, - 0x38,0x09,0xB2,0xB7,0xCC,0x1B,0x28,0xCC,0x5A,0x87, /* x */ - 0x92,0x6A,0xAD,0x83,0xFD,0x28,0x78,0x9E,0x81,0xE2, - 0xC9,0xE3,0xBF,0x10, - 0x17,0x43,0x43,0x86,0x62,0x6D,0x14,0xF3,0xDB,0xF0, /* y */ - 0x17,0x60,0xD9,0x21,0x3A,0x3E,0x1C,0xF3,0x7A,0xEC, - 0x43,0x7D,0x66,0x8A, - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x50,0x50,0x8C,0xB8,0x9F,0x65,0x28,0x24, - 0xE0,0x6B,0x81,0x73 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } - _EC_X9_62_CHAR2_191V3 = { - { NID_X9_62_characteristic_two_field,20,24,6 }, - { 0xE0,0x53,0x51,0x2D,0xC6,0x84,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x50,0x67,0xAE,0x78,0x6D,0x1F, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x02,0x01, - 0x6C,0x01,0x07,0x47,0x56,0x09,0x91,0x22,0x22,0x10, /* a */ - 0x56,0x91,0x1C,0x77,0xD7,0x7E,0x77,0xA7,0x77,0xE7, - 0xE7,0xE7,0x7F,0xCB, - 0x71,0xFE,0x1A,0xF9,0x26,0xCF,0x84,0x79,0x89,0xEF, /* b */ - 0xEF,0x8D,0xB4,0x59,0xF6,0x63,0x94,0xD9,0x0F,0x32, - 0xAD,0x3F,0x15,0xE8, - 0x37,0x5D,0x4C,0xE2,0x4F,0xDE,0x43,0x44,0x89,0xDE, /* x */ - 0x87,0x46,0xE7,0x17,0x86,0x01,0x50,0x09,0xE6,0x6E, - 0x38,0xA9,0x26,0xDD, - 0x54,0x5A,0x39,0x17,0x61,0x96,0x57,0x5D,0x98,0x59, /* y */ - 0x99,0x36,0x6E,0x6A,0xD3,0x4C,0xE0,0xA7,0x7C,0xD7, - 0x12,0x7B,0x06,0xBE, - 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ - 0x55,0x55,0x61,0x0C,0x0B,0x19,0x68,0x12,0xBF,0xB6, - 0x28,0x8A,0x3E,0xA3 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+27*6]; } - _EC_X9_62_CHAR2_208W1 = { - { NID_X9_62_characteristic_two_field,0,27,0xFE48 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x07, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0xC8,0x61,0x9E,0xD4,0x5A,0x62,0xE6,0x21,0x2E, /* b */ - 0x11,0x60,0x34,0x9E,0x2B,0xFA,0x84,0x44,0x39,0xFA, - 0xFC,0x2A,0x3F,0xD1,0x63,0x8F,0x9E, - 0x00,0x89,0xFD,0xFB,0xE4,0xAB,0xE1,0x93,0xDF,0x95, /* x */ - 0x59,0xEC,0xF0,0x7A,0xC0,0xCE,0x78,0x55,0x4E,0x27, - 0x84,0xEB,0x8C,0x1E,0xD1,0xA5,0x7A, - 0x00,0x0F,0x55,0xB5,0x1A,0x06,0xE7,0x8E,0x9A,0xC3, /* y */ - 0x8A,0x03,0x5F,0xF5,0x20,0xD8,0xB0,0x17,0x81,0xBE, - 0xB1,0xA6,0xBB,0x08,0x61,0x7D,0xE3, - 0x00,0x00,0x01,0x01,0xBA,0xF9,0x5C,0x97,0x23,0xC5, /* order */ - 0x7B,0x6C,0x21,0xDA,0x2E,0xFF,0x2D,0x5E,0xD5,0x88, - 0xBD,0xD5,0x71,0x7E,0x21,0x2F,0x9D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V1 = { - { NID_X9_62_characteristic_two_field,20,30,4 }, - { 0xD3,0x4B,0x9A,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0xCA,0x71,0xB9,0x20,0xBF,0xEF,0xB0,0x5D, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x32,0x01,0x08,0x57,0x07,0x7C,0x54,0x31,0x12,0x3A, /* a */ - 0x46,0xB8,0x08,0x90,0x67,0x56,0xF5,0x43,0x42,0x3E, - 0x8D,0x27,0x87,0x75,0x78,0x12,0x57,0x78,0xAC,0x76, - - 0x79,0x04,0x08,0xF2,0xEE,0xDA,0xF3,0x92,0xB0,0x12, /* b */ - 0xED,0xEF,0xB3,0x39,0x2F,0x30,0xF4,0x32,0x7C,0x0C, - 0xA3,0xF3,0x1F,0xC3,0x83,0xC4,0x22,0xAA,0x8C,0x16, - - 0x57,0x92,0x70,0x98,0xFA,0x93,0x2E,0x7C,0x0A,0x96, /* x */ - 0xD3,0xFD,0x5B,0x70,0x6E,0xF7,0xE5,0xF5,0xC1,0x56, - 0xE1,0x6B,0x7E,0x7C,0x86,0x03,0x85,0x52,0xE9,0x1D, - - 0x61,0xD8,0xEE,0x50,0x77,0xC3,0x3F,0xEC,0xF6,0xF1, /* y */ - 0xA1,0x6B,0x26,0x8D,0xE4,0x69,0xC3,0xC7,0x74,0x4E, - 0xA9,0xA9,0x71,0x64,0x9F,0xC7,0xA9,0x61,0x63,0x05, - - 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ - 0x00,0x00,0x00,0x00,0x00,0x0F,0x4D,0x42,0xFF,0xE1, - 0x49,0x2A,0x49,0x93,0xF1,0xCA,0xD6,0x66,0xE4,0x47 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V2 = { - { NID_X9_62_characteristic_two_field,20,30,6 }, - { 0x2A,0xA6,0x98,0x2F,0xDF,0xA4,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x5D,0x26,0x67,0x27,0x27,0x7D, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x42,0x30,0x01,0x77,0x57,0xA7,0x67,0xFA,0xE4,0x23, /* a */ - 0x98,0x56,0x9B,0x74,0x63,0x25,0xD4,0x53,0x13,0xAF, - 0x07,0x66,0x26,0x64,0x79,0xB7,0x56,0x54,0xE6,0x5F, - - 0x50,0x37,0xEA,0x65,0x41,0x96,0xCF,0xF0,0xCD,0x82, /* b */ - 0xB2,0xC1,0x4A,0x2F,0xCF,0x2E,0x3F,0xF8,0x77,0x52, - 0x85,0xB5,0x45,0x72,0x2F,0x03,0xEA,0xCD,0xB7,0x4B, - - 0x28,0xF9,0xD0,0x4E,0x90,0x00,0x69,0xC8,0xDC,0x47, /* x */ - 0xA0,0x85,0x34,0xFE,0x76,0xD2,0xB9,0x00,0xB7,0xD7, - 0xEF,0x31,0xF5,0x70,0x9F,0x20,0x0C,0x4C,0xA2,0x05, - - 0x56,0x67,0x33,0x4C,0x45,0xAF,0xF3,0xB5,0xA0,0x3B, /* y */ - 0xAD,0x9D,0xD7,0x5E,0x2C,0x71,0xA9,0x93,0x62,0x56, - 0x7D,0x54,0x53,0xF7,0xFA,0x6E,0x22,0x7E,0xC8,0x33, - - 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ - 0x55,0x55,0x55,0x55,0x55,0x3C,0x6F,0x28,0x85,0x25, - 0x9C,0x31,0xE3,0xFC,0xDF,0x15,0x46,0x24,0x52,0x2D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } - _EC_X9_62_CHAR2_239V3 = { - { NID_X9_62_characteristic_two_field,20,30,0xA }, - { 0x9E,0x07,0x6F,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ - 0x51,0x75,0xE1,0x1E,0x9F,0xDD,0x77,0xF9,0x20,0x41, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, - - 0x01,0x23,0x87,0x74,0x66,0x6A,0x67,0x76,0x6D,0x66, /* a */ - 0x76,0xF7,0x78,0xE6,0x76,0xB6,0x69,0x99,0x17,0x66, - 0x66,0xE6,0x87,0x66,0x6D,0x87,0x66,0xC6,0x6A,0x9F, - - 0x6A,0x94,0x19,0x77,0xBA,0x9F,0x6A,0x43,0x51,0x99, /* b */ - 0xAC,0xFC,0x51,0x06,0x7E,0xD5,0x87,0xF5,0x19,0xC5, - 0xEC,0xB5,0x41,0xB8,0xE4,0x41,0x11,0xDE,0x1D,0x40, - - 0x70,0xF6,0xE9,0xD0,0x4D,0x28,0x9C,0x4E,0x89,0x91, /* x */ - 0x3C,0xE3,0x53,0x0B,0xFD,0xE9,0x03,0x97,0x7D,0x42, - 0xB1,0x46,0xD5,0x39,0xBF,0x1B,0xDE,0x4E,0x9C,0x92, - - 0x2E,0x5A,0x0E,0xAF,0x6E,0x5E,0x13,0x05,0xB9,0x00, /* y */ - 0x4D,0xCE,0x5C,0x0E,0xD7,0xFE,0x59,0xA3,0x56,0x08, - 0xF3,0x38,0x37,0xC8,0x16,0xD8,0x0B,0x79,0xF4,0x61, - - 0x0C,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC, /* order */ - 0xCC,0xCC,0xCC,0xCC,0xCC,0xAC,0x49,0x12,0xD2,0xD9, - 0xDF,0x90,0x3E,0xF9,0x88,0x8B,0x8A,0x0E,0x4C,0xFF } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+35*6]; } - _EC_X9_62_CHAR2_272W1 = { - { NID_X9_62_characteristic_two_field,0,35,0xFF06 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00, - 0x00,0x00,0x00,0x00,0x0B, - 0x00,0x91,0xA0,0x91,0xF0,0x3B,0x5F,0xBA,0x4A,0xB2, /* a */ - 0xCC,0xF4,0x9C,0x4E,0xDD,0x22,0x0F,0xB0,0x28,0x71, - 0x2D,0x42,0xBE,0x75,0x2B,0x2C,0x40,0x09,0x4D,0xBA, - 0xCD,0xB5,0x86,0xFB,0x20, - 0x00,0x71,0x67,0xEF,0xC9,0x2B,0xB2,0xE3,0xCE,0x7C, /* b */ - 0x8A,0xAA,0xFF,0x34,0xE1,0x2A,0x9C,0x55,0x70,0x03, - 0xD7,0xC7,0x3A,0x6F,0xAF,0x00,0x3F,0x99,0xF6,0xCC, - 0x84,0x82,0xE5,0x40,0xF7, - 0x00,0x61,0x08,0xBA,0xBB,0x2C,0xEE,0xBC,0xF7,0x87, /* x */ - 0x05,0x8A,0x05,0x6C,0xBE,0x0C,0xFE,0x62,0x2D,0x77, - 0x23,0xA2,0x89,0xE0,0x8A,0x07,0xAE,0x13,0xEF,0x0D, - 0x10,0xD1,0x71,0xDD,0x8D, - 0x00,0x10,0xC7,0x69,0x57,0x16,0x85,0x1E,0xEF,0x6B, /* y */ - 0xA7,0xF6,0x87,0x2E,0x61,0x42,0xFB,0xD2,0x41,0xB8, - 0x30,0xFF,0x5E,0xFC,0xAC,0xEC,0xCA,0xB0,0x5E,0x02, - 0x00,0x5D,0xDE,0x9D,0x23, - 0x00,0x00,0x01,0x00,0xFA,0xF5,0x13,0x54,0xE0,0xE3, /* order */ - 0x9E,0x48,0x92,0xDF,0x6E,0x31,0x9C,0x72,0xC8,0x16, - 0x16,0x03,0xFA,0x45,0xAA,0x7B,0x99,0x8A,0x16,0x7B, - 0x8F,0x1E,0x62,0x95,0x21 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+39*6]; } - _EC_X9_62_CHAR2_304W1 = { - { NID_X9_62_characteristic_two_field,0,39,0xFE2E }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x07, - 0x00,0xFD,0x0D,0x69,0x31,0x49,0xA1,0x18,0xF6,0x51, /* a */ - 0xE6,0xDC,0xE6,0x80,0x20,0x85,0x37,0x7E,0x5F,0x88, - 0x2D,0x1B,0x51,0x0B,0x44,0x16,0x00,0x74,0xC1,0x28, - 0x80,0x78,0x36,0x5A,0x03,0x96,0xC8,0xE6,0x81, - 0x00,0xBD,0xDB,0x97,0xE5,0x55,0xA5,0x0A,0x90,0x8E, /* b */ - 0x43,0xB0,0x1C,0x79,0x8E,0xA5,0xDA,0xA6,0x78,0x8F, - 0x1E,0xA2,0x79,0x4E,0xFC,0xF5,0x71,0x66,0xB8,0xC1, - 0x40,0x39,0x60,0x1E,0x55,0x82,0x73,0x40,0xBE, - 0x00,0x19,0x7B,0x07,0x84,0x5E,0x9B,0xE2,0xD9,0x6A, /* x */ - 0xDB,0x0F,0x5F,0x3C,0x7F,0x2C,0xFF,0xBD,0x7A,0x3E, - 0xB8,0xB6,0xFE,0xC3,0x5C,0x7F,0xD6,0x7F,0x26,0xDD, - 0xF6,0x28,0x5A,0x64,0x4F,0x74,0x0A,0x26,0x14, - 0x00,0xE1,0x9F,0xBE,0xB7,0x6E,0x0D,0xA1,0x71,0x51, /* y */ - 0x7E,0xCF,0x40,0x1B,0x50,0x28,0x9B,0xF0,0x14,0x10, - 0x32,0x88,0x52,0x7A,0x9B,0x41,0x6A,0x10,0x5E,0x80, - 0x26,0x0B,0x54,0x9F,0xDC,0x1B,0x92,0xC0,0x3B, - 0x00,0x00,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC, /* order */ - 0x80,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC,0x80, - 0x01,0x02,0x2D,0x5C,0x91,0xDD,0x17,0x3F,0x8F,0xB5, - 0x61,0xDA,0x68,0x99,0x16,0x44,0x43,0x05,0x1D } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[20+45*6]; } - _EC_X9_62_CHAR2_359V1 = { - { NID_X9_62_characteristic_two_field,20,45,0x4C }, - { 0x2B,0x35,0x49,0x20,0xB7,0x24,0xD6,0x96,0xE6,0x76, /* seed */ - 0x87,0x56,0x15,0x17,0x58,0x5B,0xA1,0x33,0x2D,0xC6, - - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x01, - 0x56,0x67,0x67,0x6A,0x65,0x4B,0x20,0x75,0x4F,0x35, /* a */ - 0x6E,0xA9,0x20,0x17,0xD9,0x46,0x56,0x7C,0x46,0x67, - 0x55,0x56,0xF1,0x95,0x56,0xA0,0x46,0x16,0xB5,0x67, - 0xD2,0x23,0xA5,0xE0,0x56,0x56,0xFB,0x54,0x90,0x16, - 0xA9,0x66,0x56,0xA5,0x57, - 0x24,0x72,0xE2,0xD0,0x19,0x7C,0x49,0x36,0x3F,0x1F, /* b */ - 0xE7,0xF5,0xB6,0xDB,0x07,0x5D,0x52,0xB6,0x94,0x7D, - 0x13,0x5D,0x8C,0xA4,0x45,0x80,0x5D,0x39,0xBC,0x34, - 0x56,0x26,0x08,0x96,0x87,0x74,0x2B,0x63,0x29,0xE7, - 0x06,0x80,0x23,0x19,0x88, - 0x3C,0x25,0x8E,0xF3,0x04,0x77,0x67,0xE7,0xED,0xE0, /* x */ - 0xF1,0xFD,0xAA,0x79,0xDA,0xEE,0x38,0x41,0x36,0x6A, - 0x13,0x2E,0x16,0x3A,0xCE,0xD4,0xED,0x24,0x01,0xDF, - 0x9C,0x6B,0xDC,0xDE,0x98,0xE8,0xE7,0x07,0xC0,0x7A, - 0x22,0x39,0xB1,0xB0,0x97, - 0x53,0xD7,0xE0,0x85,0x29,0x54,0x70,0x48,0x12,0x1E, /* y */ - 0x9C,0x95,0xF3,0x79,0x1D,0xD8,0x04,0x96,0x39,0x48, - 0xF3,0x4F,0xAE,0x7B,0xF4,0x4E,0xA8,0x23,0x65,0xDC, - 0x78,0x68,0xFE,0x57,0xE4,0xAE,0x2D,0xE2,0x11,0x30, - 0x5A,0x40,0x71,0x04,0xBD, - 0x01,0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1, /* order */ - 0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1,0xAF, - 0x28,0x6B,0xC9,0xFB,0x8F,0x6B,0x85,0xC5,0x56,0x89, - 0x2C,0x20,0xA7,0xEB,0x96,0x4F,0xE7,0x71,0x9E,0x74, - 0xF4,0x90,0x75,0x8D,0x3B } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+47*6]; } - _EC_X9_62_CHAR2_368W1 = { - { NID_X9_62_characteristic_two_field,0,47,0xFF70 }, - { /* no seed */ - 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x07, - 0x00,0xE0,0xD2,0xEE,0x25,0x09,0x52,0x06,0xF5,0xE2, /* a */ - 0xA4,0xF9,0xED,0x22,0x9F,0x1F,0x25,0x6E,0x79,0xA0, - 0xE2,0xB4,0x55,0x97,0x0D,0x8D,0x0D,0x86,0x5B,0xD9, - 0x47,0x78,0xC5,0x76,0xD6,0x2F,0x0A,0xB7,0x51,0x9C, - 0xCD,0x2A,0x1A,0x90,0x6A,0xE3,0x0D, - 0x00,0xFC,0x12,0x17,0xD4,0x32,0x0A,0x90,0x45,0x2C, /* b */ - 0x76,0x0A,0x58,0xED,0xCD,0x30,0xC8,0xDD,0x06,0x9B, - 0x3C,0x34,0x45,0x38,0x37,0xA3,0x4E,0xD5,0x0C,0xB5, - 0x49,0x17,0xE1,0xC2,0x11,0x2D,0x84,0xD1,0x64,0xF4, - 0x44,0xF8,0xF7,0x47,0x86,0x04,0x6A, - 0x00,0x10,0x85,0xE2,0x75,0x53,0x81,0xDC,0xCC,0xE3, /* x */ - 0xC1,0x55,0x7A,0xFA,0x10,0xC2,0xF0,0xC0,0xC2,0x82, - 0x56,0x46,0xC5,0xB3,0x4A,0x39,0x4C,0xBC,0xFA,0x8B, - 0xC1,0x6B,0x22,0xE7,0xE7,0x89,0xE9,0x27,0xBE,0x21, - 0x6F,0x02,0xE1,0xFB,0x13,0x6A,0x5F, - 0x00,0x7B,0x3E,0xB1,0xBD,0xDC,0xBA,0x62,0xD5,0xD8, /* y */ - 0xB2,0x05,0x9B,0x52,0x57,0x97,0xFC,0x73,0x82,0x2C, - 0x59,0x05,0x9C,0x62,0x3A,0x45,0xFF,0x38,0x43,0xCE, - 0xE8,0xF8,0x7C,0xD1,0x85,0x5A,0xDA,0xA8,0x1E,0x2A, - 0x07,0x50,0xB8,0x0F,0xDA,0x23,0x10, - 0x00,0x00,0x01,0x00,0x90,0x51,0x2D,0xA9,0xAF,0x72, /* order */ - 0xB0,0x83,0x49,0xD9,0x8A,0x5D,0xD4,0xC7,0xB0,0x53, - 0x2E,0xCA,0x51,0xCE,0x03,0xE2,0xD1,0x0F,0x3B,0x7A, - 0xC5,0x79,0xBD,0x87,0xE9,0x09,0xAE,0x40,0xA6,0xF1, - 0x31,0xE9,0xCF,0xCE,0x5B,0xD9,0x67 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+54*6]; } - _EC_X9_62_CHAR2_431R1 = { - { NID_X9_62_characteristic_two_field,0,54,0x2760 }, - { /* no seed */ - 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x01, - 0x1A,0x82,0x7E,0xF0,0x0D,0xD6,0xFC,0x0E,0x23,0x4C, /* a */ - 0xAF,0x04,0x6C,0x6A,0x5D,0x8A,0x85,0x39,0x5B,0x23, - 0x6C,0xC4,0xAD,0x2C,0xF3,0x2A,0x0C,0xAD,0xBD,0xC9, - 0xDD,0xF6,0x20,0xB0,0xEB,0x99,0x06,0xD0,0x95,0x7F, - 0x6C,0x6F,0xEA,0xCD,0x61,0x54,0x68,0xDF,0x10,0x4D, - 0xE2,0x96,0xCD,0x8F, - 0x10,0xD9,0xB4,0xA3,0xD9,0x04,0x7D,0x8B,0x15,0x43, /* b */ - 0x59,0xAB,0xFB,0x1B,0x7F,0x54,0x85,0xB0,0x4C,0xEB, - 0x86,0x82,0x37,0xDD,0xC9,0xDE,0xDA,0x98,0x2A,0x67, - 0x9A,0x5A,0x91,0x9B,0x62,0x6D,0x4E,0x50,0xA8,0xDD, - 0x73,0x1B,0x10,0x7A,0x99,0x62,0x38,0x1F,0xB5,0xD8, - 0x07,0xBF,0x26,0x18, - 0x12,0x0F,0xC0,0x5D,0x3C,0x67,0xA9,0x9D,0xE1,0x61, /* x */ - 0xD2,0xF4,0x09,0x26,0x22,0xFE,0xCA,0x70,0x1B,0xE4, - 0xF5,0x0F,0x47,0x58,0x71,0x4E,0x8A,0x87,0xBB,0xF2, - 0xA6,0x58,0xEF,0x8C,0x21,0xE7,0xC5,0xEF,0xE9,0x65, - 0x36,0x1F,0x6C,0x29,0x99,0xC0,0xC2,0x47,0xB0,0xDB, - 0xD7,0x0C,0xE6,0xB7, - 0x20,0xD0,0xAF,0x89,0x03,0xA9,0x6F,0x8D,0x5F,0xA2, /* y */ - 0xC2,0x55,0x74,0x5D,0x3C,0x45,0x1B,0x30,0x2C,0x93, - 0x46,0xD9,0xB7,0xE4,0x85,0xE7,0xBC,0xE4,0x1F,0x6B, - 0x59,0x1F,0x3E,0x8F,0x6A,0xDD,0xCB,0xB0,0xBC,0x4C, - 0x2F,0x94,0x7A,0x7D,0xE1,0xA8,0x9B,0x62,0x5D,0x6A, - 0x59,0x8B,0x37,0x60, - 0x00,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34, /* order */ - 0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03, - 0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x23, - 0xC3,0x13,0xFA,0xB5,0x05,0x89,0x70,0x3B,0x5E,0xC6, - 0x8D,0x35,0x87,0xFE,0xC6,0x0D,0x16,0x1C,0xC1,0x49, - 0xC1,0xAD,0x4A,0x91 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } - _EC_WTLS_1 = { - { NID_X9_62_characteristic_two_field,0,15,2 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x02,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x01, - 0x01,0x66,0x79,0x79,0xA4,0x0B,0xA4,0x97,0xE5,0xD5, /* x */ - 0xC2,0x70,0x78,0x06,0x17, - 0x00,0xF4,0x4B,0x4A,0xF1,0xEC,0xC2,0x63,0x0E,0x08, /* y */ - 0x78,0x5C,0xEB,0xCC,0x15, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFD,0xBF, /* order */ - 0x91,0xAF,0x6D,0xEA,0x73 } - }; + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xC9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, + 0x02, 0x0A, 0x60, 0x19, 0x07, 0xB8, 0xC9, 0x53, 0xCA, 0x14, /* b */ + 0x81, 0xEB, 0x10, 0x51, 0x2F, 0x78, 0x74, 0x4A, 0x32, 0x05, + 0xFD, + 0x03, 0xF0, 0xEB, 0xA1, 0x62, 0x86, 0xA2, 0xD5, 0x7E, 0xA0, /* x */ + 0x99, 0x11, 0x68, 0xD4, 0x99, 0x46, 0x37, 0xE8, 0x34, 0x3E, + 0x36, + 0x00, 0xD5, 0x1F, 0xBC, 0x6C, 0x71, 0xA0, 0x09, 0x4F, 0xA2, /* y */ + 0xCD, 0xD5, 0x45, 0xB1, 0x1C, 0x5C, 0x0C, 0x79, 0x73, 0x24, + 0xF1, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x02, 0x92, 0xFE, 0x77, 0xE7, 0x0C, 0x12, 0xA4, 0x23, 0x4C, + 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} + _EC_SECG_CHAR2_193R1 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + 0x10, 0x3F, 0xAE, 0xC7, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, /* seed */ + 0x61, 0x51, 0x75, 0x77, 0x7F, 0xC5, 0xB1, 0x91, 0xEF, 0x30, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x80, 0x01, + 0x00, 0x17, 0x85, 0x8F, 0xEB, 0x7A, 0x98, 0x97, 0x51, 0x69, /* a */ + 0xE1, 0x71, 0xF7, 0x7B, 0x40, 0x87, 0xDE, 0x09, 0x8A, 0xC8, + 0xA9, 0x11, 0xDF, 0x7B, 0x01, + 0x00, 0xFD, 0xFB, 0x49, 0xBF, 0xE6, 0xC3, 0xA8, 0x9F, 0xAC, /* b */ + 0xAD, 0xAA, 0x7A, 0x1E, 0x5B, 0xBC, 0x7C, 0xC1, 0xC2, 0xE5, + 0xD8, 0x31, 0x47, 0x88, 0x14, + 0x01, 0xF4, 0x81, 0xBC, 0x5F, 0x0F, 0xF8, 0x4A, 0x74, 0xAD, /* x */ + 0x6C, 0xDF, 0x6F, 0xDE, 0xF4, 0xBF, 0x61, 0x79, 0x62, 0x53, + 0x72, 0xD8, 0xC0, 0xC5, 0xE1, + 0x00, 0x25, 0xE3, 0x99, 0xF2, 0x90, 0x37, 0x12, 0xCC, 0xF3, /* y */ + 0xEA, 0x9E, 0x3A, 0x1A, 0xD1, 0x7F, 0xB0, 0xB3, 0x20, 0x1B, + 0x6A, 0xF7, 0xCE, 0x1B, 0x05, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0xC7, 0xF3, 0x4A, 0x77, 0x8F, 0x44, 0x3A, + 0xCC, 0x92, 0x0E, 0xBA, 0x49 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} + _EC_SECG_CHAR2_193R2 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + 0x10, 0xB7, 0xB4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, /* seed */ + 0x17, 0x51, 0x37, 0xC8, 0xA1, 0x6F, 0xD0, 0xDA, 0x22, 0x11, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x80, 0x01, + 0x01, 0x63, 0xF3, 0x5A, 0x51, 0x37, 0xC2, 0xCE, 0x3E, 0xA6, /* a */ + 0xED, 0x86, 0x67, 0x19, 0x0B, 0x0B, 0xC4, 0x3E, 0xCD, 0x69, + 0x97, 0x77, 0x02, 0x70, 0x9B, + 0x00, 0xC9, 0xBB, 0x9E, 0x89, 0x27, 0xD4, 0xD6, 0x4C, 0x37, /* b */ + 0x7E, 0x2A, 0xB2, 0x85, 0x6A, 0x5B, 0x16, 0xE3, 0xEF, 0xB7, + 0xF6, 0x1D, 0x43, 0x16, 0xAE, + 0x00, 0xD9, 0xB6, 0x7D, 0x19, 0x2E, 0x03, 0x67, 0xC8, 0x03, /* x */ + 0xF3, 0x9E, 0x1A, 0x7E, 0x82, 0xCA, 0x14, 0xA6, 0x51, 0x35, + 0x0A, 0xAE, 0x61, 0x7E, 0x8F, + 0x01, 0xCE, 0x94, 0x33, 0x56, 0x07, 0xC3, 0x04, 0xAC, 0x29, /* y */ + 0xE7, 0xDE, 0xFB, 0xD9, 0xCA, 0x01, 0xF5, 0x96, 0xF9, 0x27, + 0x22, 0x4C, 0xDE, 0xCF, 0x6C, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x01, 0x5A, 0xAB, 0x56, 0x1B, 0x00, 0x54, 0x13, + 0xCC, 0xD4, 0xEE, 0x99, 0xD5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} + _EC_NIST_CHAR2_233K = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x01, 0x72, 0x32, 0xBA, 0x85, 0x3A, 0x7E, 0x73, 0x1A, 0xF1, /* x */ + 0x29, 0xF2, 0x2F, 0xF4, 0x14, 0x95, 0x63, 0xA4, 0x19, 0xC2, + 0x6B, 0xF5, 0x0A, 0x4C, 0x9D, 0x6E, 0xEF, 0xAD, 0x61, 0x26, + + 0x01, 0xDB, 0x53, 0x7D, 0xEC, 0xE8, 0x19, 0xB7, 0xF7, 0x0F, /* y */ + 0x55, 0x5A, 0x67, 0xC4, 0x27, 0xA8, 0xCD, 0x9B, 0xF1, 0x8A, + 0xEB, 0x9B, 0x56, 0xE0, 0xC1, 0x10, 0x56, 0xFA, 0xE6, 0xA3, + + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x9D, 0x5B, 0xB9, 0x15, + 0xBC, 0xD4, 0x6E, 0xFB, 0x1A, 0xD5, 0xF1, 0x73, 0xAB, 0xDF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_NIST_CHAR2_233B = { + { + NID_X9_62_characteristic_two_field, 20, 30, 2 + }, + { + 0x74, 0xD5, 0x9F, 0xF0, 0x7F, 0x6B, 0x41, 0x3D, 0x0E, 0xA1, /* seed */ + 0x4B, 0x34, 0x4B, 0x20, 0xA2, 0xDB, 0x04, 0x9B, 0x50, 0xC3, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x66, 0x64, 0x7E, 0xDE, 0x6C, 0x33, 0x2C, 0x7F, 0x8C, /* b */ + 0x09, 0x23, 0xBB, 0x58, 0x21, 0x3B, 0x33, 0x3B, 0x20, 0xE9, + 0xCE, 0x42, 0x81, 0xFE, 0x11, 0x5F, 0x7D, 0x8F, 0x90, 0xAD, + + 0x00, 0xFA, 0xC9, 0xDF, 0xCB, 0xAC, 0x83, 0x13, 0xBB, 0x21, /* x */ + 0x39, 0xF1, 0xBB, 0x75, 0x5F, 0xEF, 0x65, 0xBC, 0x39, 0x1F, + 0x8B, 0x36, 0xF8, 0xF8, 0xEB, 0x73, 0x71, 0xFD, 0x55, 0x8B, + + 0x01, 0x00, 0x6A, 0x08, 0xA4, 0x19, 0x03, 0x35, 0x06, 0x78, /* y */ + 0xE5, 0x85, 0x28, 0xBE, 0xBF, 0x8A, 0x0B, 0xEF, 0xF8, 0x67, + 0xA7, 0xCA, 0x36, 0x71, 0x6F, 0x7E, 0x01, 0xF8, 0x10, 0x52, + + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x13, 0xE9, 0x74, 0xE7, 0x2F, + 0x8A, 0x69, 0x22, 0x03, 0x1D, 0x26, 0x03, 0xCF, 0xE0, 0xD7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} + _EC_SECG_CHAR2_239K1 = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { /* no seed */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + + 0x29, 0xA0, 0xB6, 0xA8, 0x87, 0xA9, 0x83, 0xE9, 0x73, 0x09, /* x */ + 0x88, 0xA6, 0x87, 0x27, 0xA8, 0xB2, 0xD1, 0x26, 0xC4, 0x4C, + 0xC2, 0xCC, 0x7B, 0x2A, 0x65, 0x55, 0x19, 0x30, 0x35, 0xDC, + + 0x76, 0x31, 0x08, 0x04, 0xF1, 0x2E, 0x54, 0x9B, 0xDB, 0x01, /* y */ + 0x1C, 0x10, 0x30, 0x89, 0xE7, 0x35, 0x10, 0xAC, 0xB2, 0x75, + 0xFC, 0x31, 0x2A, 0x5D, 0xC6, 0xB7, 0x65, 0x53, 0xF0, 0xCA, + + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x5A, 0x79, 0xFE, 0xC6, 0x7C, + 0xB6, 0xE9, 0x1F, 0x1C, 0x1D, 0xA8, 0x00, 0xE4, 0x78, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 36 * 6]; +} + _EC_NIST_CHAR2_283K = { + { + NID_X9_62_characteristic_two_field, 0, 36, 4 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x05, 0x03, 0x21, 0x3F, 0x78, 0xCA, 0x44, 0x88, 0x3F, 0x1A, /* x */ + 0x3B, 0x81, 0x62, 0xF1, 0x88, 0xE5, 0x53, 0xCD, 0x26, 0x5F, + 0x23, 0xC1, 0x56, 0x7A, 0x16, 0x87, 0x69, 0x13, 0xB0, 0xC2, + 0xAC, 0x24, 0x58, 0x49, 0x28, 0x36, + 0x01, 0xCC, 0xDA, 0x38, 0x0F, 0x1C, 0x9E, 0x31, 0x8D, 0x90, /* y */ + 0xF9, 0x5D, 0x07, 0xE5, 0x42, 0x6F, 0xE8, 0x7E, 0x45, 0xC0, + 0xE8, 0x18, 0x46, 0x98, 0xE4, 0x59, 0x62, 0x36, 0x4E, 0x34, + 0x11, 0x61, 0x77, 0xDD, 0x22, 0x59, + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xE9, 0xAE, + 0x2E, 0xD0, 0x75, 0x77, 0x26, 0x5D, 0xFF, 0x7F, 0x94, 0x45, + 0x1E, 0x06, 0x1E, 0x16, 0x3C, 0x61 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 36 * 6]; +} + _EC_NIST_CHAR2_283B = { + { + NID_X9_62_characteristic_two_field, 20, 36, 2 + }, + { + 0x77, 0xE2, 0xB0, 0x73, 0x70, 0xEB, 0x0F, 0x83, 0x2A, 0x6D, /* no seed */ + 0xD5, 0xB6, 0x2D, 0xFC, 0x88, 0xCD, 0x06, 0xBB, 0x84, 0xBE, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x02, 0x7B, 0x68, 0x0A, 0xC8, 0xB8, 0x59, 0x6D, 0xA5, 0xA4, /* b */ + 0xAF, 0x8A, 0x19, 0xA0, 0x30, 0x3F, 0xCA, 0x97, 0xFD, 0x76, + 0x45, 0x30, 0x9F, 0xA2, 0xA5, 0x81, 0x48, 0x5A, 0xF6, 0x26, + 0x3E, 0x31, 0x3B, 0x79, 0xA2, 0xF5, + 0x05, 0xF9, 0x39, 0x25, 0x8D, 0xB7, 0xDD, 0x90, 0xE1, 0x93, /* x */ + 0x4F, 0x8C, 0x70, 0xB0, 0xDF, 0xEC, 0x2E, 0xED, 0x25, 0xB8, + 0x55, 0x7E, 0xAC, 0x9C, 0x80, 0xE2, 0xE1, 0x98, 0xF8, 0xCD, + 0xBE, 0xCD, 0x86, 0xB1, 0x20, 0x53, + 0x03, 0x67, 0x68, 0x54, 0xFE, 0x24, 0x14, 0x1C, 0xB9, 0x8F, /* y */ + 0xE6, 0xD4, 0xB2, 0x0D, 0x02, 0xB4, 0x51, 0x6F, 0xF7, 0x02, + 0x35, 0x0E, 0xDD, 0xB0, 0x82, 0x67, 0x79, 0xC8, 0x13, 0xF0, + 0xDF, 0x45, 0xBE, 0x81, 0x12, 0xF4, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xEF, 0x90, + 0x39, 0x96, 0x60, 0xFC, 0x93, 0x8A, 0x90, 0x16, 0x5B, 0x04, + 0x2A, 0x7C, 0xEF, 0xAD, 0xB3, 0x07 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 52 * 6]; +} + _EC_NIST_CHAR2_409K = { + { + NID_X9_62_characteristic_two_field, 0, 52, 4 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x60, 0xF0, 0x5F, 0x65, 0x8F, 0x49, 0xC1, 0xAD, 0x3A, /* x */ + 0xB1, 0x89, 0x0F, 0x71, 0x84, 0x21, 0x0E, 0xFD, 0x09, 0x87, + 0xE3, 0x07, 0xC8, 0x4C, 0x27, 0xAC, 0xCF, 0xB8, 0xF9, 0xF6, + 0x7C, 0xC2, 0xC4, 0x60, 0x18, 0x9E, 0xB5, 0xAA, 0xAA, 0x62, + 0xEE, 0x22, 0x2E, 0xB1, 0xB3, 0x55, 0x40, 0xCF, 0xE9, 0x02, + 0x37, 0x46, + 0x01, 0xE3, 0x69, 0x05, 0x0B, 0x7C, 0x4E, 0x42, 0xAC, 0xBA, /* y */ + 0x1D, 0xAC, 0xBF, 0x04, 0x29, 0x9C, 0x34, 0x60, 0x78, 0x2F, + 0x91, 0x8E, 0xA4, 0x27, 0xE6, 0x32, 0x51, 0x65, 0xE9, 0xEA, + 0x10, 0xE3, 0xDA, 0x5F, 0x6C, 0x42, 0xE9, 0xC5, 0x52, 0x15, + 0xAA, 0x9C, 0xA2, 0x7A, 0x58, 0x63, 0xEC, 0x48, 0xD8, 0xE0, + 0x28, 0x6B, + 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0x5F, 0x83, 0xB2, + 0xD4, 0xEA, 0x20, 0x40, 0x0E, 0xC4, 0x55, 0x7D, 0x5E, 0xD3, + 0xE3, 0xE7, 0xCA, 0x5B, 0x4B, 0x5C, 0x83, 0xB8, 0xE0, 0x1E, + 0x5F, 0xCF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 52 * 6]; +} + _EC_NIST_CHAR2_409B = { + { + NID_X9_62_characteristic_two_field, 20, 52, 2 + }, + { + 0x40, 0x99, 0xB5, 0xA4, 0x57, 0xF9, 0xD6, 0x9F, 0x79, 0x21, /* seed */ + 0x3D, 0x09, 0x4C, 0x4B, 0xCD, 0x4D, 0x42, 0x62, 0x21, 0x0B, + + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x00, 0x21, 0xA5, 0xC2, 0xC8, 0xEE, 0x9F, 0xEB, 0x5C, 0x4B, /* b */ + 0x9A, 0x75, 0x3B, 0x7B, 0x47, 0x6B, 0x7F, 0xD6, 0x42, 0x2E, + 0xF1, 0xF3, 0xDD, 0x67, 0x47, 0x61, 0xFA, 0x99, 0xD6, 0xAC, + 0x27, 0xC8, 0xA9, 0xA1, 0x97, 0xB2, 0x72, 0x82, 0x2F, 0x6C, + 0xD5, 0x7A, 0x55, 0xAA, 0x4F, 0x50, 0xAE, 0x31, 0x7B, 0x13, + 0x54, 0x5F, + 0x01, 0x5D, 0x48, 0x60, 0xD0, 0x88, 0xDD, 0xB3, 0x49, 0x6B, /* x */ + 0x0C, 0x60, 0x64, 0x75, 0x62, 0x60, 0x44, 0x1C, 0xDE, 0x4A, + 0xF1, 0x77, 0x1D, 0x4D, 0xB0, 0x1F, 0xFE, 0x5B, 0x34, 0xE5, + 0x97, 0x03, 0xDC, 0x25, 0x5A, 0x86, 0x8A, 0x11, 0x80, 0x51, + 0x56, 0x03, 0xAE, 0xAB, 0x60, 0x79, 0x4E, 0x54, 0xBB, 0x79, + 0x96, 0xA7, + 0x00, 0x61, 0xB1, 0xCF, 0xAB, 0x6B, 0xE5, 0xF3, 0x2B, 0xBF, /* y */ + 0xA7, 0x83, 0x24, 0xED, 0x10, 0x6A, 0x76, 0x36, 0xB9, 0xC5, + 0xA7, 0xBD, 0x19, 0x8D, 0x01, 0x58, 0xAA, 0x4F, 0x54, 0x88, + 0xD0, 0x8F, 0x38, 0x51, 0x4F, 0x1F, 0xDF, 0x4B, 0x4F, 0x40, + 0xD2, 0x18, 0x1B, 0x36, 0x81, 0xC3, 0x64, 0xBA, 0x02, 0x73, + 0xC7, 0x06, + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xE2, 0xAA, 0xD6, + 0xA6, 0x12, 0xF3, 0x33, 0x07, 0xBE, 0x5F, 0xA4, 0x7C, 0x3C, + 0x9E, 0x05, 0x2F, 0x83, 0x81, 0x64, 0xCD, 0x37, 0xD9, 0xA2, + 0x11, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 72 * 6]; +} + _EC_NIST_CHAR2_571K = { + { + NID_X9_62_characteristic_two_field, 0, 72, 4 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x25, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x02, 0x6E, 0xB7, 0xA8, 0x59, 0x92, 0x3F, 0xBC, 0x82, 0x18, /* x */ + 0x96, 0x31, 0xF8, 0x10, 0x3F, 0xE4, 0xAC, 0x9C, 0xA2, 0x97, + 0x00, 0x12, 0xD5, 0xD4, 0x60, 0x24, 0x80, 0x48, 0x01, 0x84, + 0x1C, 0xA4, 0x43, 0x70, 0x95, 0x84, 0x93, 0xB2, 0x05, 0xE6, + 0x47, 0xDA, 0x30, 0x4D, 0xB4, 0xCE, 0xB0, 0x8C, 0xBB, 0xD1, + 0xBA, 0x39, 0x49, 0x47, 0x76, 0xFB, 0x98, 0x8B, 0x47, 0x17, + 0x4D, 0xCA, 0x88, 0xC7, 0xE2, 0x94, 0x52, 0x83, 0xA0, 0x1C, + 0x89, 0x72, + 0x03, 0x49, 0xDC, 0x80, 0x7F, 0x4F, 0xBF, 0x37, 0x4F, 0x4A, /* y */ + 0xEA, 0xDE, 0x3B, 0xCA, 0x95, 0x31, 0x4D, 0xD5, 0x8C, 0xEC, + 0x9F, 0x30, 0x7A, 0x54, 0xFF, 0xC6, 0x1E, 0xFC, 0x00, 0x6D, + 0x8A, 0x2C, 0x9D, 0x49, 0x79, 0xC0, 0xAC, 0x44, 0xAE, 0xA7, + 0x4F, 0xBE, 0xBB, 0xB9, 0xF7, 0x72, 0xAE, 0xDC, 0xB6, 0x20, + 0xB0, 0x1A, 0x7B, 0xA7, 0xAF, 0x1B, 0x32, 0x04, 0x30, 0xC8, + 0x59, 0x19, 0x84, 0xF6, 0x01, 0xCD, 0x4C, 0x14, 0x3E, 0xF1, + 0xC7, 0xA3, + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x13, 0x18, 0x50, 0xE1, + 0xF1, 0x9A, 0x63, 0xE4, 0xB3, 0x91, 0xA8, 0xDB, 0x91, 0x7F, + 0x41, 0x38, 0xB6, 0x30, 0xD8, 0x4B, 0xE5, 0xD6, 0x39, 0x38, + 0x1E, 0x91, 0xDE, 0xB4, 0x5C, 0xFE, 0x77, 0x8F, 0x63, 0x7C, + 0x10, 0x01 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 72 * 6]; +} + _EC_NIST_CHAR2_571B = { + { + NID_X9_62_characteristic_two_field, 20, 72, 2 + }, + { + 0x2A, 0xA0, 0x58, 0xF7, 0x3A, 0x0E, 0x33, 0xAB, 0x48, 0x6B, /* seed */ + 0x0F, 0x61, 0x04, 0x10, 0xC5, 0x3A, 0x7F, 0x13, 0x23, 0x10, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0x25, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x01, + 0x02, 0xF4, 0x0E, 0x7E, 0x22, 0x21, 0xF2, 0x95, 0xDE, 0x29, /* b */ + 0x71, 0x17, 0xB7, 0xF3, 0xD6, 0x2F, 0x5C, 0x6A, 0x97, 0xFF, + 0xCB, 0x8C, 0xEF, 0xF1, 0xCD, 0x6B, 0xA8, 0xCE, 0x4A, 0x9A, + 0x18, 0xAD, 0x84, 0xFF, 0xAB, 0xBD, 0x8E, 0xFA, 0x59, 0x33, + 0x2B, 0xE7, 0xAD, 0x67, 0x56, 0xA6, 0x6E, 0x29, 0x4A, 0xFD, + 0x18, 0x5A, 0x78, 0xFF, 0x12, 0xAA, 0x52, 0x0E, 0x4D, 0xE7, + 0x39, 0xBA, 0xCA, 0x0C, 0x7F, 0xFE, 0xFF, 0x7F, 0x29, 0x55, + 0x72, 0x7A, + 0x03, 0x03, 0x00, 0x1D, 0x34, 0xB8, 0x56, 0x29, 0x6C, 0x16, /* x */ + 0xC0, 0xD4, 0x0D, 0x3C, 0xD7, 0x75, 0x0A, 0x93, 0xD1, 0xD2, + 0x95, 0x5F, 0xA8, 0x0A, 0xA5, 0xF4, 0x0F, 0xC8, 0xDB, 0x7B, + 0x2A, 0xBD, 0xBD, 0xE5, 0x39, 0x50, 0xF4, 0xC0, 0xD2, 0x93, + 0xCD, 0xD7, 0x11, 0xA3, 0x5B, 0x67, 0xFB, 0x14, 0x99, 0xAE, + 0x60, 0x03, 0x86, 0x14, 0xF1, 0x39, 0x4A, 0xBF, 0xA3, 0xB4, + 0xC8, 0x50, 0xD9, 0x27, 0xE1, 0xE7, 0x76, 0x9C, 0x8E, 0xEC, + 0x2D, 0x19, + 0x03, 0x7B, 0xF2, 0x73, 0x42, 0xDA, 0x63, 0x9B, 0x6D, 0xCC, /* y */ + 0xFF, 0xFE, 0xB7, 0x3D, 0x69, 0xD7, 0x8C, 0x6C, 0x27, 0xA6, + 0x00, 0x9C, 0xBB, 0xCA, 0x19, 0x80, 0xF8, 0x53, 0x39, 0x21, + 0xE8, 0xA6, 0x84, 0x42, 0x3E, 0x43, 0xBA, 0xB0, 0x8A, 0x57, + 0x62, 0x91, 0xAF, 0x8F, 0x46, 0x1B, 0xB2, 0xA8, 0xB3, 0x53, + 0x1D, 0x2F, 0x04, 0x85, 0xC1, 0x9B, 0x16, 0xE2, 0xF1, 0x51, + 0x6E, 0x23, 0xDD, 0x3C, 0x1A, 0x48, 0x27, 0xAF, 0x1B, 0x8A, + 0xC1, 0x5B, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xE6, 0x61, 0xCE, 0x18, + 0xFF, 0x55, 0x98, 0x73, 0x08, 0x05, 0x9B, 0x18, 0x68, 0x23, + 0x85, 0x1E, 0xC7, 0xDD, 0x9C, 0xA1, 0x16, 0x1D, 0xE9, 0x3D, + 0x51, 0x74, 0xD6, 0x6E, 0x83, 0x82, 0xE9, 0xBB, 0x2F, 0xE8, + 0x4E, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V1 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0xD2, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, + 0xF4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x54, /* seed */ + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x07, 0x25, 0x46, 0xB5, 0x43, 0x52, 0x34, 0xA4, 0x22, 0xE0, /* a */ + 0x78, 0x96, 0x75, 0xF4, 0x32, 0xC8, 0x94, 0x35, 0xDE, 0x52, + 0x42, + 0x00, 0xC9, 0x51, 0x7D, 0x06, 0xD5, 0x24, 0x0D, 0x3C, 0xFF, /* b */ + 0x38, 0xC7, 0x4B, 0x20, 0xB6, 0xCD, 0x4D, 0x6F, 0x9D, 0xD4, + 0xD9, + 0x07, 0xAF, 0x69, 0x98, 0x95, 0x46, 0x10, 0x3D, 0x79, 0x32, /* x */ + 0x9F, 0xCC, 0x3D, 0x74, 0x88, 0x0F, 0x33, 0xBB, 0xE8, 0x03, + 0xCB, + 0x01, 0xEC, 0x23, 0x21, 0x1B, 0x59, 0x66, 0xAD, 0xEA, 0x1D, /* y */ + 0x3F, 0x87, 0xF7, 0xEA, 0x58, 0x48, 0xAE, 0xF0, 0xB7, 0xCA, + 0x9F, + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x01, 0xE6, 0x0F, 0xC8, 0x82, 0x1C, 0xC7, 0x4D, 0xAE, 0xAF, + 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V2 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0x53, 0x81, 0x4C, 0x05, 0x0D, 0x44, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0x0C, 0xA4, 0xE2, 0x9F, 0xFD, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x01, 0x08, 0xB3, 0x9E, 0x77, 0xC4, 0xB1, 0x08, 0xBE, 0xD9, /* a */ + 0x81, 0xED, 0x0E, 0x89, 0x0E, 0x11, 0x7C, 0x51, 0x1C, 0xF0, + 0x72, + 0x06, 0x67, 0xAC, 0xEB, 0x38, 0xAF, 0x4E, 0x48, 0x8C, 0x40, /* b */ + 0x74, 0x33, 0xFF, 0xAE, 0x4F, 0x1C, 0x81, 0x16, 0x38, 0xDF, + 0x20, + 0x00, 0x24, 0x26, 0x6E, 0x4E, 0xB5, 0x10, 0x6D, 0x0A, 0x96, /* x */ + 0x4D, 0x92, 0xC4, 0x86, 0x0E, 0x26, 0x71, 0xDB, 0x9B, 0x6C, + 0xC5, + 0x07, 0x9F, 0x68, 0x4D, 0xDF, 0x66, 0x84, 0xC5, 0xCD, 0x25, /* y */ + 0x8B, 0x38, 0x90, 0x02, 0x1B, 0x23, 0x86, 0xDF, 0xD1, 0x9F, + 0xC5, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFD, 0xF6, 0x4D, 0xE1, 0x15, 0x1A, 0xDB, 0xB7, 0x8F, 0x10, + 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} + _EC_X9_62_CHAR2_163V3 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + 0x50, 0xCB, 0xF1, 0xD9, 0x5C, 0xA9, 0x4D, 0x69, 0x6E, 0x67, /* seed */ + 0x68, 0x75, 0x61, 0x51, 0x75, 0xF1, 0x6A, 0x36, 0xA3, 0xB8, + + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x07, + 0x07, 0xA5, 0x26, 0xC6, 0x3D, 0x3E, 0x25, 0xA2, 0x56, 0xA0, /* a */ + 0x07, 0x69, 0x9F, 0x54, 0x47, 0xE3, 0x2A, 0xE4, 0x56, 0xB5, + 0x0E, + 0x03, 0xF7, 0x06, 0x17, 0x98, 0xEB, 0x99, 0xE2, 0x38, 0xFD, /* b */ + 0x6F, 0x1B, 0xF9, 0x5B, 0x48, 0xFE, 0xEB, 0x48, 0x54, 0x25, + 0x2B, + 0x02, 0xF9, 0xF8, 0x7B, 0x7C, 0x57, 0x4D, 0x0B, 0xDE, 0xCF, /* x */ + 0x8A, 0x22, 0xE6, 0x52, 0x47, 0x75, 0xF9, 0x8C, 0xDE, 0xBD, + 0xCB, + 0x05, 0xB9, 0x35, 0x59, 0x0C, 0x15, 0x5E, 0x17, 0xEA, 0x48, /* y */ + 0xEB, 0x3F, 0xF3, 0x71, 0x8B, 0x89, 0x3D, 0xF5, 0x9A, 0x05, + 0xD0, + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFE, 0x1A, 0xEE, 0x14, 0x0F, 0x11, 0x0A, 0xFF, 0x96, 0x13, + 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 23 * 6]; +} + _EC_X9_62_CHAR2_176V1 = { + { + NID_X9_62_characteristic_two_field, 0, 23, 0xFF6E + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, + 0x00, 0x00, 0x07, + 0x00, 0xE4, 0xE6, 0xDB, 0x29, 0x95, 0x06, 0x5C, 0x40, 0x7D, /* a */ + 0x9D, 0x39, 0xB8, 0xD0, 0x96, 0x7B, 0x96, 0x70, 0x4B, 0xA8, + 0xE9, 0xC9, 0x0B, + 0x00, 0x5D, 0xDA, 0x47, 0x0A, 0xBE, 0x64, 0x14, 0xDE, 0x8E, /* b */ + 0xC1, 0x33, 0xAE, 0x28, 0xE9, 0xBB, 0xD7, 0xFC, 0xEC, 0x0A, + 0xE0, 0xFF, 0xF2, + 0x00, 0x8D, 0x16, 0xC2, 0x86, 0x67, 0x98, 0xB6, 0x00, 0xF9, /* x */ + 0xF0, 0x8B, 0xB4, 0xA8, 0xE8, 0x60, 0xF3, 0x29, 0x8C, 0xE0, + 0x4A, 0x57, 0x98, + 0x00, 0x6F, 0xA4, 0x53, 0x9C, 0x2D, 0xAD, 0xDD, 0xD6, 0xBA, /* y */ + 0xB5, 0x16, 0x7D, 0x61, 0xB4, 0x36, 0xE1, 0xD9, 0x2B, 0xB1, + 0x6A, 0x56, 0x2C, + 0x00, 0x00, 0x01, 0x00, 0x92, 0x53, 0x73, 0x97, 0xEC, 0xA4, /* order */ + 0xF6, 0x14, 0x57, 0x99, 0xD6, 0x2B, 0x0A, 0x19, 0xCE, 0x06, + 0xFE, 0x26, 0xAD + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V1 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 2 + }, + { + 0x4E, 0x13, 0xCA, 0x54, 0x27, 0x44, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x55, 0x2F, 0x27, 0x9A, 0x8C, 0x84, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x28, 0x66, 0x53, 0x7B, 0x67, 0x67, 0x52, 0x63, 0x6A, 0x68, /* a */ + 0xF5, 0x65, 0x54, 0xE1, 0x26, 0x40, 0x27, 0x6B, 0x64, 0x9E, + 0xF7, 0x52, 0x62, 0x67, + 0x2E, 0x45, 0xEF, 0x57, 0x1F, 0x00, 0x78, 0x6F, 0x67, 0xB0, /* b */ + 0x08, 0x1B, 0x94, 0x95, 0xA3, 0xD9, 0x54, 0x62, 0xF5, 0xDE, + 0x0A, 0xA1, 0x85, 0xEC, + 0x36, 0xB3, 0xDA, 0xF8, 0xA2, 0x32, 0x06, 0xF9, 0xC4, 0xF2, /* x */ + 0x99, 0xD7, 0xB2, 0x1A, 0x9C, 0x36, 0x91, 0x37, 0xF2, 0xC8, + 0x4A, 0xE1, 0xAA, 0x0D, + 0x76, 0x5B, 0xE7, 0x34, 0x33, 0xB3, 0xF9, 0x5E, 0x33, 0x29, /* y */ + 0x32, 0xE7, 0x0E, 0xA2, 0x45, 0xCA, 0x24, 0x18, 0xEA, 0x0E, + 0xF9, 0x80, 0x18, 0xFB, + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x04, 0xA2, 0x0E, 0x90, 0xC3, 0x90, 0x67, 0xC8, + 0x93, 0xBB, 0xB9, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V2 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 4 + }, + { + 0x08, 0x71, 0xEF, 0x2F, 0xEF, 0x24, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0xBE, 0xE0, 0xD9, 0x5C, 0x15, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x40, 0x10, 0x28, 0x77, 0x4D, 0x77, 0x77, 0xC7, 0xB7, 0x66, /* a */ + 0x6D, 0x13, 0x66, 0xEA, 0x43, 0x20, 0x71, 0x27, 0x4F, 0x89, + 0xFF, 0x01, 0xE7, 0x18, + 0x06, 0x20, 0x04, 0x8D, 0x28, 0xBC, 0xBD, 0x03, 0xB6, 0x24, /* b */ + 0x9C, 0x99, 0x18, 0x2B, 0x7C, 0x8C, 0xD1, 0x97, 0x00, 0xC3, + 0x62, 0xC4, 0x6A, 0x01, + 0x38, 0x09, 0xB2, 0xB7, 0xCC, 0x1B, 0x28, 0xCC, 0x5A, 0x87, /* x */ + 0x92, 0x6A, 0xAD, 0x83, 0xFD, 0x28, 0x78, 0x9E, 0x81, 0xE2, + 0xC9, 0xE3, 0xBF, 0x10, + 0x17, 0x43, 0x43, 0x86, 0x62, 0x6D, 0x14, 0xF3, 0xDB, 0xF0, /* y */ + 0x17, 0x60, 0xD9, 0x21, 0x3A, 0x3E, 0x1C, 0xF3, 0x7A, 0xEC, + 0x43, 0x7D, 0x66, 0x8A, + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x50, 0x50, 0x8C, 0xB8, 0x9F, 0x65, 0x28, 0x24, + 0xE0, 0x6B, 0x81, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} + _EC_X9_62_CHAR2_191V3 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 6 + }, + { + 0xE0, 0x53, 0x51, 0x2D, 0xC6, 0x84, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x50, 0x67, 0xAE, 0x78, 0x6D, 0x1F, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, 0x01, + 0x6C, 0x01, 0x07, 0x47, 0x56, 0x09, 0x91, 0x22, 0x22, 0x10, /* a */ + 0x56, 0x91, 0x1C, 0x77, 0xD7, 0x7E, 0x77, 0xA7, 0x77, 0xE7, + 0xE7, 0xE7, 0x7F, 0xCB, + 0x71, 0xFE, 0x1A, 0xF9, 0x26, 0xCF, 0x84, 0x79, 0x89, 0xEF, /* b */ + 0xEF, 0x8D, 0xB4, 0x59, 0xF6, 0x63, 0x94, 0xD9, 0x0F, 0x32, + 0xAD, 0x3F, 0x15, 0xE8, + 0x37, 0x5D, 0x4C, 0xE2, 0x4F, 0xDE, 0x43, 0x44, 0x89, 0xDE, /* x */ + 0x87, 0x46, 0xE7, 0x17, 0x86, 0x01, 0x50, 0x09, 0xE6, 0x6E, + 0x38, 0xA9, 0x26, 0xDD, + 0x54, 0x5A, 0x39, 0x17, 0x61, 0x96, 0x57, 0x5D, 0x98, 0x59, /* y */ + 0x99, 0x36, 0x6E, 0x6A, 0xD3, 0x4C, 0xE0, 0xA7, 0x7C, 0xD7, + 0x12, 0x7B, 0x06, 0xBE, + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, /* order */ + 0x55, 0x55, 0x61, 0x0C, 0x0B, 0x19, 0x68, 0x12, 0xBF, 0xB6, + 0x28, 0x8A, 0x3E, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 27 * 6]; +} + _EC_X9_62_CHAR2_208W1 = { + { + NID_X9_62_characteristic_two_field, 0, 27, 0xFE48 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0xC8, 0x61, 0x9E, 0xD4, 0x5A, 0x62, 0xE6, 0x21, 0x2E, /* b */ + 0x11, 0x60, 0x34, 0x9E, 0x2B, 0xFA, 0x84, 0x44, 0x39, 0xFA, + 0xFC, 0x2A, 0x3F, 0xD1, 0x63, 0x8F, 0x9E, + 0x00, 0x89, 0xFD, 0xFB, 0xE4, 0xAB, 0xE1, 0x93, 0xDF, 0x95, /* x */ + 0x59, 0xEC, 0xF0, 0x7A, 0xC0, 0xCE, 0x78, 0x55, 0x4E, 0x27, + 0x84, 0xEB, 0x8C, 0x1E, 0xD1, 0xA5, 0x7A, + 0x00, 0x0F, 0x55, 0xB5, 0x1A, 0x06, 0xE7, 0x8E, 0x9A, 0xC3, /* y */ + 0x8A, 0x03, 0x5F, 0xF5, 0x20, 0xD8, 0xB0, 0x17, 0x81, 0xBE, + 0xB1, 0xA6, 0xBB, 0x08, 0x61, 0x7D, 0xE3, + 0x00, 0x00, 0x01, 0x01, 0xBA, 0xF9, 0x5C, 0x97, 0x23, 0xC5, /* order */ + 0x7B, 0x6C, 0x21, 0xDA, 0x2E, 0xFF, 0x2D, 0x5E, 0xD5, 0x88, + 0xBD, 0xD5, 0x71, 0x7E, 0x21, 0x2F, 0x9D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V1 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 4 + }, + { + 0xD3, 0x4B, 0x9A, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0xCA, 0x71, 0xB9, 0x20, 0xBF, 0xEF, 0xB0, 0x5D, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x32, 0x01, 0x08, 0x57, 0x07, 0x7C, 0x54, 0x31, 0x12, 0x3A, /* a */ + 0x46, 0xB8, 0x08, 0x90, 0x67, 0x56, 0xF5, 0x43, 0x42, 0x3E, + 0x8D, 0x27, 0x87, 0x75, 0x78, 0x12, 0x57, 0x78, 0xAC, 0x76, + + 0x79, 0x04, 0x08, 0xF2, 0xEE, 0xDA, 0xF3, 0x92, 0xB0, 0x12, /* b */ + 0xED, 0xEF, 0xB3, 0x39, 0x2F, 0x30, 0xF4, 0x32, 0x7C, 0x0C, + 0xA3, 0xF3, 0x1F, 0xC3, 0x83, 0xC4, 0x22, 0xAA, 0x8C, 0x16, + + 0x57, 0x92, 0x70, 0x98, 0xFA, 0x93, 0x2E, 0x7C, 0x0A, 0x96, /* x */ + 0xD3, 0xFD, 0x5B, 0x70, 0x6E, 0xF7, 0xE5, 0xF5, 0xC1, 0x56, + 0xE1, 0x6B, 0x7E, 0x7C, 0x86, 0x03, 0x85, 0x52, 0xE9, 0x1D, + + 0x61, 0xD8, 0xEE, 0x50, 0x77, 0xC3, 0x3F, 0xEC, 0xF6, 0xF1, /* y */ + 0xA1, 0x6B, 0x26, 0x8D, 0xE4, 0x69, 0xC3, 0xC7, 0x74, 0x4E, + 0xA9, 0xA9, 0x71, 0x64, 0x9F, 0xC7, 0xA9, 0x61, 0x63, 0x05, + + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* order */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x0F, 0x4D, 0x42, 0xFF, 0xE1, + 0x49, 0x2A, 0x49, 0x93, 0xF1, 0xCA, 0xD6, 0x66, 0xE4, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V2 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 6 + }, + { + 0x2A, 0xA6, 0x98, 0x2F, 0xDF, 0xA4, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x5D, 0x26, 0x67, 0x27, 0x27, 0x7D, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x42, 0x30, 0x01, 0x77, 0x57, 0xA7, 0x67, 0xFA, 0xE4, 0x23, /* a */ + 0x98, 0x56, 0x9B, 0x74, 0x63, 0x25, 0xD4, 0x53, 0x13, 0xAF, + 0x07, 0x66, 0x26, 0x64, 0x79, 0xB7, 0x56, 0x54, 0xE6, 0x5F, + + 0x50, 0x37, 0xEA, 0x65, 0x41, 0x96, 0xCF, 0xF0, 0xCD, 0x82, /* b */ + 0xB2, 0xC1, 0x4A, 0x2F, 0xCF, 0x2E, 0x3F, 0xF8, 0x77, 0x52, + 0x85, 0xB5, 0x45, 0x72, 0x2F, 0x03, 0xEA, 0xCD, 0xB7, 0x4B, + + 0x28, 0xF9, 0xD0, 0x4E, 0x90, 0x00, 0x69, 0xC8, 0xDC, 0x47, /* x */ + 0xA0, 0x85, 0x34, 0xFE, 0x76, 0xD2, 0xB9, 0x00, 0xB7, 0xD7, + 0xEF, 0x31, 0xF5, 0x70, 0x9F, 0x20, 0x0C, 0x4C, 0xA2, 0x05, + + 0x56, 0x67, 0x33, 0x4C, 0x45, 0xAF, 0xF3, 0xB5, 0xA0, 0x3B, /* y */ + 0xAD, 0x9D, 0xD7, 0x5E, 0x2C, 0x71, 0xA9, 0x93, 0x62, 0x56, + 0x7D, 0x54, 0x53, 0xF7, 0xFA, 0x6E, 0x22, 0x7E, 0xC8, 0x33, + + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, /* order */ + 0x55, 0x55, 0x55, 0x55, 0x55, 0x3C, 0x6F, 0x28, 0x85, 0x25, + 0x9C, 0x31, 0xE3, 0xFC, 0xDF, 0x15, 0x46, 0x24, 0x52, 0x2D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} + _EC_X9_62_CHAR2_239V3 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 0xA + }, + { + 0x9E, 0x07, 0x6F, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, /* seed */ + 0x51, 0x75, 0xE1, 0x1E, 0x9F, 0xDD, 0x77, 0xF9, 0x20, 0x41, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + + 0x01, 0x23, 0x87, 0x74, 0x66, 0x6A, 0x67, 0x76, 0x6D, 0x66, /* a */ + 0x76, 0xF7, 0x78, 0xE6, 0x76, 0xB6, 0x69, 0x99, 0x17, 0x66, + 0x66, 0xE6, 0x87, 0x66, 0x6D, 0x87, 0x66, 0xC6, 0x6A, 0x9F, + + 0x6A, 0x94, 0x19, 0x77, 0xBA, 0x9F, 0x6A, 0x43, 0x51, 0x99, /* b */ + 0xAC, 0xFC, 0x51, 0x06, 0x7E, 0xD5, 0x87, 0xF5, 0x19, 0xC5, + 0xEC, 0xB5, 0x41, 0xB8, 0xE4, 0x41, 0x11, 0xDE, 0x1D, 0x40, + + 0x70, 0xF6, 0xE9, 0xD0, 0x4D, 0x28, 0x9C, 0x4E, 0x89, 0x91, /* x */ + 0x3C, 0xE3, 0x53, 0x0B, 0xFD, 0xE9, 0x03, 0x97, 0x7D, 0x42, + 0xB1, 0x46, 0xD5, 0x39, 0xBF, 0x1B, 0xDE, 0x4E, 0x9C, 0x92, + + 0x2E, 0x5A, 0x0E, 0xAF, 0x6E, 0x5E, 0x13, 0x05, 0xB9, 0x00, /* y */ + 0x4D, 0xCE, 0x5C, 0x0E, 0xD7, 0xFE, 0x59, 0xA3, 0x56, 0x08, + 0xF3, 0x38, 0x37, 0xC8, 0x16, 0xD8, 0x0B, 0x79, 0xF4, 0x61, + + 0x0C, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, /* order */ + 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xAC, 0x49, 0x12, 0xD2, 0xD9, + 0xDF, 0x90, 0x3E, 0xF9, 0x88, 0x8B, 0x8A, 0x0E, 0x4C, 0xFF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 35 * 6]; +} + _EC_X9_62_CHAR2_272W1 = { + { + NID_X9_62_characteristic_two_field, 0, 35, 0xFF06 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x0B, + 0x00, 0x91, 0xA0, 0x91, 0xF0, 0x3B, 0x5F, 0xBA, 0x4A, 0xB2, /* a */ + 0xCC, 0xF4, 0x9C, 0x4E, 0xDD, 0x22, 0x0F, 0xB0, 0x28, 0x71, + 0x2D, 0x42, 0xBE, 0x75, 0x2B, 0x2C, 0x40, 0x09, 0x4D, 0xBA, + 0xCD, 0xB5, 0x86, 0xFB, 0x20, + 0x00, 0x71, 0x67, 0xEF, 0xC9, 0x2B, 0xB2, 0xE3, 0xCE, 0x7C, /* b */ + 0x8A, 0xAA, 0xFF, 0x34, 0xE1, 0x2A, 0x9C, 0x55, 0x70, 0x03, + 0xD7, 0xC7, 0x3A, 0x6F, 0xAF, 0x00, 0x3F, 0x99, 0xF6, 0xCC, + 0x84, 0x82, 0xE5, 0x40, 0xF7, + 0x00, 0x61, 0x08, 0xBA, 0xBB, 0x2C, 0xEE, 0xBC, 0xF7, 0x87, /* x */ + 0x05, 0x8A, 0x05, 0x6C, 0xBE, 0x0C, 0xFE, 0x62, 0x2D, 0x77, + 0x23, 0xA2, 0x89, 0xE0, 0x8A, 0x07, 0xAE, 0x13, 0xEF, 0x0D, + 0x10, 0xD1, 0x71, 0xDD, 0x8D, + 0x00, 0x10, 0xC7, 0x69, 0x57, 0x16, 0x85, 0x1E, 0xEF, 0x6B, /* y */ + 0xA7, 0xF6, 0x87, 0x2E, 0x61, 0x42, 0xFB, 0xD2, 0x41, 0xB8, + 0x30, 0xFF, 0x5E, 0xFC, 0xAC, 0xEC, 0xCA, 0xB0, 0x5E, 0x02, + 0x00, 0x5D, 0xDE, 0x9D, 0x23, + 0x00, 0x00, 0x01, 0x00, 0xFA, 0xF5, 0x13, 0x54, 0xE0, 0xE3, /* order */ + 0x9E, 0x48, 0x92, 0xDF, 0x6E, 0x31, 0x9C, 0x72, 0xC8, 0x16, + 0x16, 0x03, 0xFA, 0x45, 0xAA, 0x7B, 0x99, 0x8A, 0x16, 0x7B, + 0x8F, 0x1E, 0x62, 0x95, 0x21 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 39 * 6]; +} + _EC_X9_62_CHAR2_304W1 = { + { + NID_X9_62_characteristic_two_field, 0, 39, 0xFE2E + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x07, + 0x00, 0xFD, 0x0D, 0x69, 0x31, 0x49, 0xA1, 0x18, 0xF6, 0x51, /* a */ + 0xE6, 0xDC, 0xE6, 0x80, 0x20, 0x85, 0x37, 0x7E, 0x5F, 0x88, + 0x2D, 0x1B, 0x51, 0x0B, 0x44, 0x16, 0x00, 0x74, 0xC1, 0x28, + 0x80, 0x78, 0x36, 0x5A, 0x03, 0x96, 0xC8, 0xE6, 0x81, + 0x00, 0xBD, 0xDB, 0x97, 0xE5, 0x55, 0xA5, 0x0A, 0x90, 0x8E, /* b */ + 0x43, 0xB0, 0x1C, 0x79, 0x8E, 0xA5, 0xDA, 0xA6, 0x78, 0x8F, + 0x1E, 0xA2, 0x79, 0x4E, 0xFC, 0xF5, 0x71, 0x66, 0xB8, 0xC1, + 0x40, 0x39, 0x60, 0x1E, 0x55, 0x82, 0x73, 0x40, 0xBE, + 0x00, 0x19, 0x7B, 0x07, 0x84, 0x5E, 0x9B, 0xE2, 0xD9, 0x6A, /* x */ + 0xDB, 0x0F, 0x5F, 0x3C, 0x7F, 0x2C, 0xFF, 0xBD, 0x7A, 0x3E, + 0xB8, 0xB6, 0xFE, 0xC3, 0x5C, 0x7F, 0xD6, 0x7F, 0x26, 0xDD, + 0xF6, 0x28, 0x5A, 0x64, 0x4F, 0x74, 0x0A, 0x26, 0x14, + 0x00, 0xE1, 0x9F, 0xBE, 0xB7, 0x6E, 0x0D, 0xA1, 0x71, 0x51, /* y */ + 0x7E, 0xCF, 0x40, 0x1B, 0x50, 0x28, 0x9B, 0xF0, 0x14, 0x10, + 0x32, 0x88, 0x52, 0x7A, 0x9B, 0x41, 0x6A, 0x10, 0x5E, 0x80, + 0x26, 0x0B, 0x54, 0x9F, 0xDC, 0x1B, 0x92, 0xC0, 0x3B, + 0x00, 0x00, 0x01, 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, /* order */ + 0x80, 0x01, 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, 0x80, + 0x01, 0x02, 0x2D, 0x5C, 0x91, 0xDD, 0x17, 0x3F, 0x8F, 0xB5, + 0x61, 0xDA, 0x68, 0x99, 0x16, 0x44, 0x43, 0x05, 0x1D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 45 * 6]; +} + _EC_X9_62_CHAR2_359V1 = { + { + NID_X9_62_characteristic_two_field, 20, 45, 0x4C + }, + { + 0x2B, 0x35, 0x49, 0x20, 0xB7, 0x24, 0xD6, 0x96, 0xE6, 0x76, /* seed */ + 0x87, 0x56, 0x15, 0x17, 0x58, 0x5B, 0xA1, 0x33, 0x2D, 0xC6, + + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x56, 0x67, 0x67, 0x6A, 0x65, 0x4B, 0x20, 0x75, 0x4F, 0x35, /* a */ + 0x6E, 0xA9, 0x20, 0x17, 0xD9, 0x46, 0x56, 0x7C, 0x46, 0x67, + 0x55, 0x56, 0xF1, 0x95, 0x56, 0xA0, 0x46, 0x16, 0xB5, 0x67, + 0xD2, 0x23, 0xA5, 0xE0, 0x56, 0x56, 0xFB, 0x54, 0x90, 0x16, + 0xA9, 0x66, 0x56, 0xA5, 0x57, + 0x24, 0x72, 0xE2, 0xD0, 0x19, 0x7C, 0x49, 0x36, 0x3F, 0x1F, /* b */ + 0xE7, 0xF5, 0xB6, 0xDB, 0x07, 0x5D, 0x52, 0xB6, 0x94, 0x7D, + 0x13, 0x5D, 0x8C, 0xA4, 0x45, 0x80, 0x5D, 0x39, 0xBC, 0x34, + 0x56, 0x26, 0x08, 0x96, 0x87, 0x74, 0x2B, 0x63, 0x29, 0xE7, + 0x06, 0x80, 0x23, 0x19, 0x88, + 0x3C, 0x25, 0x8E, 0xF3, 0x04, 0x77, 0x67, 0xE7, 0xED, 0xE0, /* x */ + 0xF1, 0xFD, 0xAA, 0x79, 0xDA, 0xEE, 0x38, 0x41, 0x36, 0x6A, + 0x13, 0x2E, 0x16, 0x3A, 0xCE, 0xD4, 0xED, 0x24, 0x01, 0xDF, + 0x9C, 0x6B, 0xDC, 0xDE, 0x98, 0xE8, 0xE7, 0x07, 0xC0, 0x7A, + 0x22, 0x39, 0xB1, 0xB0, 0x97, + 0x53, 0xD7, 0xE0, 0x85, 0x29, 0x54, 0x70, 0x48, 0x12, 0x1E, /* y */ + 0x9C, 0x95, 0xF3, 0x79, 0x1D, 0xD8, 0x04, 0x96, 0x39, 0x48, + 0xF3, 0x4F, 0xAE, 0x7B, 0xF4, 0x4E, 0xA8, 0x23, 0x65, 0xDC, + 0x78, 0x68, 0xFE, 0x57, 0xE4, 0xAE, 0x2D, 0xE2, 0x11, 0x30, + 0x5A, 0x40, 0x71, 0x04, 0xBD, + 0x01, 0xAF, 0x28, 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, /* order */ + 0xAF, 0x28, 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, 0xAF, + 0x28, 0x6B, 0xC9, 0xFB, 0x8F, 0x6B, 0x85, 0xC5, 0x56, 0x89, + 0x2C, 0x20, 0xA7, 0xEB, 0x96, 0x4F, 0xE7, 0x71, 0x9E, 0x74, + 0xF4, 0x90, 0x75, 0x8D, 0x3B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 47 * 6]; +} + _EC_X9_62_CHAR2_368W1 = { + { + NID_X9_62_characteristic_two_field, 0, 47, 0xFF70 + }, + { /* no seed */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x20, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + 0x00, 0xE0, 0xD2, 0xEE, 0x25, 0x09, 0x52, 0x06, 0xF5, 0xE2, /* a */ + 0xA4, 0xF9, 0xED, 0x22, 0x9F, 0x1F, 0x25, 0x6E, 0x79, 0xA0, + 0xE2, 0xB4, 0x55, 0x97, 0x0D, 0x8D, 0x0D, 0x86, 0x5B, 0xD9, + 0x47, 0x78, 0xC5, 0x76, 0xD6, 0x2F, 0x0A, 0xB7, 0x51, 0x9C, + 0xCD, 0x2A, 0x1A, 0x90, 0x6A, 0xE3, 0x0D, + 0x00, 0xFC, 0x12, 0x17, 0xD4, 0x32, 0x0A, 0x90, 0x45, 0x2C, /* b */ + 0x76, 0x0A, 0x58, 0xED, 0xCD, 0x30, 0xC8, 0xDD, 0x06, 0x9B, + 0x3C, 0x34, 0x45, 0x38, 0x37, 0xA3, 0x4E, 0xD5, 0x0C, 0xB5, + 0x49, 0x17, 0xE1, 0xC2, 0x11, 0x2D, 0x84, 0xD1, 0x64, 0xF4, + 0x44, 0xF8, 0xF7, 0x47, 0x86, 0x04, 0x6A, + 0x00, 0x10, 0x85, 0xE2, 0x75, 0x53, 0x81, 0xDC, 0xCC, 0xE3, /* x */ + 0xC1, 0x55, 0x7A, 0xFA, 0x10, 0xC2, 0xF0, 0xC0, 0xC2, 0x82, + 0x56, 0x46, 0xC5, 0xB3, 0x4A, 0x39, 0x4C, 0xBC, 0xFA, 0x8B, + 0xC1, 0x6B, 0x22, 0xE7, 0xE7, 0x89, 0xE9, 0x27, 0xBE, 0x21, + 0x6F, 0x02, 0xE1, 0xFB, 0x13, 0x6A, 0x5F, + 0x00, 0x7B, 0x3E, 0xB1, 0xBD, 0xDC, 0xBA, 0x62, 0xD5, 0xD8, /* y */ + 0xB2, 0x05, 0x9B, 0x52, 0x57, 0x97, 0xFC, 0x73, 0x82, 0x2C, + 0x59, 0x05, 0x9C, 0x62, 0x3A, 0x45, 0xFF, 0x38, 0x43, 0xCE, + 0xE8, 0xF8, 0x7C, 0xD1, 0x85, 0x5A, 0xDA, 0xA8, 0x1E, 0x2A, + 0x07, 0x50, 0xB8, 0x0F, 0xDA, 0x23, 0x10, + 0x00, 0x00, 0x01, 0x00, 0x90, 0x51, 0x2D, 0xA9, 0xAF, 0x72, /* order */ + 0xB0, 0x83, 0x49, 0xD9, 0x8A, 0x5D, 0xD4, 0xC7, 0xB0, 0x53, + 0x2E, 0xCA, 0x51, 0xCE, 0x03, 0xE2, 0xD1, 0x0F, 0x3B, 0x7A, + 0xC5, 0x79, 0xBD, 0x87, 0xE9, 0x09, 0xAE, 0x40, 0xA6, 0xF1, + 0x31, 0xE9, 0xCF, 0xCE, 0x5B, 0xD9, 0x67 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 54 * 6]; +} + _EC_X9_62_CHAR2_431R1 = { + { + NID_X9_62_characteristic_two_field, 0, 54, 0x2760 + }, + { /* no seed */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + 0x1A, 0x82, 0x7E, 0xF0, 0x0D, 0xD6, 0xFC, 0x0E, 0x23, 0x4C, /* a */ + 0xAF, 0x04, 0x6C, 0x6A, 0x5D, 0x8A, 0x85, 0x39, 0x5B, 0x23, + 0x6C, 0xC4, 0xAD, 0x2C, 0xF3, 0x2A, 0x0C, 0xAD, 0xBD, 0xC9, + 0xDD, 0xF6, 0x20, 0xB0, 0xEB, 0x99, 0x06, 0xD0, 0x95, 0x7F, + 0x6C, 0x6F, 0xEA, 0xCD, 0x61, 0x54, 0x68, 0xDF, 0x10, 0x4D, + 0xE2, 0x96, 0xCD, 0x8F, + 0x10, 0xD9, 0xB4, 0xA3, 0xD9, 0x04, 0x7D, 0x8B, 0x15, 0x43, /* b */ + 0x59, 0xAB, 0xFB, 0x1B, 0x7F, 0x54, 0x85, 0xB0, 0x4C, 0xEB, + 0x86, 0x82, 0x37, 0xDD, 0xC9, 0xDE, 0xDA, 0x98, 0x2A, 0x67, + 0x9A, 0x5A, 0x91, 0x9B, 0x62, 0x6D, 0x4E, 0x50, 0xA8, 0xDD, + 0x73, 0x1B, 0x10, 0x7A, 0x99, 0x62, 0x38, 0x1F, 0xB5, 0xD8, + 0x07, 0xBF, 0x26, 0x18, + 0x12, 0x0F, 0xC0, 0x5D, 0x3C, 0x67, 0xA9, 0x9D, 0xE1, 0x61, /* x */ + 0xD2, 0xF4, 0x09, 0x26, 0x22, 0xFE, 0xCA, 0x70, 0x1B, 0xE4, + 0xF5, 0x0F, 0x47, 0x58, 0x71, 0x4E, 0x8A, 0x87, 0xBB, 0xF2, + 0xA6, 0x58, 0xEF, 0x8C, 0x21, 0xE7, 0xC5, 0xEF, 0xE9, 0x65, + 0x36, 0x1F, 0x6C, 0x29, 0x99, 0xC0, 0xC2, 0x47, 0xB0, 0xDB, + 0xD7, 0x0C, 0xE6, 0xB7, + 0x20, 0xD0, 0xAF, 0x89, 0x03, 0xA9, 0x6F, 0x8D, 0x5F, 0xA2, /* y */ + 0xC2, 0x55, 0x74, 0x5D, 0x3C, 0x45, 0x1B, 0x30, 0x2C, 0x93, + 0x46, 0xD9, 0xB7, 0xE4, 0x85, 0xE7, 0xBC, 0xE4, 0x1F, 0x6B, + 0x59, 0x1F, 0x3E, 0x8F, 0x6A, 0xDD, 0xCB, 0xB0, 0xBC, 0x4C, + 0x2F, 0x94, 0x7A, 0x7D, 0xE1, 0xA8, 0x9B, 0x62, 0x5D, 0x6A, + 0x59, 0x8B, 0x37, 0x60, + 0x00, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, /* order */ + 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, + 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x23, + 0xC3, 0x13, 0xFA, 0xB5, 0x05, 0x89, 0x70, 0x3B, 0x5E, 0xC6, + 0x8D, 0x35, 0x87, 0xFE, 0xC6, 0x0D, 0x16, 0x1C, 0xC1, 0x49, + 0xC1, 0xAD, 0x4A, 0x91 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} + _EC_WTLS_1 = { + { + NID_X9_62_characteristic_two_field, 0, 15, 2 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x02, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x01, + 0x01, 0x66, 0x79, 0x79, 0xA4, 0x0B, 0xA4, 0x97, 0xE5, 0xD5, /* x */ + 0xC2, 0x70, 0x78, 0x06, 0x17, + 0x00, 0xF4, 0x4B, 0x4A, 0xF1, 0xEC, 0xC2, 0x63, 0x0E, 0x08, /* y */ + 0x78, 0x5C, 0xEB, 0xCC, 0x15, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFD, 0xBF, /* order */ + 0x91, 0xAF, 0x6D, 0xEA, 0x73 + } +}; /* IPSec curves */ /* NOTE: The of curves over a extension field of non prime degree @@ -1768,57 +2151,69 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_IPSEC_155_ID3 = { - { NID_X9_62_characteristic_two_field,0,20,3 }, - { /* no seed */ - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x01, +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_IPSEC_155_ID3 = { + { + NID_X9_62_characteristic_two_field, 0, 20, 3 + }, + { /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x07,0x33,0x8f, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, 0x33, 0x8f, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x7b, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7b, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xc8, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xc8, - 0x02,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA, /* order */ - 0xC7,0xF3,0xC7,0x88,0x1B,0xD0,0x86,0x8F,0xA8,0x6C } - }; + 0x02, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, /* order */ + 0xC7, 0xF3, 0xC7, 0x88, 0x1B, 0xD0, 0x86, 0x8F, 0xA8, 0x6C + } +}; /* NOTE: The of curves over a extension field of non prime degree * is not recommended (Weil-descent). * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_IPSEC_185_ID4 = { - { NID_X9_62_characteristic_two_field,0,24,2 }, - { /* no seed */ - 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ - 0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x01, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x1e,0xe9, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x18, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x0d, - 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ - 0xFF,0xFF,0xED,0xF9,0x7C,0x44,0xDB,0x9F,0x24,0x20, - 0xBA,0xFC,0xA7,0x5E } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_IPSEC_185_ID4 = { + { + NID_X9_62_characteristic_two_field, 0, 24, 2 + }, + { /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x20, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x1e, 0xe9, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x18, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x0d, + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* order */ + 0xFF, 0xFF, 0xED, 0xF9, 0x7C, 0x44, 0xDB, 0x9F, 0x24, 0x20, + 0xBA, 0xFC, 0xA7, 0x5E + } +}; #endif @@ -1830,687 +2225,761 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } * those defined in ANSI X9.62. */ -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_brainpoolP160r1 = { - { NID_X9_62_prime_field, 0,20,1 }, - { /* no seed */ - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* p */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0F, - 0x34,0x0E,0x7B,0xE2,0xA2,0x80,0xEB,0x74,0xE2,0xBE, /* a */ - 0x61,0xBA,0xDA,0x74,0x5D,0x97,0xE8,0xF7,0xC3,0x00, - 0x1E,0x58,0x9A,0x85,0x95,0x42,0x34,0x12,0x13,0x4F, /* b */ - 0xAA,0x2D,0xBD,0xEC,0x95,0xC8,0xD8,0x67,0x5E,0x58, - 0xBE,0xD5,0xAF,0x16,0xEA,0x3F,0x6A,0x4F,0x62,0x93, /* x */ - 0x8C,0x46,0x31,0xEB,0x5A,0xF7,0xBD,0xBC,0xDB,0xC3, - 0x16,0x67,0xCB,0x47,0x7A,0x1A,0x8E,0xC3,0x38,0xF9, /* y */ - 0x47,0x41,0x66,0x9C,0x97,0x63,0x16,0xDA,0x63,0x21, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* order */ - 0x59,0x91,0xD4,0x50,0x29,0x40,0x9E,0x60,0xFC,0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } - _EC_brainpoolP160t1 = { - { NID_X9_62_prime_field, 0,20,1 }, - { /* no seed */ - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* p */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0F, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* a */ - 0xC7,0xAD,0x95,0xB3,0xD8,0x13,0x95,0x15,0x62,0x0C, - 0x7A,0x55,0x6B,0x6D,0xAE,0x53,0x5B,0x7B,0x51,0xED, /* b */ - 0x2C,0x4D,0x7D,0xAA,0x7A,0x0B,0x5C,0x55,0xF3,0x80, - 0xB1,0x99,0xB1,0x3B,0x9B,0x34,0xEF,0xC1,0x39,0x7E, /* x */ - 0x64,0xBA,0xEB,0x05,0xAC,0xC2,0x65,0xFF,0x23,0x78, - 0xAD,0xD6,0x71,0x8B,0x7C,0x7C,0x19,0x61,0xF0,0x99, /* y */ - 0x1B,0x84,0x24,0x43,0x77,0x21,0x52,0xC9,0xE0,0xAD, - 0xE9,0x5E,0x4A,0x5F,0x73,0x70,0x59,0xDC,0x60,0xDF, /* order */ - 0x59,0x91,0xD4,0x50,0x29,0x40,0x9E,0x60,0xFC,0x09 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_brainpoolP192r1 = { - { NID_X9_62_prime_field, 0,24,1 }, - { /* no seed */ - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* p */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x97, - 0x6A,0x91,0x17,0x40,0x76,0xB1,0xE0,0xE1,0x9C,0x39, /* a */ - 0xC0,0x31,0xFE,0x86,0x85,0xC1,0xCA,0xE0,0x40,0xE5, - 0xC6,0x9A,0x28,0xEF, - 0x46,0x9A,0x28,0xEF,0x7C,0x28,0xCC,0xA3,0xDC,0x72, /* b */ - 0x1D,0x04,0x4F,0x44,0x96,0xBC,0xCA,0x7E,0xF4,0x14, - 0x6F,0xBF,0x25,0xC9, - 0xC0,0xA0,0x64,0x7E,0xAA,0xB6,0xA4,0x87,0x53,0xB0, /* x */ - 0x33,0xC5,0x6C,0xB0,0xF0,0x90,0x0A,0x2F,0x5C,0x48, - 0x53,0x37,0x5F,0xD6, - 0x14,0xB6,0x90,0x86,0x6A,0xBD,0x5B,0xB8,0x8B,0x5F, /* y */ - 0x48,0x28,0xC1,0x49,0x00,0x02,0xE6,0x77,0x3F,0xA2, - 0xFA,0x29,0x9B,0x8F, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* order */ - 0x46,0x2F,0x9E,0x9E,0x91,0x6B,0x5B,0xE8,0xF1,0x02, - 0x9A,0xC4,0xAC,0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } - _EC_brainpoolP192t1 = { - { NID_X9_62_prime_field, 0,24,1 }, - { /* no seed */ - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* p */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x97, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* a */ - 0x46,0x30,0x93,0xD1,0x8D,0xB7,0x8F,0xCE,0x47,0x6D, - 0xE1,0xA8,0x62,0x94, - 0x13,0xD5,0x6F,0xFA,0xEC,0x78,0x68,0x1E,0x68,0xF9, /* b */ - 0xDE,0xB4,0x3B,0x35,0xBE,0xC2,0xFB,0x68,0x54,0x2E, - 0x27,0x89,0x7B,0x79, - 0x3A,0xE9,0xE5,0x8C,0x82,0xF6,0x3C,0x30,0x28,0x2E, /* x */ - 0x1F,0xE7,0xBB,0xF4,0x3F,0xA7,0x2C,0x44,0x6A,0xF6, - 0xF4,0x61,0x81,0x29, - 0x09,0x7E,0x2C,0x56,0x67,0xC2,0x22,0x3A,0x90,0x2A, /* y */ - 0xB5,0xCA,0x44,0x9D,0x00,0x84,0xB7,0xE5,0xB3,0xDE, - 0x7C,0xCC,0x01,0xC9, - 0xC3,0x02,0xF4,0x1D,0x93,0x2A,0x36,0xCD,0xA7,0xA3, /* order */ - 0x46,0x2F,0x9E,0x9E,0x91,0x6B,0x5B,0xE8,0xF1,0x02, - 0x9A,0xC4,0xAC,0xC1 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_brainpoolP224r1 = { - { NID_X9_62_prime_field, 0,28,1 }, - { /* no seed */ - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* p */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFF, - 0x68,0xA5,0xE6,0x2C,0xA9,0xCE,0x6C,0x1C,0x29,0x98, /* a */ - 0x03,0xA6,0xC1,0x53,0x0B,0x51,0x4E,0x18,0x2A,0xD8, - 0xB0,0x04,0x2A,0x59,0xCA,0xD2,0x9F,0x43, - 0x25,0x80,0xF6,0x3C,0xCF,0xE4,0x41,0x38,0x87,0x07, /* b */ - 0x13,0xB1,0xA9,0x23,0x69,0xE3,0x3E,0x21,0x35,0xD2, - 0x66,0xDB,0xB3,0x72,0x38,0x6C,0x40,0x0B, - 0x0D,0x90,0x29,0xAD,0x2C,0x7E,0x5C,0xF4,0x34,0x08, /* x */ - 0x23,0xB2,0xA8,0x7D,0xC6,0x8C,0x9E,0x4C,0xE3,0x17, - 0x4C,0x1E,0x6E,0xFD,0xEE,0x12,0xC0,0x7D, - 0x58,0xAA,0x56,0xF7,0x72,0xC0,0x72,0x6F,0x24,0xC6, /* y */ - 0xB8,0x9E,0x4E,0xCD,0xAC,0x24,0x35,0x4B,0x9E,0x99, - 0xCA,0xA3,0xF6,0xD3,0x76,0x14,0x02,0xCD, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* order */ - 0x30,0x25,0x75,0xD0,0xFB,0x98,0xD1,0x16,0xBC,0x4B, - 0x6D,0xDE,0xBC,0xA3,0xA5,0xA7,0x93,0x9F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } - _EC_brainpoolP224t1 = { - { NID_X9_62_prime_field, 0,28,1 }, - { /* no seed */ - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* p */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFF, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* a */ - 0x30,0x25,0x75,0xD1,0xD7,0x87,0xB0,0x9F,0x07,0x57, - 0x97,0xDA,0x89,0xF5,0x7E,0xC8,0xC0,0xFC, - 0x4B,0x33,0x7D,0x93,0x41,0x04,0xCD,0x7B,0xEF,0x27, /* b */ - 0x1B,0xF6,0x0C,0xED,0x1E,0xD2,0x0D,0xA1,0x4C,0x08, - 0xB3,0xBB,0x64,0xF1,0x8A,0x60,0x88,0x8D, - 0x6A,0xB1,0xE3,0x44,0xCE,0x25,0xFF,0x38,0x96,0x42, /* x */ - 0x4E,0x7F,0xFE,0x14,0x76,0x2E,0xCB,0x49,0xF8,0x92, - 0x8A,0xC0,0xC7,0x60,0x29,0xB4,0xD5,0x80, - 0x03,0x74,0xE9,0xF5,0x14,0x3E,0x56,0x8C,0xD2,0x3F, /* y */ - 0x3F,0x4D,0x7C,0x0D,0x4B,0x1E,0x41,0xC8,0xCC,0x0D, - 0x1C,0x6A,0xBD,0x5F,0x1A,0x46,0xDB,0x4C, - 0xD7,0xC1,0x34,0xAA,0x26,0x43,0x66,0x86,0x2A,0x18, /* order */ - 0x30,0x25,0x75,0xD0,0xFB,0x98,0xD1,0x16,0xBC,0x4B, - 0x6D,0xDE,0xBC,0xA3,0xA5,0xA7,0x93,0x9F } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_brainpoolP256r1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* p */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x77, - 0x7D,0x5A,0x09,0x75,0xFC,0x2C,0x30,0x57,0xEE,0xF6, /* a */ - 0x75,0x30,0x41,0x7A,0xFF,0xE7,0xFB,0x80,0x55,0xC1, - 0x26,0xDC,0x5C,0x6C,0xE9,0x4A,0x4B,0x44,0xF3,0x30, - 0xB5,0xD9, - 0x26,0xDC,0x5C,0x6C,0xE9,0x4A,0x4B,0x44,0xF3,0x30, /* b */ - 0xB5,0xD9,0xBB,0xD7,0x7C,0xBF,0x95,0x84,0x16,0x29, - 0x5C,0xF7,0xE1,0xCE,0x6B,0xCC,0xDC,0x18,0xFF,0x8C, - 0x07,0xB6, - 0x8B,0xD2,0xAE,0xB9,0xCB,0x7E,0x57,0xCB,0x2C,0x4B, /* x */ - 0x48,0x2F,0xFC,0x81,0xB7,0xAF,0xB9,0xDE,0x27,0xE1, - 0xE3,0xBD,0x23,0xC2,0x3A,0x44,0x53,0xBD,0x9A,0xCE, - 0x32,0x62, - 0x54,0x7E,0xF8,0x35,0xC3,0xDA,0xC4,0xFD,0x97,0xF8, /* y */ - 0x46,0x1A,0x14,0x61,0x1D,0xC9,0xC2,0x77,0x45,0x13, - 0x2D,0xED,0x8E,0x54,0x5C,0x1D,0x54,0xC7,0x2F,0x04, - 0x69,0x97, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* order */ - 0x0A,0x90,0x9D,0x83,0x8D,0x71,0x8C,0x39,0x7A,0xA3, - 0xB5,0x61,0xA6,0xF7,0x90,0x1E,0x0E,0x82,0x97,0x48, - 0x56,0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_brainpoolP256t1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* p */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x77, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* a */ - 0x0A,0x90,0x9D,0x83,0x8D,0x72,0x6E,0x3B,0xF6,0x23, - 0xD5,0x26,0x20,0x28,0x20,0x13,0x48,0x1D,0x1F,0x6E, - 0x53,0x74, - 0x66,0x2C,0x61,0xC4,0x30,0xD8,0x4E,0xA4,0xFE,0x66, /* b */ - 0xA7,0x73,0x3D,0x0B,0x76,0xB7,0xBF,0x93,0xEB,0xC4, - 0xAF,0x2F,0x49,0x25,0x6A,0xE5,0x81,0x01,0xFE,0xE9, - 0x2B,0x04, - 0xA3,0xE8,0xEB,0x3C,0xC1,0xCF,0xE7,0xB7,0x73,0x22, /* x */ - 0x13,0xB2,0x3A,0x65,0x61,0x49,0xAF,0xA1,0x42,0xC4, - 0x7A,0xAF,0xBC,0x2B,0x79,0xA1,0x91,0x56,0x2E,0x13, - 0x05,0xF4, - 0x2D,0x99,0x6C,0x82,0x34,0x39,0xC5,0x6D,0x7F,0x7B, /* y */ - 0x22,0xE1,0x46,0x44,0x41,0x7E,0x69,0xBC,0xB6,0xDE, - 0x39,0xD0,0x27,0x00,0x1D,0xAB,0xE8,0xF3,0x5B,0x25, - 0xC9,0xBE, - 0xA9,0xFB,0x57,0xDB,0xA1,0xEE,0xA9,0xBC,0x3E,0x66, /* order */ - 0x0A,0x90,0x9D,0x83,0x8D,0x71,0x8C,0x39,0x7A,0xA3, - 0xB5,0x61,0xA6,0xF7,0x90,0x1E,0x0E,0x82,0x97,0x48, - 0x56,0xA7 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+40*6]; } - _EC_brainpoolP320r1 = { - { NID_X9_62_prime_field, 0,40,1 }, - { /* no seed */ - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* p */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x27, - 0x3E,0xE3,0x0B,0x56,0x8F,0xBA,0xB0,0xF8,0x83,0xCC, /* a */ - 0xEB,0xD4,0x6D,0x3F,0x3B,0xB8,0xA2,0xA7,0x35,0x13, - 0xF5,0xEB,0x79,0xDA,0x66,0x19,0x0E,0xB0,0x85,0xFF, - 0xA9,0xF4,0x92,0xF3,0x75,0xA9,0x7D,0x86,0x0E,0xB4, - 0x52,0x08,0x83,0x94,0x9D,0xFD,0xBC,0x42,0xD3,0xAD, /* b */ - 0x19,0x86,0x40,0x68,0x8A,0x6F,0xE1,0x3F,0x41,0x34, - 0x95,0x54,0xB4,0x9A,0xCC,0x31,0xDC,0xCD,0x88,0x45, - 0x39,0x81,0x6F,0x5E,0xB4,0xAC,0x8F,0xB1,0xF1,0xA6, - 0x43,0xBD,0x7E,0x9A,0xFB,0x53,0xD8,0xB8,0x52,0x89, /* x */ - 0xBC,0xC4,0x8E,0xE5,0xBF,0xE6,0xF2,0x01,0x37,0xD1, - 0x0A,0x08,0x7E,0xB6,0xE7,0x87,0x1E,0x2A,0x10,0xA5, - 0x99,0xC7,0x10,0xAF,0x8D,0x0D,0x39,0xE2,0x06,0x11, - 0x14,0xFD,0xD0,0x55,0x45,0xEC,0x1C,0xC8,0xAB,0x40, /* y */ - 0x93,0x24,0x7F,0x77,0x27,0x5E,0x07,0x43,0xFF,0xED, - 0x11,0x71,0x82,0xEA,0xA9,0xC7,0x78,0x77,0xAA,0xAC, - 0x6A,0xC7,0xD3,0x52,0x45,0xD1,0x69,0x2E,0x8E,0xE1, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* order */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA5, - 0xB6,0x8F,0x12,0xA3,0x2D,0x48,0x2E,0xC7,0xEE,0x86, - 0x58,0xE9,0x86,0x91,0x55,0x5B,0x44,0xC5,0x93,0x11 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+40*6]; } - _EC_brainpoolP320t1 = { - { NID_X9_62_prime_field, 0,40,1 }, - { /* no seed */ - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* p */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x27, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* a */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA6, - 0xF6,0xF4,0x0D,0xEF,0x4F,0x92,0xB9,0xEC,0x78,0x93, - 0xEC,0x28,0xFC,0xD4,0x12,0xB1,0xF1,0xB3,0x2E,0x24, - 0xA7,0xF5,0x61,0xE0,0x38,0xEB,0x1E,0xD5,0x60,0xB3, /* b */ - 0xD1,0x47,0xDB,0x78,0x20,0x13,0x06,0x4C,0x19,0xF2, - 0x7E,0xD2,0x7C,0x67,0x80,0xAA,0xF7,0x7F,0xB8,0xA5, - 0x47,0xCE,0xB5,0xB4,0xFE,0xF4,0x22,0x34,0x03,0x53, - 0x92,0x5B,0xE9,0xFB,0x01,0xAF,0xC6,0xFB,0x4D,0x3E, /* x */ - 0x7D,0x49,0x90,0x01,0x0F,0x81,0x34,0x08,0xAB,0x10, - 0x6C,0x4F,0x09,0xCB,0x7E,0xE0,0x78,0x68,0xCC,0x13, - 0x6F,0xFF,0x33,0x57,0xF6,0x24,0xA2,0x1B,0xED,0x52, - 0x63,0xBA,0x3A,0x7A,0x27,0x48,0x3E,0xBF,0x66,0x71, /* y */ - 0xDB,0xEF,0x7A,0xBB,0x30,0xEB,0xEE,0x08,0x4E,0x58, - 0xA0,0xB0,0x77,0xAD,0x42,0xA5,0xA0,0x98,0x9D,0x1E, - 0xE7,0x1B,0x1B,0x9B,0xC0,0x45,0x5F,0xB0,0xD2,0xC3, - 0xD3,0x5E,0x47,0x20,0x36,0xBC,0x4F,0xB7,0xE1,0x3C, /* order */ - 0x78,0x5E,0xD2,0x01,0xE0,0x65,0xF9,0x8F,0xCF,0xA5, - 0xB6,0x8F,0x12,0xA3,0x2D,0x48,0x2E,0xC7,0xEE,0x86, - 0x58,0xE9,0x86,0x91,0x55,0x5B,0x44,0xC5,0x93,0x11 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+48*6]; } - _EC_brainpoolP384r1 = { - { NID_X9_62_prime_field, 0,48,1 }, - { /* no seed */ - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* p */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x53, - 0x7B,0xC3,0x82,0xC6,0x3D,0x8C,0x15,0x0C,0x3C,0x72, /* a */ - 0x08,0x0A,0xCE,0x05,0xAF,0xA0,0xC2,0xBE,0xA2,0x8E, - 0x4F,0xB2,0x27,0x87,0x13,0x91,0x65,0xEF,0xBA,0x91, - 0xF9,0x0F,0x8A,0xA5,0x81,0x4A,0x50,0x3A,0xD4,0xEB, - 0x04,0xA8,0xC7,0xDD,0x22,0xCE,0x28,0x26, - 0x04,0xA8,0xC7,0xDD,0x22,0xCE,0x28,0x26,0x8B,0x39, /* b */ - 0xB5,0x54,0x16,0xF0,0x44,0x7C,0x2F,0xB7,0x7D,0xE1, - 0x07,0xDC,0xD2,0xA6,0x2E,0x88,0x0E,0xA5,0x3E,0xEB, - 0x62,0xD5,0x7C,0xB4,0x39,0x02,0x95,0xDB,0xC9,0x94, - 0x3A,0xB7,0x86,0x96,0xFA,0x50,0x4C,0x11, - 0x1D,0x1C,0x64,0xF0,0x68,0xCF,0x45,0xFF,0xA2,0xA6, /* x */ - 0x3A,0x81,0xB7,0xC1,0x3F,0x6B,0x88,0x47,0xA3,0xE7, - 0x7E,0xF1,0x4F,0xE3,0xDB,0x7F,0xCA,0xFE,0x0C,0xBD, - 0x10,0xE8,0xE8,0x26,0xE0,0x34,0x36,0xD6,0x46,0xAA, - 0xEF,0x87,0xB2,0xE2,0x47,0xD4,0xAF,0x1E, - 0x8A,0xBE,0x1D,0x75,0x20,0xF9,0xC2,0xA4,0x5C,0xB1, /* y */ - 0xEB,0x8E,0x95,0xCF,0xD5,0x52,0x62,0xB7,0x0B,0x29, - 0xFE,0xEC,0x58,0x64,0xE1,0x9C,0x05,0x4F,0xF9,0x91, - 0x29,0x28,0x0E,0x46,0x46,0x21,0x77,0x91,0x81,0x11, - 0x42,0x82,0x03,0x41,0x26,0x3C,0x53,0x15, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* order */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB3,0x1F,0x16,0x6E,0x6C,0xAC,0x04, - 0x25,0xA7,0xCF,0x3A,0xB6,0xAF,0x6B,0x7F,0xC3,0x10, - 0x3B,0x88,0x32,0x02,0xE9,0x04,0x65,0x65 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+48*6]; } - _EC_brainpoolP384t1 = { - { NID_X9_62_prime_field, 0,48,1 }, - { /* no seed */ - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* p */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x53, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* a */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB4,0x12,0xB1,0xDA,0x19,0x7F,0xB7, - 0x11,0x23,0xAC,0xD3,0xA7,0x29,0x90,0x1D,0x1A,0x71, - 0x87,0x47,0x00,0x13,0x31,0x07,0xEC,0x50, - 0x7F,0x51,0x9E,0xAD,0xA7,0xBD,0xA8,0x1B,0xD8,0x26, /* b */ - 0xDB,0xA6,0x47,0x91,0x0F,0x8C,0x4B,0x93,0x46,0xED, - 0x8C,0xCD,0xC6,0x4E,0x4B,0x1A,0xBD,0x11,0x75,0x6D, - 0xCE,0x1D,0x20,0x74,0xAA,0x26,0x3B,0x88,0x80,0x5C, - 0xED,0x70,0x35,0x5A,0x33,0xB4,0x71,0xEE, - 0x18,0xDE,0x98,0xB0,0x2D,0xB9,0xA3,0x06,0xF2,0xAF, /* x */ - 0xCD,0x72,0x35,0xF7,0x2A,0x81,0x9B,0x80,0xAB,0x12, - 0xEB,0xD6,0x53,0x17,0x24,0x76,0xFE,0xCD,0x46,0x2A, - 0xAB,0xFF,0xC4,0xFF,0x19,0x1B,0x94,0x6A,0x5F,0x54, - 0xD8,0xD0,0xAA,0x2F,0x41,0x88,0x08,0xCC, - 0x25,0xAB,0x05,0x69,0x62,0xD3,0x06,0x51,0xA1,0x14, /* y */ - 0xAF,0xD2,0x75,0x5A,0xD3,0x36,0x74,0x7F,0x93,0x47, - 0x5B,0x7A,0x1F,0xCA,0x3B,0x88,0xF2,0xB6,0xA2,0x08, - 0xCC,0xFE,0x46,0x94,0x08,0x58,0x4D,0xC2,0xB2,0x91, - 0x26,0x75,0xBF,0x5B,0x9E,0x58,0x29,0x28, - 0x8C,0xB9,0x1E,0x82,0xA3,0x38,0x6D,0x28,0x0F,0x5D, /* order */ - 0x6F,0x7E,0x50,0xE6,0x41,0xDF,0x15,0x2F,0x71,0x09, - 0xED,0x54,0x56,0xB3,0x1F,0x16,0x6E,0x6C,0xAC,0x04, - 0x25,0xA7,0xCF,0x3A,0xB6,0xAF,0x6B,0x7F,0xC3,0x10, - 0x3B,0x88,0x32,0x02,0xE9,0x04,0x65,0x65 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+64*6]; } - _EC_brainpoolP512r1 = { - { NID_X9_62_prime_field, 0,64,1 }, - { /* no seed */ - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* p */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF3, - 0x78,0x30,0xA3,0x31,0x8B,0x60,0x3B,0x89,0xE2,0x32, /* a */ - 0x71,0x45,0xAC,0x23,0x4C,0xC5,0x94,0xCB,0xDD,0x8D, - 0x3D,0xF9,0x16,0x10,0xA8,0x34,0x41,0xCA,0xEA,0x98, - 0x63,0xBC,0x2D,0xED,0x5D,0x5A,0xA8,0x25,0x3A,0xA1, - 0x0A,0x2E,0xF1,0xC9,0x8B,0x9A,0xC8,0xB5,0x7F,0x11, - 0x17,0xA7,0x2B,0xF2,0xC7,0xB9,0xE7,0xC1,0xAC,0x4D, - 0x77,0xFC,0x94,0xCA, - 0x3D,0xF9,0x16,0x10,0xA8,0x34,0x41,0xCA,0xEA,0x98, /* b */ - 0x63,0xBC,0x2D,0xED,0x5D,0x5A,0xA8,0x25,0x3A,0xA1, - 0x0A,0x2E,0xF1,0xC9,0x8B,0x9A,0xC8,0xB5,0x7F,0x11, - 0x17,0xA7,0x2B,0xF2,0xC7,0xB9,0xE7,0xC1,0xAC,0x4D, - 0x77,0xFC,0x94,0xCA,0xDC,0x08,0x3E,0x67,0x98,0x40, - 0x50,0xB7,0x5E,0xBA,0xE5,0xDD,0x28,0x09,0xBD,0x63, - 0x80,0x16,0xF7,0x23, - 0x81,0xAE,0xE4,0xBD,0xD8,0x2E,0xD9,0x64,0x5A,0x21, /* x */ - 0x32,0x2E,0x9C,0x4C,0x6A,0x93,0x85,0xED,0x9F,0x70, - 0xB5,0xD9,0x16,0xC1,0xB4,0x3B,0x62,0xEE,0xF4,0xD0, - 0x09,0x8E,0xFF,0x3B,0x1F,0x78,0xE2,0xD0,0xD4,0x8D, - 0x50,0xD1,0x68,0x7B,0x93,0xB9,0x7D,0x5F,0x7C,0x6D, - 0x50,0x47,0x40,0x6A,0x5E,0x68,0x8B,0x35,0x22,0x09, - 0xBC,0xB9,0xF8,0x22, - 0x7D,0xDE,0x38,0x5D,0x56,0x63,0x32,0xEC,0xC0,0xEA, /* y */ - 0xBF,0xA9,0xCF,0x78,0x22,0xFD,0xF2,0x09,0xF7,0x00, - 0x24,0xA5,0x7B,0x1A,0xA0,0x00,0xC5,0x5B,0x88,0x1F, - 0x81,0x11,0xB2,0xDC,0xDE,0x49,0x4A,0x5F,0x48,0x5E, - 0x5B,0xCA,0x4B,0xD8,0x8A,0x27,0x63,0xAE,0xD1,0xCA, - 0x2B,0x2F,0xA8,0xF0,0x54,0x06,0x78,0xCD,0x1E,0x0F, - 0x3A,0xD8,0x08,0x92, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* order */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x70,0x55,0x3E,0x5C,0x41,0x4C,0xA9,0x26,0x19, - 0x41,0x86,0x61,0x19,0x7F,0xAC,0x10,0x47,0x1D,0xB1, - 0xD3,0x81,0x08,0x5D,0xDA,0xDD,0xB5,0x87,0x96,0x82, - 0x9C,0xA9,0x00,0x69 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+64*6]; } - _EC_brainpoolP512t1 = { - { NID_X9_62_prime_field, 0,64,1 }, - { /* no seed */ - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* p */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF3, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* a */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x71,0x7D,0x4D,0x9B,0x00,0x9B,0xC6,0x68,0x42, - 0xAE,0xCD,0xA1,0x2A,0xE6,0xA3,0x80,0xE6,0x28,0x81, - 0xFF,0x2F,0x2D,0x82,0xC6,0x85,0x28,0xAA,0x60,0x56, - 0x58,0x3A,0x48,0xF0, - 0x7C,0xBB,0xBC,0xF9,0x44,0x1C,0xFA,0xB7,0x6E,0x18, /* b */ - 0x90,0xE4,0x68,0x84,0xEA,0xE3,0x21,0xF7,0x0C,0x0B, - 0xCB,0x49,0x81,0x52,0x78,0x97,0x50,0x4B,0xEC,0x3E, - 0x36,0xA6,0x2B,0xCD,0xFA,0x23,0x04,0x97,0x65,0x40, - 0xF6,0x45,0x00,0x85,0xF2,0xDA,0xE1,0x45,0xC2,0x25, - 0x53,0xB4,0x65,0x76,0x36,0x89,0x18,0x0E,0xA2,0x57, - 0x18,0x67,0x42,0x3E, - 0x64,0x0E,0xCE,0x5C,0x12,0x78,0x87,0x17,0xB9,0xC1, /* x */ - 0xBA,0x06,0xCB,0xC2,0xA6,0xFE,0xBA,0x85,0x84,0x24, - 0x58,0xC5,0x6D,0xDE,0x9D,0xB1,0x75,0x8D,0x39,0xC0, - 0x31,0x3D,0x82,0xBA,0x51,0x73,0x5C,0xDB,0x3E,0xA4, - 0x99,0xAA,0x77,0xA7,0xD6,0x94,0x3A,0x64,0xF7,0xA3, - 0xF2,0x5F,0xE2,0x6F,0x06,0xB5,0x1B,0xAA,0x26,0x96, - 0xFA,0x90,0x35,0xDA, - 0x5B,0x53,0x4B,0xD5,0x95,0xF5,0xAF,0x0F,0xA2,0xC8, /* y */ - 0x92,0x37,0x6C,0x84,0xAC,0xE1,0xBB,0x4E,0x30,0x19, - 0xB7,0x16,0x34,0xC0,0x11,0x31,0x15,0x9C,0xAE,0x03, - 0xCE,0xE9,0xD9,0x93,0x21,0x84,0xBE,0xEF,0x21,0x6B, - 0xD7,0x1D,0xF2,0xDA,0xDF,0x86,0xA6,0x27,0x30,0x6E, - 0xCF,0xF9,0x6D,0xBB,0x8B,0xAC,0xE1,0x98,0xB6,0x1E, - 0x00,0xF8,0xB3,0x32, - 0xAA,0xDD,0x9D,0xB8,0xDB,0xE9,0xC4,0x8B,0x3F,0xD4, /* order */ - 0xE6,0xAE,0x33,0xC9,0xFC,0x07,0xCB,0x30,0x8D,0xB3, - 0xB3,0xC9,0xD2,0x0E,0xD6,0x63,0x9C,0xCA,0x70,0x33, - 0x08,0x70,0x55,0x3E,0x5C,0x41,0x4C,0xA9,0x26,0x19, - 0x41,0x86,0x61,0x19,0x7F,0xAC,0x10,0x47,0x1D,0xB1, - 0xD3,0x81,0x08,0x5D,0xDA,0xDD,0xB5,0x87,0x96,0x82, - 0x9C,0xA9,0x00,0x69 } - }; - -static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } - _EC_FRP256v1 = { - { NID_X9_62_prime_field, 0,32,1 }, - { /* no seed */ - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* p */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x39,0x61,0xAD,0xBC, - 0xAB,0xC8,0xCA,0x6D,0xE8,0xFC,0xF3,0x53,0xD8,0x6E, - 0x9C,0x03, - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* a */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x39,0x61,0xAD,0xBC, - 0xAB,0xC8,0xCA,0x6D,0xE8,0xFC,0xF3,0x53,0xD8,0x6E, - 0x9C,0x00, - 0xEE,0x35,0x3F,0xCA,0x54,0x28,0xA9,0x30,0x0D,0x4A, /* b */ - 0xBA,0x75,0x4A,0x44,0xC0,0x0F,0xDF,0xEC,0x0C,0x9A, - 0xE4,0xB1,0xA1,0x80,0x30,0x75,0xED,0x96,0x7B,0x7B, - 0xB7,0x3F, - 0xB6,0xB3,0xD4,0xC3,0x56,0xC1,0x39,0xEB,0x31,0x18, /* x */ - 0x3D,0x47,0x49,0xD4,0x23,0x95,0x8C,0x27,0xD2,0xDC, - 0xAF,0x98,0xB7,0x01,0x64,0xC9,0x7A,0x2D,0xD9,0x8F, - 0x5C,0xFF, - 0x61,0x42,0xE0,0xF7,0xC8,0xB2,0x04,0x91,0x1F,0x92, /* y */ - 0x71,0xF0,0xF3,0xEC,0xEF,0x8C,0x27,0x01,0xC3,0x07, - 0xE8,0xE4,0xC9,0xE1,0x83,0x11,0x5A,0x15,0x54,0x06, - 0x2C,0xFB, - 0xF1,0xFD,0x17,0x8C,0x0B,0x3A,0xD5,0x8F,0x10,0x12, /* order */ - 0x6D,0xE8,0xCE,0x42,0x43,0x5B,0x53,0xDC,0x67,0xE1, - 0x40,0xD2,0xBF,0x94,0x1F,0xFD,0xD4,0x59,0xC6,0xD6, - 0x55,0xE1 } - }; +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_brainpoolP160r1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { /* no seed */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* p */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + 0x34, 0x0E, 0x7B, 0xE2, 0xA2, 0x80, 0xEB, 0x74, 0xE2, 0xBE, /* a */ + 0x61, 0xBA, 0xDA, 0x74, 0x5D, 0x97, 0xE8, 0xF7, 0xC3, 0x00, + 0x1E, 0x58, 0x9A, 0x85, 0x95, 0x42, 0x34, 0x12, 0x13, 0x4F, /* b */ + 0xAA, 0x2D, 0xBD, 0xEC, 0x95, 0xC8, 0xD8, 0x67, 0x5E, 0x58, + 0xBE, 0xD5, 0xAF, 0x16, 0xEA, 0x3F, 0x6A, 0x4F, 0x62, 0x93, /* x */ + 0x8C, 0x46, 0x31, 0xEB, 0x5A, 0xF7, 0xBD, 0xBC, 0xDB, 0xC3, + 0x16, 0x67, 0xCB, 0x47, 0x7A, 0x1A, 0x8E, 0xC3, 0x38, 0xF9, /* y */ + 0x47, 0x41, 0x66, 0x9C, 0x97, 0x63, 0x16, 0xDA, 0x63, 0x21, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* order */ + 0x59, 0x91, 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} + _EC_brainpoolP160t1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { /* no seed */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* p */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* a */ + 0xC7, 0xAD, 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0C, + 0x7A, 0x55, 0x6B, 0x6D, 0xAE, 0x53, 0x5B, 0x7B, 0x51, 0xED, /* b */ + 0x2C, 0x4D, 0x7D, 0xAA, 0x7A, 0x0B, 0x5C, 0x55, 0xF3, 0x80, + 0xB1, 0x99, 0xB1, 0x3B, 0x9B, 0x34, 0xEF, 0xC1, 0x39, 0x7E, /* x */ + 0x64, 0xBA, 0xEB, 0x05, 0xAC, 0xC2, 0x65, 0xFF, 0x23, 0x78, + 0xAD, 0xD6, 0x71, 0x8B, 0x7C, 0x7C, 0x19, 0x61, 0xF0, 0x99, /* y */ + 0x1B, 0x84, 0x24, 0x43, 0x77, 0x21, 0x52, 0xC9, 0xE0, 0xAD, + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, /* order */ + 0x59, 0x91, 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_brainpoolP192r1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* p */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x97, + 0x6A, 0x91, 0x17, 0x40, 0x76, 0xB1, 0xE0, 0xE1, 0x9C, 0x39, /* a */ + 0xC0, 0x31, 0xFE, 0x86, 0x85, 0xC1, 0xCA, 0xE0, 0x40, 0xE5, + 0xC6, 0x9A, 0x28, 0xEF, + 0x46, 0x9A, 0x28, 0xEF, 0x7C, 0x28, 0xCC, 0xA3, 0xDC, 0x72, /* b */ + 0x1D, 0x04, 0x4F, 0x44, 0x96, 0xBC, 0xCA, 0x7E, 0xF4, 0x14, + 0x6F, 0xBF, 0x25, 0xC9, + 0xC0, 0xA0, 0x64, 0x7E, 0xAA, 0xB6, 0xA4, 0x87, 0x53, 0xB0, /* x */ + 0x33, 0xC5, 0x6C, 0xB0, 0xF0, 0x90, 0x0A, 0x2F, 0x5C, 0x48, + 0x53, 0x37, 0x5F, 0xD6, + 0x14, 0xB6, 0x90, 0x86, 0x6A, 0xBD, 0x5B, 0xB8, 0x8B, 0x5F, /* y */ + 0x48, 0x28, 0xC1, 0x49, 0x00, 0x02, 0xE6, 0x77, 0x3F, 0xA2, + 0xFA, 0x29, 0x9B, 0x8F, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* order */ + 0x46, 0x2F, 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, + 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} + _EC_brainpoolP192t1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { /* no seed */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* p */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x97, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* a */ + 0x46, 0x30, 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, + 0xE1, 0xA8, 0x62, 0x94, + 0x13, 0xD5, 0x6F, 0xFA, 0xEC, 0x78, 0x68, 0x1E, 0x68, 0xF9, /* b */ + 0xDE, 0xB4, 0x3B, 0x35, 0xBE, 0xC2, 0xFB, 0x68, 0x54, 0x2E, + 0x27, 0x89, 0x7B, 0x79, + 0x3A, 0xE9, 0xE5, 0x8C, 0x82, 0xF6, 0x3C, 0x30, 0x28, 0x2E, /* x */ + 0x1F, 0xE7, 0xBB, 0xF4, 0x3F, 0xA7, 0x2C, 0x44, 0x6A, 0xF6, + 0xF4, 0x61, 0x81, 0x29, + 0x09, 0x7E, 0x2C, 0x56, 0x67, 0xC2, 0x22, 0x3A, 0x90, 0x2A, /* y */ + 0xB5, 0xCA, 0x44, 0x9D, 0x00, 0x84, 0xB7, 0xE5, 0xB3, 0xDE, + 0x7C, 0xCC, 0x01, 0xC9, + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, /* order */ + 0x46, 0x2F, 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, + 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_brainpoolP224r1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* p */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFF, + 0x68, 0xA5, 0xE6, 0x2C, 0xA9, 0xCE, 0x6C, 0x1C, 0x29, 0x98, /* a */ + 0x03, 0xA6, 0xC1, 0x53, 0x0B, 0x51, 0x4E, 0x18, 0x2A, 0xD8, + 0xB0, 0x04, 0x2A, 0x59, 0xCA, 0xD2, 0x9F, 0x43, + 0x25, 0x80, 0xF6, 0x3C, 0xCF, 0xE4, 0x41, 0x38, 0x87, 0x07, /* b */ + 0x13, 0xB1, 0xA9, 0x23, 0x69, 0xE3, 0x3E, 0x21, 0x35, 0xD2, + 0x66, 0xDB, 0xB3, 0x72, 0x38, 0x6C, 0x40, 0x0B, + 0x0D, 0x90, 0x29, 0xAD, 0x2C, 0x7E, 0x5C, 0xF4, 0x34, 0x08, /* x */ + 0x23, 0xB2, 0xA8, 0x7D, 0xC6, 0x8C, 0x9E, 0x4C, 0xE3, 0x17, + 0x4C, 0x1E, 0x6E, 0xFD, 0xEE, 0x12, 0xC0, 0x7D, + 0x58, 0xAA, 0x56, 0xF7, 0x72, 0xC0, 0x72, 0x6F, 0x24, 0xC6, /* y */ + 0xB8, 0x9E, 0x4E, 0xCD, 0xAC, 0x24, 0x35, 0x4B, 0x9E, 0x99, + 0xCA, 0xA3, 0xF6, 0xD3, 0x76, 0x14, 0x02, 0xCD, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* order */ + 0x30, 0x25, 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, + 0x6D, 0xDE, 0xBC, 0xA3, 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} + _EC_brainpoolP224t1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { /* no seed */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* p */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFF, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* a */ + 0x30, 0x25, 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, + 0x97, 0xDA, 0x89, 0xF5, 0x7E, 0xC8, 0xC0, 0xFC, + 0x4B, 0x33, 0x7D, 0x93, 0x41, 0x04, 0xCD, 0x7B, 0xEF, 0x27, /* b */ + 0x1B, 0xF6, 0x0C, 0xED, 0x1E, 0xD2, 0x0D, 0xA1, 0x4C, 0x08, + 0xB3, 0xBB, 0x64, 0xF1, 0x8A, 0x60, 0x88, 0x8D, + 0x6A, 0xB1, 0xE3, 0x44, 0xCE, 0x25, 0xFF, 0x38, 0x96, 0x42, /* x */ + 0x4E, 0x7F, 0xFE, 0x14, 0x76, 0x2E, 0xCB, 0x49, 0xF8, 0x92, + 0x8A, 0xC0, 0xC7, 0x60, 0x29, 0xB4, 0xD5, 0x80, + 0x03, 0x74, 0xE9, 0xF5, 0x14, 0x3E, 0x56, 0x8C, 0xD2, 0x3F, /* y */ + 0x3F, 0x4D, 0x7C, 0x0D, 0x4B, 0x1E, 0x41, 0xC8, 0xCC, 0x0D, + 0x1C, 0x6A, 0xBD, 0x5F, 0x1A, 0x46, 0xDB, 0x4C, + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, /* order */ + 0x30, 0x25, 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, + 0x6D, 0xDE, 0xBC, 0xA3, 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_brainpoolP256r1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* p */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x77, + 0x7D, 0x5A, 0x09, 0x75, 0xFC, 0x2C, 0x30, 0x57, 0xEE, 0xF6, /* a */ + 0x75, 0x30, 0x41, 0x7A, 0xFF, 0xE7, 0xFB, 0x80, 0x55, 0xC1, + 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, + 0xB5, 0xD9, + 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, /* b */ + 0xB5, 0xD9, 0xBB, 0xD7, 0x7C, 0xBF, 0x95, 0x84, 0x16, 0x29, + 0x5C, 0xF7, 0xE1, 0xCE, 0x6B, 0xCC, 0xDC, 0x18, 0xFF, 0x8C, + 0x07, 0xB6, + 0x8B, 0xD2, 0xAE, 0xB9, 0xCB, 0x7E, 0x57, 0xCB, 0x2C, 0x4B, /* x */ + 0x48, 0x2F, 0xFC, 0x81, 0xB7, 0xAF, 0xB9, 0xDE, 0x27, 0xE1, + 0xE3, 0xBD, 0x23, 0xC2, 0x3A, 0x44, 0x53, 0xBD, 0x9A, 0xCE, + 0x32, 0x62, + 0x54, 0x7E, 0xF8, 0x35, 0xC3, 0xDA, 0xC4, 0xFD, 0x97, 0xF8, /* y */ + 0x46, 0x1A, 0x14, 0x61, 0x1D, 0xC9, 0xC2, 0x77, 0x45, 0x13, + 0x2D, 0xED, 0x8E, 0x54, 0x5C, 0x1D, 0x54, 0xC7, 0x2F, 0x04, + 0x69, 0x97, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* order */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, + 0xB5, 0x61, 0xA6, 0xF7, 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, + 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_brainpoolP256t1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* p */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x77, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* a */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, + 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, + 0x53, 0x74, + 0x66, 0x2C, 0x61, 0xC4, 0x30, 0xD8, 0x4E, 0xA4, 0xFE, 0x66, /* b */ + 0xA7, 0x73, 0x3D, 0x0B, 0x76, 0xB7, 0xBF, 0x93, 0xEB, 0xC4, + 0xAF, 0x2F, 0x49, 0x25, 0x6A, 0xE5, 0x81, 0x01, 0xFE, 0xE9, + 0x2B, 0x04, + 0xA3, 0xE8, 0xEB, 0x3C, 0xC1, 0xCF, 0xE7, 0xB7, 0x73, 0x22, /* x */ + 0x13, 0xB2, 0x3A, 0x65, 0x61, 0x49, 0xAF, 0xA1, 0x42, 0xC4, + 0x7A, 0xAF, 0xBC, 0x2B, 0x79, 0xA1, 0x91, 0x56, 0x2E, 0x13, + 0x05, 0xF4, + 0x2D, 0x99, 0x6C, 0x82, 0x34, 0x39, 0xC5, 0x6D, 0x7F, 0x7B, /* y */ + 0x22, 0xE1, 0x46, 0x44, 0x41, 0x7E, 0x69, 0xBC, 0xB6, 0xDE, + 0x39, 0xD0, 0x27, 0x00, 0x1D, 0xAB, 0xE8, 0xF3, 0x5B, 0x25, + 0xC9, 0xBE, + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, /* order */ + 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, + 0xB5, 0x61, 0xA6, 0xF7, 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, + 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} + _EC_brainpoolP320r1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { /* no seed */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* p */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x27, + 0x3E, 0xE3, 0x0B, 0x56, 0x8F, 0xBA, 0xB0, 0xF8, 0x83, 0xCC, /* a */ + 0xEB, 0xD4, 0x6D, 0x3F, 0x3B, 0xB8, 0xA2, 0xA7, 0x35, 0x13, + 0xF5, 0xEB, 0x79, 0xDA, 0x66, 0x19, 0x0E, 0xB0, 0x85, 0xFF, + 0xA9, 0xF4, 0x92, 0xF3, 0x75, 0xA9, 0x7D, 0x86, 0x0E, 0xB4, + 0x52, 0x08, 0x83, 0x94, 0x9D, 0xFD, 0xBC, 0x42, 0xD3, 0xAD, /* b */ + 0x19, 0x86, 0x40, 0x68, 0x8A, 0x6F, 0xE1, 0x3F, 0x41, 0x34, + 0x95, 0x54, 0xB4, 0x9A, 0xCC, 0x31, 0xDC, 0xCD, 0x88, 0x45, + 0x39, 0x81, 0x6F, 0x5E, 0xB4, 0xAC, 0x8F, 0xB1, 0xF1, 0xA6, + 0x43, 0xBD, 0x7E, 0x9A, 0xFB, 0x53, 0xD8, 0xB8, 0x52, 0x89, /* x */ + 0xBC, 0xC4, 0x8E, 0xE5, 0xBF, 0xE6, 0xF2, 0x01, 0x37, 0xD1, + 0x0A, 0x08, 0x7E, 0xB6, 0xE7, 0x87, 0x1E, 0x2A, 0x10, 0xA5, + 0x99, 0xC7, 0x10, 0xAF, 0x8D, 0x0D, 0x39, 0xE2, 0x06, 0x11, + 0x14, 0xFD, 0xD0, 0x55, 0x45, 0xEC, 0x1C, 0xC8, 0xAB, 0x40, /* y */ + 0x93, 0x24, 0x7F, 0x77, 0x27, 0x5E, 0x07, 0x43, 0xFF, 0xED, + 0x11, 0x71, 0x82, 0xEA, 0xA9, 0xC7, 0x78, 0x77, 0xAA, 0xAC, + 0x6A, 0xC7, 0xD3, 0x52, 0x45, 0xD1, 0x69, 0x2E, 0x8E, 0xE1, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* order */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, + 0xB6, 0x8F, 0x12, 0xA3, 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, + 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} + _EC_brainpoolP320t1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { /* no seed */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* p */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x27, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* a */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, + 0xF6, 0xF4, 0x0D, 0xEF, 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, + 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, 0xF1, 0xB3, 0x2E, 0x24, + 0xA7, 0xF5, 0x61, 0xE0, 0x38, 0xEB, 0x1E, 0xD5, 0x60, 0xB3, /* b */ + 0xD1, 0x47, 0xDB, 0x78, 0x20, 0x13, 0x06, 0x4C, 0x19, 0xF2, + 0x7E, 0xD2, 0x7C, 0x67, 0x80, 0xAA, 0xF7, 0x7F, 0xB8, 0xA5, + 0x47, 0xCE, 0xB5, 0xB4, 0xFE, 0xF4, 0x22, 0x34, 0x03, 0x53, + 0x92, 0x5B, 0xE9, 0xFB, 0x01, 0xAF, 0xC6, 0xFB, 0x4D, 0x3E, /* x */ + 0x7D, 0x49, 0x90, 0x01, 0x0F, 0x81, 0x34, 0x08, 0xAB, 0x10, + 0x6C, 0x4F, 0x09, 0xCB, 0x7E, 0xE0, 0x78, 0x68, 0xCC, 0x13, + 0x6F, 0xFF, 0x33, 0x57, 0xF6, 0x24, 0xA2, 0x1B, 0xED, 0x52, + 0x63, 0xBA, 0x3A, 0x7A, 0x27, 0x48, 0x3E, 0xBF, 0x66, 0x71, /* y */ + 0xDB, 0xEF, 0x7A, 0xBB, 0x30, 0xEB, 0xEE, 0x08, 0x4E, 0x58, + 0xA0, 0xB0, 0x77, 0xAD, 0x42, 0xA5, 0xA0, 0x98, 0x9D, 0x1E, + 0xE7, 0x1B, 0x1B, 0x9B, 0xC0, 0x45, 0x5F, 0xB0, 0xD2, 0xC3, + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, /* order */ + 0x78, 0x5E, 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, + 0xB6, 0x8F, 0x12, 0xA3, 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, + 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} + _EC_brainpoolP384r1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { /* no seed */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* p */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + 0x7B, 0xC3, 0x82, 0xC6, 0x3D, 0x8C, 0x15, 0x0C, 0x3C, 0x72, /* a */ + 0x08, 0x0A, 0xCE, 0x05, 0xAF, 0xA0, 0xC2, 0xBE, 0xA2, 0x8E, + 0x4F, 0xB2, 0x27, 0x87, 0x13, 0x91, 0x65, 0xEF, 0xBA, 0x91, + 0xF9, 0x0F, 0x8A, 0xA5, 0x81, 0x4A, 0x50, 0x3A, 0xD4, 0xEB, + 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, + 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, 0x8B, 0x39, /* b */ + 0xB5, 0x54, 0x16, 0xF0, 0x44, 0x7C, 0x2F, 0xB7, 0x7D, 0xE1, + 0x07, 0xDC, 0xD2, 0xA6, 0x2E, 0x88, 0x0E, 0xA5, 0x3E, 0xEB, + 0x62, 0xD5, 0x7C, 0xB4, 0x39, 0x02, 0x95, 0xDB, 0xC9, 0x94, + 0x3A, 0xB7, 0x86, 0x96, 0xFA, 0x50, 0x4C, 0x11, + 0x1D, 0x1C, 0x64, 0xF0, 0x68, 0xCF, 0x45, 0xFF, 0xA2, 0xA6, /* x */ + 0x3A, 0x81, 0xB7, 0xC1, 0x3F, 0x6B, 0x88, 0x47, 0xA3, 0xE7, + 0x7E, 0xF1, 0x4F, 0xE3, 0xDB, 0x7F, 0xCA, 0xFE, 0x0C, 0xBD, + 0x10, 0xE8, 0xE8, 0x26, 0xE0, 0x34, 0x36, 0xD6, 0x46, 0xAA, + 0xEF, 0x87, 0xB2, 0xE2, 0x47, 0xD4, 0xAF, 0x1E, + 0x8A, 0xBE, 0x1D, 0x75, 0x20, 0xF9, 0xC2, 0xA4, 0x5C, 0xB1, /* y */ + 0xEB, 0x8E, 0x95, 0xCF, 0xD5, 0x52, 0x62, 0xB7, 0x0B, 0x29, + 0xFE, 0xEC, 0x58, 0x64, 0xE1, 0x9C, 0x05, 0x4F, 0xF9, 0x91, + 0x29, 0x28, 0x0E, 0x46, 0x46, 0x21, 0x77, 0x91, 0x81, 0x11, + 0x42, 0x82, 0x03, 0x41, 0x26, 0x3C, 0x53, 0x15, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* order */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB3, 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, + 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, 0x6B, 0x7F, 0xC3, 0x10, + 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} + _EC_brainpoolP384t1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { /* no seed */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* p */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* a */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, + 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, + 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x50, + 0x7F, 0x51, 0x9E, 0xAD, 0xA7, 0xBD, 0xA8, 0x1B, 0xD8, 0x26, /* b */ + 0xDB, 0xA6, 0x47, 0x91, 0x0F, 0x8C, 0x4B, 0x93, 0x46, 0xED, + 0x8C, 0xCD, 0xC6, 0x4E, 0x4B, 0x1A, 0xBD, 0x11, 0x75, 0x6D, + 0xCE, 0x1D, 0x20, 0x74, 0xAA, 0x26, 0x3B, 0x88, 0x80, 0x5C, + 0xED, 0x70, 0x35, 0x5A, 0x33, 0xB4, 0x71, 0xEE, + 0x18, 0xDE, 0x98, 0xB0, 0x2D, 0xB9, 0xA3, 0x06, 0xF2, 0xAF, /* x */ + 0xCD, 0x72, 0x35, 0xF7, 0x2A, 0x81, 0x9B, 0x80, 0xAB, 0x12, + 0xEB, 0xD6, 0x53, 0x17, 0x24, 0x76, 0xFE, 0xCD, 0x46, 0x2A, + 0xAB, 0xFF, 0xC4, 0xFF, 0x19, 0x1B, 0x94, 0x6A, 0x5F, 0x54, + 0xD8, 0xD0, 0xAA, 0x2F, 0x41, 0x88, 0x08, 0xCC, + 0x25, 0xAB, 0x05, 0x69, 0x62, 0xD3, 0x06, 0x51, 0xA1, 0x14, /* y */ + 0xAF, 0xD2, 0x75, 0x5A, 0xD3, 0x36, 0x74, 0x7F, 0x93, 0x47, + 0x5B, 0x7A, 0x1F, 0xCA, 0x3B, 0x88, 0xF2, 0xB6, 0xA2, 0x08, + 0xCC, 0xFE, 0x46, 0x94, 0x08, 0x58, 0x4D, 0xC2, 0xB2, 0x91, + 0x26, 0x75, 0xBF, 0x5B, 0x9E, 0x58, 0x29, 0x28, + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, /* order */ + 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, + 0xED, 0x54, 0x56, 0xB3, 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, + 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, 0x6B, 0x7F, 0xC3, 0x10, + 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} + _EC_brainpoolP512r1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { /* no seed */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* p */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + 0x78, 0x30, 0xA3, 0x31, 0x8B, 0x60, 0x3B, 0x89, 0xE2, 0x32, /* a */ + 0x71, 0x45, 0xAC, 0x23, 0x4C, 0xC5, 0x94, 0xCB, 0xDD, 0x8D, + 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, + 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, + 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, + 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, + 0x77, 0xFC, 0x94, 0xCA, + 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, /* b */ + 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, + 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, + 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, + 0x77, 0xFC, 0x94, 0xCA, 0xDC, 0x08, 0x3E, 0x67, 0x98, 0x40, + 0x50, 0xB7, 0x5E, 0xBA, 0xE5, 0xDD, 0x28, 0x09, 0xBD, 0x63, + 0x80, 0x16, 0xF7, 0x23, + 0x81, 0xAE, 0xE4, 0xBD, 0xD8, 0x2E, 0xD9, 0x64, 0x5A, 0x21, /* x */ + 0x32, 0x2E, 0x9C, 0x4C, 0x6A, 0x93, 0x85, 0xED, 0x9F, 0x70, + 0xB5, 0xD9, 0x16, 0xC1, 0xB4, 0x3B, 0x62, 0xEE, 0xF4, 0xD0, + 0x09, 0x8E, 0xFF, 0x3B, 0x1F, 0x78, 0xE2, 0xD0, 0xD4, 0x8D, + 0x50, 0xD1, 0x68, 0x7B, 0x93, 0xB9, 0x7D, 0x5F, 0x7C, 0x6D, + 0x50, 0x47, 0x40, 0x6A, 0x5E, 0x68, 0x8B, 0x35, 0x22, 0x09, + 0xBC, 0xB9, 0xF8, 0x22, + 0x7D, 0xDE, 0x38, 0x5D, 0x56, 0x63, 0x32, 0xEC, 0xC0, 0xEA, /* y */ + 0xBF, 0xA9, 0xCF, 0x78, 0x22, 0xFD, 0xF2, 0x09, 0xF7, 0x00, + 0x24, 0xA5, 0x7B, 0x1A, 0xA0, 0x00, 0xC5, 0x5B, 0x88, 0x1F, + 0x81, 0x11, 0xB2, 0xDC, 0xDE, 0x49, 0x4A, 0x5F, 0x48, 0x5E, + 0x5B, 0xCA, 0x4B, 0xD8, 0x8A, 0x27, 0x63, 0xAE, 0xD1, 0xCA, + 0x2B, 0x2F, 0xA8, 0xF0, 0x54, 0x06, 0x78, 0xCD, 0x1E, 0x0F, + 0x3A, 0xD8, 0x08, 0x92, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* order */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, 0x4C, 0xA9, 0x26, 0x19, + 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, 0x1D, 0xB1, + 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} + _EC_brainpoolP512t1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { /* no seed */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* p */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* a */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, + 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, + 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF0, + 0x7C, 0xBB, 0xBC, 0xF9, 0x44, 0x1C, 0xFA, 0xB7, 0x6E, 0x18, /* b */ + 0x90, 0xE4, 0x68, 0x84, 0xEA, 0xE3, 0x21, 0xF7, 0x0C, 0x0B, + 0xCB, 0x49, 0x81, 0x52, 0x78, 0x97, 0x50, 0x4B, 0xEC, 0x3E, + 0x36, 0xA6, 0x2B, 0xCD, 0xFA, 0x23, 0x04, 0x97, 0x65, 0x40, + 0xF6, 0x45, 0x00, 0x85, 0xF2, 0xDA, 0xE1, 0x45, 0xC2, 0x25, + 0x53, 0xB4, 0x65, 0x76, 0x36, 0x89, 0x18, 0x0E, 0xA2, 0x57, + 0x18, 0x67, 0x42, 0x3E, + 0x64, 0x0E, 0xCE, 0x5C, 0x12, 0x78, 0x87, 0x17, 0xB9, 0xC1, /* x */ + 0xBA, 0x06, 0xCB, 0xC2, 0xA6, 0xFE, 0xBA, 0x85, 0x84, 0x24, + 0x58, 0xC5, 0x6D, 0xDE, 0x9D, 0xB1, 0x75, 0x8D, 0x39, 0xC0, + 0x31, 0x3D, 0x82, 0xBA, 0x51, 0x73, 0x5C, 0xDB, 0x3E, 0xA4, + 0x99, 0xAA, 0x77, 0xA7, 0xD6, 0x94, 0x3A, 0x64, 0xF7, 0xA3, + 0xF2, 0x5F, 0xE2, 0x6F, 0x06, 0xB5, 0x1B, 0xAA, 0x26, 0x96, + 0xFA, 0x90, 0x35, 0xDA, + 0x5B, 0x53, 0x4B, 0xD5, 0x95, 0xF5, 0xAF, 0x0F, 0xA2, 0xC8, /* y */ + 0x92, 0x37, 0x6C, 0x84, 0xAC, 0xE1, 0xBB, 0x4E, 0x30, 0x19, + 0xB7, 0x16, 0x34, 0xC0, 0x11, 0x31, 0x15, 0x9C, 0xAE, 0x03, + 0xCE, 0xE9, 0xD9, 0x93, 0x21, 0x84, 0xBE, 0xEF, 0x21, 0x6B, + 0xD7, 0x1D, 0xF2, 0xDA, 0xDF, 0x86, 0xA6, 0x27, 0x30, 0x6E, + 0xCF, 0xF9, 0x6D, 0xBB, 0x8B, 0xAC, 0xE1, 0x98, 0xB6, 0x1E, + 0x00, 0xF8, 0xB3, 0x32, + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, /* order */ + 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, + 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, + 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, 0x4C, 0xA9, 0x26, 0x19, + 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, 0x1D, 0xB1, + 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} + _EC_FRP256v1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { /* no seed */ + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* p */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x39, 0x61, 0xAD, 0xBC, + 0xAB, 0xC8, 0xCA, 0x6D, 0xE8, 0xFC, 0xF3, 0x53, 0xD8, 0x6E, + 0x9C, 0x03, + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* a */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x39, 0x61, 0xAD, 0xBC, + 0xAB, 0xC8, 0xCA, 0x6D, 0xE8, 0xFC, 0xF3, 0x53, 0xD8, 0x6E, + 0x9C, 0x00, + 0xEE, 0x35, 0x3F, 0xCA, 0x54, 0x28, 0xA9, 0x30, 0x0D, 0x4A, /* b */ + 0xBA, 0x75, 0x4A, 0x44, 0xC0, 0x0F, 0xDF, 0xEC, 0x0C, 0x9A, + 0xE4, 0xB1, 0xA1, 0x80, 0x30, 0x75, 0xED, 0x96, 0x7B, 0x7B, + 0xB7, 0x3F, + 0xB6, 0xB3, 0xD4, 0xC3, 0x56, 0xC1, 0x39, 0xEB, 0x31, 0x18, /* x */ + 0x3D, 0x47, 0x49, 0xD4, 0x23, 0x95, 0x8C, 0x27, 0xD2, 0xDC, + 0xAF, 0x98, 0xB7, 0x01, 0x64, 0xC9, 0x7A, 0x2D, 0xD9, 0x8F, + 0x5C, 0xFF, + 0x61, 0x42, 0xE0, 0xF7, 0xC8, 0xB2, 0x04, 0x91, 0x1F, 0x92, /* y */ + 0x71, 0xF0, 0xF3, 0xEC, 0xEF, 0x8C, 0x27, 0x01, 0xC3, 0x07, + 0xE8, 0xE4, 0xC9, 0xE1, 0x83, 0x11, 0x5A, 0x15, 0x54, 0x06, + 0x2C, 0xFB, + 0xF1, 0xFD, 0x17, 0x8C, 0x0B, 0x3A, 0xD5, 0x8F, 0x10, 0x12, /* order */ + 0x6D, 0xE8, 0xCE, 0x42, 0x43, 0x5B, 0x53, 0xDC, 0x67, 0xE1, + 0x40, 0xD2, 0xBF, 0x94, 0x1F, 0xFD, 0xD4, 0x59, 0xC6, 0xD6, + 0x55, 0xE1 + } +}; typedef struct _ec_list_element_st { - int nid; + int nid; const EC_CURVE_DATA *data; - const EC_METHOD *(*meth)(void); + const EC_METHOD *(*meth) (void); const char *comment; - } ec_list_element; +} ec_list_element; static const ec_list_element curve_list[] = { /* prime field curves */ /* secg curves */ - { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, - { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field" }, - { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field" }, - { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field" }, - { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field" }, - { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field" }, - { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, + {NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field"}, + {NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field"}, + {NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field"}, + {NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field"}, + {NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field"}, + {NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field"}, + {NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field"}, /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ - { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, - { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, + {NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field"}, + {NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" }, + {NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field"}, #else - { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, + {NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field"}, #endif - { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, + {NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field"}, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ - { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, + {NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" }, + {NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field"}, #else - { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, + {NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field"}, #endif /* X9.62 curves */ - { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, - { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, - { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field" }, - { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, - { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, - { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, + {NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field"}, + {NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field"}, #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" }, + {NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field"}, #else - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, + {NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field"}, #endif #ifndef OPENSSL_NO_EC2M /* characteristic two field curves */ /* NIST/SECG curves */ - { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field" }, - { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field" }, - { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field" }, - { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field" }, - { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field" }, - { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field" }, - { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field" }, - { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field" }, - { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field" }, + {NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field"}, + {NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field"}, + {NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field"}, + {NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field"}, + {NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field"}, + {NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field"}, + {NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field"}, + {NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field"}, + {NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field"}, /* X9.62 curves */ - { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field" }, - { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field" }, - { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field" }, - { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field" }, - { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field" }, - { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field" }, - { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field" }, - { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field" }, - { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field" }, - { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field" }, - /* the WAP/WTLS curves - * [unlike SECG, spec has its own OIDs for curves from X9.62] */ - { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + {NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field"}, + {NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field"}, + {NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field"}, + {NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field"}, + {NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field"}, + {NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field"}, + {NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field"}, + /* + * the WAP/WTLS curves [unlike SECG, spec has its own OIDs for curves + * from X9.62] + */ + {NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field"}, #endif - { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field" }, + {NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field"}, #ifndef OPENSSL_NO_EC2M - { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + {NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field"}, #endif - { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curve over a 224 bit prime field" }, + {NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curve over a 224 bit prime field"}, #ifndef OPENSSL_NO_EC2M /* IPSec curves */ - { NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, - { NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, + {NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, + {NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, #endif /* RFC 5639 curves */ - { NID_brainpoolP160r1, &_EC_brainpoolP160r1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, - { NID_brainpoolP160t1, &_EC_brainpoolP160t1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, - { NID_brainpoolP192r1, &_EC_brainpoolP192r1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, - { NID_brainpoolP192t1, &_EC_brainpoolP192t1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, - { NID_brainpoolP224r1, &_EC_brainpoolP224r1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, - { NID_brainpoolP224t1, &_EC_brainpoolP224t1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, - { NID_brainpoolP256r1, &_EC_brainpoolP256r1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, - { NID_brainpoolP256t1, &_EC_brainpoolP256t1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, - { NID_brainpoolP320r1, &_EC_brainpoolP320r1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, - { NID_brainpoolP320t1, &_EC_brainpoolP320t1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, - { NID_brainpoolP384r1, &_EC_brainpoolP384r1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, - { NID_brainpoolP384t1, &_EC_brainpoolP384t1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, - { NID_brainpoolP512r1, &_EC_brainpoolP512r1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, - { NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, + {NID_brainpoolP160r1, &_EC_brainpoolP160r1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP160t1, &_EC_brainpoolP160t1.h, 0, "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP192r1, &_EC_brainpoolP192r1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP192t1, &_EC_brainpoolP192t1.h, 0, "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP224r1, &_EC_brainpoolP224r1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP224t1, &_EC_brainpoolP224t1.h, 0, "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP256r1, &_EC_brainpoolP256r1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP256t1, &_EC_brainpoolP256t1.h, 0, "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP320r1, &_EC_brainpoolP320r1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP320t1, &_EC_brainpoolP320t1.h, 0, "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP384r1, &_EC_brainpoolP384r1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP384t1, &_EC_brainpoolP384t1.h, 0, "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP512r1, &_EC_brainpoolP512r1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, + {NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, /* ANSSI */ - { NID_FRP256v1, &_EC_FRP256v1.h, 0, "FRP256v1"} + {NID_FRP256v1, &_EC_FRP256v1.h, 0, "FRP256v1"} }; #define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element)) -static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) - { - EC_GROUP *group=NULL; - EC_POINT *P=NULL; - BN_CTX *ctx=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; - int ok=0; - int seed_len,param_len; +static EC_GROUP * +ec_group_new_from_data(const ec_list_element curve) +{ + EC_GROUP *group = NULL; + EC_POINT *P = NULL; + BN_CTX *ctx = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *order = NULL; + int ok = 0; + int seed_len, param_len; const EC_METHOD *meth; const EC_CURVE_DATA *data; const unsigned char *params; - if ((ctx = BN_CTX_new()) == NULL) - { + if ((ctx = BN_CTX_new()) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE); goto err; - } - + } data = curve.data; - seed_len = data->seed_len; + seed_len = data->seed_len; param_len = data->param_len; - params = (const unsigned char *)(data+1); /* skip header */ - params += seed_len; /* skip seed */ + params = (const unsigned char *) (data + 1); /* skip header */ + params += seed_len; /* skip seed */ - if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL)) - || !(a = BN_bin2bn(params+1*param_len, param_len, NULL)) - || !(b = BN_bin2bn(params+2*param_len, param_len, NULL))) - { + if (!(p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) || + !(a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) || + !(b = BN_bin2bn(params + 2 * param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - - if (curve.meth != 0) - { + } + if (curve.meth != 0) { meth = curve.meth(); if (((group = EC_GROUP_new(meth)) == NULL) || - (!(group->meth->group_set_curve(group, p, a, b, ctx)))) - { + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } - else if (data->field_type == NID_X9_62_prime_field) - { - if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) - { + } else if (data->field_type == NID_X9_62_prime_field) { + if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } + } #ifndef OPENSSL_NO_EC2M - else /* field_type == NID_X9_62_characteristic_two_field */ - { - if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) - { + else { /* field_type == + * NID_X9_62_characteristic_two_field */ + if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } + } #endif - if ((P = EC_POINT_new(group)) == NULL) - { + if ((P = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - - if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL)) - || !(y = BN_bin2bn(params+4*param_len, param_len, NULL))) - { + } + if (!(x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) + || !(y = BN_bin2bn(params + 4 * param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) - { + } + if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - if (!(order = BN_bin2bn(params+5*param_len, param_len, NULL)) - || !BN_set_word(x, (BN_ULONG)data->cofactor)) - { + } + if (!(order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) + || !BN_set_word(x, (BN_ULONG) data->cofactor)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; - } - if (!EC_GROUP_set_generator(group, P, order, x)) - { + } + if (!EC_GROUP_set_generator(group, P, order, x)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } - if (seed_len) - { - if (!EC_GROUP_set_seed(group, params-seed_len, seed_len)) - { + } + if (seed_len) { + if (!EC_GROUP_set_seed(group, params - seed_len, seed_len)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; - } } - ok=1; + } + ok = 1; err: - if (!ok) - { + if (!ok) { EC_GROUP_free(group); group = NULL; - } + } if (P) EC_POINT_free(P); if (ctx) @@ -2528,48 +2997,45 @@ err: if (y) BN_free(y); return group; - } +} -EC_GROUP *EC_GROUP_new_by_curve_name(int nid) - { +EC_GROUP * +EC_GROUP_new_by_curve_name(int nid) +{ size_t i; EC_GROUP *ret = NULL; if (nid <= 0) return NULL; - for (i=0; i -EC_KEY *EC_KEY_new(void) - { +EC_KEY * +EC_KEY_new(void) +{ EC_KEY *ret; - ret=(EC_KEY *)malloc(sizeof(EC_KEY)); - if (ret == NULL) - { + ret = (EC_KEY *) malloc(sizeof(EC_KEY)); + if (ret == NULL) { ECerr(EC_F_EC_KEY_NEW, ERR_R_MALLOC_FAILURE); - return(NULL); - } - - ret->version = 1; + return (NULL); + } + ret->version = 1; ret->flags = 0; - ret->group = NULL; + ret->group = NULL; ret->pub_key = NULL; - ret->priv_key= NULL; - ret->enc_flag= 0; + ret->priv_key = NULL; + ret->enc_flag = 0; ret->conv_form = POINT_CONVERSION_UNCOMPRESSED; - ret->references= 1; + ret->references = 1; ret->method_data = NULL; - return(ret); - } + return (ret); +} -EC_KEY *EC_KEY_new_by_curve_name(int nid) - { +EC_KEY * +EC_KEY_new_by_curve_name(int nid) +{ EC_KEY *ret = EC_KEY_new(); if (ret == NULL) return NULL; ret->group = EC_GROUP_new_by_curve_name(nid); - if (ret->group == NULL) - { + if (ret->group == NULL) { EC_KEY_free(ret); return NULL; - } - return ret; } + return ret; +} -void EC_KEY_free(EC_KEY *r) - { +void +EC_KEY_free(EC_KEY * r) +{ int i; - if (r == NULL) return; + if (r == NULL) + return; - i=CRYPTO_add(&r->references,-1,CRYPTO_LOCK_EC); - if (i > 0) return; + i = CRYPTO_add(&r->references, -1, CRYPTO_LOCK_EC); + if (i > 0) + return; - if (r->group != NULL) + if (r->group != NULL) EC_GROUP_free(r->group); - if (r->pub_key != NULL) + if (r->pub_key != NULL) EC_POINT_free(r->pub_key); if (r->priv_key != NULL) BN_clear_free(r->priv_key); EC_EX_DATA_free_all_data(&r->method_data); - OPENSSL_cleanse((void *)r, sizeof(EC_KEY)); + OPENSSL_cleanse((void *) r, sizeof(EC_KEY)); free(r); - } +} -EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) - { +EC_KEY * +EC_KEY_copy(EC_KEY * dest, const EC_KEY * src) +{ EC_EXTRA_DATA *d; - if (dest == NULL || src == NULL) - { + if (dest == NULL || src == NULL) { ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } + } /* copy the parameters */ - if (src->group) - { + if (src->group) { const EC_METHOD *meth = EC_GROUP_method_of(src->group); /* clear the old group */ if (dest->group) @@ -146,10 +147,9 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) return NULL; if (!EC_GROUP_copy(dest->group, src->group)) return NULL; - } - /* copy the public key */ - if (src->pub_key && src->group) - { + } + /* copy the public key */ + if (src->pub_key && src->group) { if (dest->pub_key) EC_POINT_free(dest->pub_key); dest->pub_key = EC_POINT_new(src->group); @@ -157,83 +157,81 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) return NULL; if (!EC_POINT_copy(dest->pub_key, src->pub_key)) return NULL; - } + } /* copy the private key */ - if (src->priv_key) - { - if (dest->priv_key == NULL) - { + if (src->priv_key) { + if (dest->priv_key == NULL) { dest->priv_key = BN_new(); if (dest->priv_key == NULL) return NULL; - } + } if (!BN_copy(dest->priv_key, src->priv_key)) return NULL; - } + } /* copy method/extra data */ EC_EX_DATA_free_all_data(&dest->method_data); - for (d = src->method_data; d != NULL; d = d->next) - { + for (d = src->method_data; d != NULL; d = d->next) { void *t = d->dup_func(d->data); - + if (t == NULL) return 0; - if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, d->free_func, d->clear_free_func)) + if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, + d->free_func, d->clear_free_func)) return 0; - } + } /* copy the rest */ - dest->enc_flag = src->enc_flag; + dest->enc_flag = src->enc_flag; dest->conv_form = src->conv_form; - dest->version = src->version; + dest->version = src->version; dest->flags = src->flags; return dest; - } +} -EC_KEY *EC_KEY_dup(const EC_KEY *ec_key) - { +EC_KEY * +EC_KEY_dup(const EC_KEY * ec_key) +{ EC_KEY *ret = EC_KEY_new(); if (ret == NULL) return NULL; - if (EC_KEY_copy(ret, ec_key) == NULL) - { + if (EC_KEY_copy(ret, ec_key) == NULL) { EC_KEY_free(ret); return NULL; - } - return ret; } + return ret; +} -int EC_KEY_up_ref(EC_KEY *r) - { +int +EC_KEY_up_ref(EC_KEY * r) +{ int i = CRYPTO_add(&r->references, 1, CRYPTO_LOCK_EC); return ((i > 1) ? 1 : 0); - } +} -int EC_KEY_generate_key(EC_KEY *eckey) - { - int ok = 0; - BN_CTX *ctx = NULL; - BIGNUM *priv_key = NULL, *order = NULL; +int +EC_KEY_generate_key(EC_KEY * eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + BIGNUM *priv_key = NULL, *order = NULL; EC_POINT *pub_key = NULL; - if (!eckey || !eckey->group) - { + if (!eckey || !eckey->group) { ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if ((order = BN_new()) == NULL) goto err; - if ((ctx = BN_CTX_new()) == NULL) goto err; + } + if ((order = BN_new()) == NULL) + goto err; + if ((ctx = BN_CTX_new()) == NULL) + goto err; - if (eckey->priv_key == NULL) - { + if (eckey->priv_key == NULL) { priv_key = BN_new(); if (priv_key == NULL) goto err; - } - else + } else priv_key = eckey->priv_key; if (!EC_GROUP_get_order(eckey->group, order, ctx)) @@ -244,127 +242,115 @@ int EC_KEY_generate_key(EC_KEY *eckey) goto err; while (BN_is_zero(priv_key)); - if (eckey->pub_key == NULL) - { + if (eckey->pub_key == NULL) { pub_key = EC_POINT_new(eckey->group); if (pub_key == NULL) goto err; - } - else + } else pub_key = eckey->pub_key; if (!EC_POINT_mul(eckey->group, pub_key, priv_key, NULL, NULL, ctx)) goto err; eckey->priv_key = priv_key; - eckey->pub_key = pub_key; + eckey->pub_key = pub_key; - ok=1; + ok = 1; -err: +err: if (order) BN_free(order); - if (pub_key != NULL && eckey->pub_key == NULL) + if (pub_key != NULL && eckey->pub_key == NULL) EC_POINT_free(pub_key); if (priv_key != NULL && eckey->priv_key == NULL) BN_free(priv_key); if (ctx != NULL) BN_CTX_free(ctx); - return(ok); - } + return (ok); +} -int EC_KEY_check_key(const EC_KEY *eckey) - { - int ok = 0; - BN_CTX *ctx = NULL; - const BIGNUM *order = NULL; +int +EC_KEY_check_key(const EC_KEY * eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + const BIGNUM *order = NULL; EC_POINT *point = NULL; - if (!eckey || !eckey->group || !eckey->pub_key) - { + if (!eckey || !eckey->group || !eckey->pub_key) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) - { + } + if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_AT_INFINITY); goto err; - } - + } if ((ctx = BN_CTX_new()) == NULL) goto err; if ((point = EC_POINT_new(eckey->group)) == NULL) goto err; /* testing whether the pub_key is on the elliptic curve */ - if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx)) - { + if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } + } /* testing whether pub_key * order is the point at infinity */ order = &eckey->group->order; - if (BN_is_zero(order)) - { + if (BN_is_zero(order)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER); goto err; - } - if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) - { + } + if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB); goto err; - } - if (!EC_POINT_is_at_infinity(eckey->group, point)) - { + } + if (!EC_POINT_is_at_infinity(eckey->group, point)) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER); goto err; - } - /* in case the priv_key is present : - * check if generator * priv_key == pub_key + } + /* + * in case the priv_key is present : check if generator * priv_key == + * pub_key */ - if (eckey->priv_key) - { - if (BN_cmp(eckey->priv_key, order) >= 0) - { + if (eckey->priv_key) { + if (BN_cmp(eckey->priv_key, order) >= 0) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER); goto err; - } + } if (!EC_POINT_mul(eckey->group, point, eckey->priv_key, - NULL, NULL, ctx)) - { + NULL, NULL, ctx)) { ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB); goto err; - } - if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, - ctx) != 0) - { + } + if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, + ctx) != 0) { ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY); goto err; - } } + } ok = 1; err: - if (ctx != NULL) + if (ctx != NULL) BN_CTX_free(ctx); if (point != NULL) EC_POINT_free(point); - return(ok); - } + return (ok); +} -int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) - { +int +EC_KEY_set_public_key_affine_coordinates(EC_KEY * key, BIGNUM * x, BIGNUM * y) +{ BN_CTX *ctx = NULL; BIGNUM *tx, *ty; EC_POINT *point = NULL; int ok = 0, tmp_nid, is_char_two = 0; - if (!key || !key->group || !x || !y) - { + if (!key || !key->group || !x || !y) { ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, - ERR_R_PASSED_NULL_PARAMETER); + ERR_R_PASSED_NULL_PARAMETER); return 0; - } + } ctx = BN_CTX_new(); if (!ctx) goto err; @@ -376,41 +362,38 @@ int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(key->group)); - if (tmp_nid == NID_X9_62_characteristic_two_field) + if (tmp_nid == NID_X9_62_characteristic_two_field) is_char_two = 1; tx = BN_CTX_get(ctx); ty = BN_CTX_get(ctx); #ifndef OPENSSL_NO_EC2M - if (is_char_two) - { + if (is_char_two) { if (!EC_POINT_set_affine_coordinates_GF2m(key->group, point, - x, y, ctx)) + x, y, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(key->group, point, - tx, ty, ctx)) + tx, ty, ctx)) goto err; - } - else + } else #endif - { + { if (!EC_POINT_set_affine_coordinates_GFp(key->group, point, - x, y, ctx)) + x, y, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GFp(key->group, point, - tx, ty, ctx)) + tx, ty, ctx)) goto err; - } - /* Check if retrieved coordinates match originals: if not values - * are out of range. + } + /* + * Check if retrieved coordinates match originals: if not values are + * out of range. */ - if (BN_cmp(x, tx) || BN_cmp(y, ty)) - { + if (BN_cmp(x, tx) || BN_cmp(y, ty)) { ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, - EC_R_COORDINATES_OUT_OF_RANGE); + EC_R_COORDINATES_OUT_OF_RANGE); goto err; - } - + } if (!EC_KEY_set_public_key(key, point)) goto err; @@ -419,79 +402,92 @@ int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) ok = 1; - err: +err: if (ctx) BN_CTX_free(ctx); if (point) EC_POINT_free(point); return ok; - } +} -const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key) - { +const EC_GROUP * +EC_KEY_get0_group(const EC_KEY * key) +{ return key->group; - } +} -int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group) - { +int +EC_KEY_set_group(EC_KEY * key, const EC_GROUP * group) +{ if (key->group != NULL) EC_GROUP_free(key->group); key->group = EC_GROUP_dup(group); return (key->group == NULL) ? 0 : 1; - } +} -const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key) - { +const BIGNUM * +EC_KEY_get0_private_key(const EC_KEY * key) +{ return key->priv_key; - } +} -int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *priv_key) - { +int +EC_KEY_set_private_key(EC_KEY * key, const BIGNUM * priv_key) +{ if (key->priv_key) BN_clear_free(key->priv_key); key->priv_key = BN_dup(priv_key); return (key->priv_key == NULL) ? 0 : 1; - } +} -const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key) - { +const EC_POINT * +EC_KEY_get0_public_key(const EC_KEY * key) +{ return key->pub_key; - } +} -int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub_key) - { +int +EC_KEY_set_public_key(EC_KEY * key, const EC_POINT * pub_key) +{ if (key->pub_key != NULL) EC_POINT_free(key->pub_key); key->pub_key = EC_POINT_dup(pub_key, key->group); return (key->pub_key == NULL) ? 0 : 1; - } +} -unsigned int EC_KEY_get_enc_flags(const EC_KEY *key) - { +unsigned int +EC_KEY_get_enc_flags(const EC_KEY * key) +{ return key->enc_flag; - } +} -void EC_KEY_set_enc_flags(EC_KEY *key, unsigned int flags) - { +void +EC_KEY_set_enc_flags(EC_KEY * key, unsigned int flags) +{ key->enc_flag = flags; - } +} -point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key) - { +point_conversion_form_t +EC_KEY_get_conv_form(const EC_KEY * key) +{ return key->conv_form; - } +} -void EC_KEY_set_conv_form(EC_KEY *key, point_conversion_form_t cform) - { +void +EC_KEY_set_conv_form(EC_KEY * key, point_conversion_form_t cform) +{ key->conv_form = cform; if (key->group != NULL) EC_GROUP_set_point_conversion_form(key->group, cform); - } - -void *EC_KEY_get_key_method_data(EC_KEY *key, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +} + +void * +EC_KEY_get_key_method_data(EC_KEY *key, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ void *ret; CRYPTO_r_lock(CRYPTO_LOCK_EC); @@ -499,11 +495,14 @@ void *EC_KEY_get_key_method_data(EC_KEY *key, CRYPTO_r_unlock(CRYPTO_LOCK_EC); return ret; - } - -void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +} + +void * +EC_KEY_insert_key_method_data(EC_KEY * key, void *data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA *ex_data; CRYPTO_w_lock(CRYPTO_LOCK_EC); @@ -513,32 +512,37 @@ void *EC_KEY_insert_key_method_data(EC_KEY *key, void *data, CRYPTO_w_unlock(CRYPTO_LOCK_EC); return ex_data; - } +} -void EC_KEY_set_asn1_flag(EC_KEY *key, int flag) - { +void +EC_KEY_set_asn1_flag(EC_KEY * key, int flag) +{ if (key->group != NULL) EC_GROUP_set_asn1_flag(key->group, flag); - } +} -int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx) - { +int +EC_KEY_precompute_mult(EC_KEY * key, BN_CTX * ctx) +{ if (key->group == NULL) return 0; return EC_GROUP_precompute_mult(key->group, ctx); - } +} -int EC_KEY_get_flags(const EC_KEY *key) - { +int +EC_KEY_get_flags(const EC_KEY * key) +{ return key->flags; - } +} -void EC_KEY_set_flags(EC_KEY *key, int flags) - { +void +EC_KEY_set_flags(EC_KEY * key, int flags) +{ key->flags |= flags; - } +} -void EC_KEY_clear_flags(EC_KEY *key, int flags) - { +void +EC_KEY_clear_flags(EC_KEY * key, int flags) +{ key->flags &= ~flags; - } +} diff --git a/lib/libssl/src/crypto/ec/ec_lib.c b/lib/libssl/src/crypto/ec/ec_lib.c index 546fd08e382..b37efac246a 100644 --- a/lib/libssl/src/crypto/ec/ec_lib.c +++ b/lib/libssl/src/crypto/ec/ec_lib.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Binary polynomial ECC support in OpenSSL originally developed by + * Binary polynomial ECC support in OpenSSL originally developed by * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. */ @@ -73,28 +73,24 @@ static const char EC_version[] = "EC" OPENSSL_VERSION_PTEXT; /* functions for EC_GROUP objects */ -EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) - { +EC_GROUP * +EC_GROUP_new(const EC_METHOD * meth) +{ EC_GROUP *ret; - if (meth == NULL) - { + if (meth == NULL) { ECerr(EC_F_EC_GROUP_NEW, EC_R_SLOT_FULL); return NULL; - } - if (meth->group_init == 0) - { + } + if (meth->group_init == 0) { ECerr(EC_F_EC_GROUP_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return NULL; - } - + } ret = malloc(sizeof *ret); - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_GROUP_NEW, ERR_R_MALLOC_FAILURE); return NULL; - } - + } ret->meth = meth; ret->extra_data = NULL; @@ -103,26 +99,26 @@ EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) BN_init(&ret->order); BN_init(&ret->cofactor); - ret->curve_name = 0; - ret->asn1_flag = 0; - ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED; + ret->curve_name = 0; + ret->asn1_flag = 0; + ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED; ret->seed = NULL; ret->seed_len = 0; - if (!meth->group_init(ret)) - { + if (!meth->group_init(ret)) { free(ret); return NULL; - } - - return ret; } + return ret; +} -void EC_GROUP_free(EC_GROUP *group) - { - if (!group) return; +void +EC_GROUP_free(EC_GROUP * group) +{ + if (!group) + return; if (group->meth->group_finish != 0) group->meth->group_finish(group); @@ -138,12 +134,14 @@ void EC_GROUP_free(EC_GROUP *group) free(group->seed); free(group); - } - +} + -void EC_GROUP_clear_free(EC_GROUP *group) - { - if (!group) return; +void +EC_GROUP_clear_free(EC_GROUP * group) +{ + if (!group) + return; if (group->meth->group_clear_finish != 0) group->meth->group_clear_finish(group); @@ -157,74 +155,69 @@ void EC_GROUP_clear_free(EC_GROUP *group) BN_clear_free(&group->order); BN_clear_free(&group->cofactor); - if (group->seed) - { + if (group->seed) { OPENSSL_cleanse(group->seed, group->seed_len); free(group->seed); - } - + } OPENSSL_cleanse(group, sizeof *group); free(group); - } +} -int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +EC_GROUP_copy(EC_GROUP * dest, const EC_GROUP * src) +{ EC_EXTRA_DATA *d; - if (dest->meth->group_copy == 0) - { + if (dest->meth->group_copy == 0) { ECerr(EC_F_EC_GROUP_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (dest->meth != src->meth) - { + } + if (dest->meth != src->meth) { ECerr(EC_F_EC_GROUP_COPY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } + } if (dest == src) return 1; - + EC_EX_DATA_free_all_data(&dest->extra_data); - for (d = src->extra_data; d != NULL; d = d->next) - { + for (d = src->extra_data; d != NULL; d = d->next) { void *t = d->dup_func(d->data); - + if (t == NULL) return 0; - if (!EC_EX_DATA_set_data(&dest->extra_data, t, d->dup_func, d->free_func, d->clear_free_func)) + if (!EC_EX_DATA_set_data(&dest->extra_data, t, d->dup_func, + d->free_func, d->clear_free_func)) return 0; - } + } - if (src->generator != NULL) - { - if (dest->generator == NULL) - { + if (src->generator != NULL) { + if (dest->generator == NULL) { dest->generator = EC_POINT_new(dest); - if (dest->generator == NULL) return 0; - } - if (!EC_POINT_copy(dest->generator, src->generator)) return 0; + if (dest->generator == NULL) + return 0; } - else - { + if (!EC_POINT_copy(dest->generator, src->generator)) + return 0; + } else { /* src->generator == NULL */ - if (dest->generator != NULL) - { + if (dest->generator != NULL) { EC_POINT_clear_free(dest->generator); dest->generator = NULL; - } } + } - if (!BN_copy(&dest->order, &src->order)) return 0; - if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0; + if (!BN_copy(&dest->order, &src->order)) + return 0; + if (!BN_copy(&dest->cofactor, &src->cofactor)) + return 0; dest->curve_name = src->curve_name; - dest->asn1_flag = src->asn1_flag; - dest->asn1_form = src->asn1_form; + dest->asn1_flag = src->asn1_flag; + dest->asn1_form = src->asn1_form; - if (src->seed) - { + if (src->seed) { if (dest->seed) free(dest->seed); dest->seed = malloc(src->seed_len); @@ -233,153 +226,168 @@ int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src) if (!memcpy(dest->seed, src->seed, src->seed_len)) return 0; dest->seed_len = src->seed_len; - } - else - { + } else { if (dest->seed) free(dest->seed); dest->seed = NULL; dest->seed_len = 0; - } - + } + return dest->meth->group_copy(dest, src); - } +} -EC_GROUP *EC_GROUP_dup(const EC_GROUP *a) - { +EC_GROUP * +EC_GROUP_dup(const EC_GROUP * a) +{ EC_GROUP *t = NULL; int ok = 0; - if (a == NULL) return NULL; + if (a == NULL) + return NULL; - if ((t = EC_GROUP_new(a->meth)) == NULL) return(NULL); - if (!EC_GROUP_copy(t, a)) goto err; + if ((t = EC_GROUP_new(a->meth)) == NULL) + return (NULL); + if (!EC_GROUP_copy(t, a)) + goto err; ok = 1; - err: - if (!ok) - { - if (t) EC_GROUP_free(t); +err: + if (!ok) { + if (t) + EC_GROUP_free(t); return NULL; - } - else return t; - } + } else + return t; +} -const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group) - { +const EC_METHOD * +EC_GROUP_method_of(const EC_GROUP *group) +{ return group->meth; - } +} -int EC_METHOD_get_field_type(const EC_METHOD *meth) - { - return meth->field_type; - } +int +EC_METHOD_get_field_type(const EC_METHOD *meth) +{ + return meth->field_type; +} -int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor) - { - if (generator == NULL) - { +int +EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, + const BIGNUM *order, const BIGNUM *cofactor) +{ + if (generator == NULL) { ECerr(EC_F_EC_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER); - return 0 ; - } - - if (group->generator == NULL) - { + return 0; + } + if (group->generator == NULL) { group->generator = EC_POINT_new(group); - if (group->generator == NULL) return 0; - } - if (!EC_POINT_copy(group->generator, generator)) return 0; + if (group->generator == NULL) + return 0; + } + if (!EC_POINT_copy(group->generator, generator)) + return 0; - if (order != NULL) - { if (!BN_copy(&group->order, order)) return 0; } - else + if (order != NULL) { + if (!BN_copy(&group->order, order)) + return 0; + } else BN_zero(&group->order); - if (cofactor != NULL) - { if (!BN_copy(&group->cofactor, cofactor)) return 0; } - else + if (cofactor != NULL) { + if (!BN_copy(&group->cofactor, cofactor)) + return 0; + } else BN_zero(&group->cofactor); return 1; - } +} -const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group) - { +const EC_POINT * +EC_GROUP_get0_generator(const EC_GROUP *group) +{ return group->generator; - } +} -int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) - { +int +EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) +{ if (!BN_copy(order, &group->order)) return 0; return !BN_is_zero(order); - } +} -int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx) - { +int +EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx) +{ if (!BN_copy(cofactor, &group->cofactor)) return 0; return !BN_is_zero(&group->cofactor); - } +} -void EC_GROUP_set_curve_name(EC_GROUP *group, int nid) - { +void +EC_GROUP_set_curve_name(EC_GROUP * group, int nid) +{ group->curve_name = nid; - } +} -int EC_GROUP_get_curve_name(const EC_GROUP *group) - { +int +EC_GROUP_get_curve_name(const EC_GROUP * group) +{ return group->curve_name; - } +} -void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag) - { +void +EC_GROUP_set_asn1_flag(EC_GROUP * group, int flag) +{ group->asn1_flag = flag; - } +} -int EC_GROUP_get_asn1_flag(const EC_GROUP *group) - { +int +EC_GROUP_get_asn1_flag(const EC_GROUP * group) +{ return group->asn1_flag; - } +} -void EC_GROUP_set_point_conversion_form(EC_GROUP *group, - point_conversion_form_t form) - { +void +EC_GROUP_set_point_conversion_form(EC_GROUP * group, + point_conversion_form_t form) +{ group->asn1_form = form; - } +} -point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group) - { +point_conversion_form_t +EC_GROUP_get_point_conversion_form(const EC_GROUP * group) +{ return group->asn1_form; - } +} -size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len) - { - if (group->seed) - { +size_t +EC_GROUP_set_seed(EC_GROUP * group, const unsigned char *p, size_t len) +{ + if (group->seed) { free(group->seed); group->seed = NULL; group->seed_len = 0; - } - + } if (!len || !p) return 1; @@ -389,94 +397,101 @@ size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len) group->seed_len = len; return len; - } +} -unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group) - { +unsigned char * +EC_GROUP_get0_seed(const EC_GROUP * group) +{ return group->seed; - } +} -size_t EC_GROUP_get_seed_len(const EC_GROUP *group) - { +size_t +EC_GROUP_get_seed_len(const EC_GROUP * group) +{ return group->seed_len; - } +} -int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_set_curve == 0) - { +int +EC_GROUP_set_curve_GFp(EC_GROUP * group, const BIGNUM * p, const BIGNUM * a, + const BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_set_curve == 0) { ECerr(EC_F_EC_GROUP_SET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_set_curve(group, p, a, b, ctx); } + return group->meth->group_set_curve(group, p, a, b, ctx); +} -int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_get_curve == 0) - { +int +EC_GROUP_get_curve_GFp(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, + BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_get_curve == 0) { ECerr(EC_F_EC_GROUP_GET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_curve(group, p, a, b, ctx); } + return group->meth->group_get_curve(group, p, a, b, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_set_curve == 0) - { +int +EC_GROUP_set_curve_GF2m(EC_GROUP * group, const BIGNUM * p, const BIGNUM * a, + const BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_set_curve == 0) { ECerr(EC_F_EC_GROUP_SET_CURVE_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_set_curve(group, p, a, b, ctx); } + return group->meth->group_set_curve(group, p, a, b, ctx); +} -int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { - if (group->meth->group_get_curve == 0) - { +int +EC_GROUP_get_curve_GF2m(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, + BIGNUM * b, BN_CTX * ctx) +{ + if (group->meth->group_get_curve == 0) { ECerr(EC_F_EC_GROUP_GET_CURVE_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_curve(group, p, a, b, ctx); } + return group->meth->group_get_curve(group, p, a, b, ctx); +} #endif -int EC_GROUP_get_degree(const EC_GROUP *group) - { - if (group->meth->group_get_degree == 0) - { +int +EC_GROUP_get_degree(const EC_GROUP * group) +{ + if (group->meth->group_get_degree == 0) { ECerr(EC_F_EC_GROUP_GET_DEGREE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_get_degree(group); } + return group->meth->group_get_degree(group); +} -int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { - if (group->meth->group_check_discriminant == 0) - { +int +EC_GROUP_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ + if (group->meth->group_check_discriminant == 0) { ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - return group->meth->group_check_discriminant(group, ctx); } + return group->meth->group_check_discriminant(group, ctx); +} -int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) - { - int r = 0; +int +EC_GROUP_cmp(const EC_GROUP * a, const EC_GROUP * b, BN_CTX * ctx) +{ + int r = 0; BIGNUM *a1, *a2, *a3, *b1, *b2, *b3; BN_CTX *ctx_new = NULL; - /* compare the field types*/ + /* compare the field types */ if (EC_METHOD_get_field_type(EC_GROUP_method_of(a)) != EC_METHOD_get_field_type(EC_GROUP_method_of(b))) return 1; @@ -489,7 +504,7 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) ctx_new = ctx = BN_CTX_new(); if (!ctx) return -1; - + BN_CTX_start(ctx); a1 = BN_CTX_get(ctx); a2 = BN_CTX_get(ctx); @@ -497,16 +512,15 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) b1 = BN_CTX_get(ctx); b2 = BN_CTX_get(ctx); b3 = BN_CTX_get(ctx); - if (!b3) - { + if (!b3) { BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return -1; - } - - /* XXX This approach assumes that the external representation - * of curves over the same field type is the same. + } + /* + * XXX This approach assumes that the external representation of + * curves over the same field type is the same. */ if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) || !b->meth->group_get_curve(b, b1, b2, b3, ctx)) @@ -517,51 +531,50 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) /* XXX EC_POINT_cmp() assumes that the methods are equal */ if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a), - EC_GROUP_get0_generator(b), ctx)) + EC_GROUP_get0_generator(b), ctx)) r = 1; - if (!r) - { + if (!r) { /* compare the order and cofactor */ if (!EC_GROUP_get_order(a, a1, ctx) || !EC_GROUP_get_order(b, b1, ctx) || !EC_GROUP_get_cofactor(a, a2, ctx) || - !EC_GROUP_get_cofactor(b, b2, ctx)) - { + !EC_GROUP_get_cofactor(b, b2, ctx)) { BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return -1; - } + } if (BN_cmp(a1, b1) || BN_cmp(a2, b2)) r = 1; - } - + } BN_CTX_end(ctx); if (ctx_new) BN_CTX_free(ctx); return r; - } +} /* this has 'package' visibility */ -int EC_EX_DATA_set_data(EC_EXTRA_DATA **ex_data, void *data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +int +EC_EX_DATA_set_data(EC_EXTRA_DATA ** ex_data, void *data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return 0; - for (d = *ex_data; d != NULL; d = d->next) - { - if (d->dup_func == dup_func && d->free_func == free_func && d->clear_free_func == clear_free_func) - { + for (d = *ex_data; d != NULL; d = d->next) { + if (d->dup_func == dup_func && d->free_func == free_func && + d->clear_free_func == clear_free_func) { ECerr(EC_F_EC_EX_DATA_SET_DATA, EC_R_SLOT_FULL); return 0; - } } + } if (data == NULL) /* no explicit entry needed */ @@ -580,163 +593,169 @@ int EC_EX_DATA_set_data(EC_EXTRA_DATA **ex_data, void *data, *ex_data = d; return 1; - } +} /* this has 'package' visibility */ -void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void * +EC_EX_DATA_get_data(const EC_EXTRA_DATA * ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ const EC_EXTRA_DATA *d; - for (d = ex_data; d != NULL; d = d->next) - { + for (d = ex_data; d != NULL; d = d->next) { if (d->dup_func == dup_func && d->free_func == free_func && d->clear_free_func == clear_free_func) return d->data; - } - - return NULL; } + return NULL; +} + /* this has 'package' visibility */ -void EC_EX_DATA_free_data(EC_EXTRA_DATA **ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void +EC_EX_DATA_free_data(EC_EXTRA_DATA ** ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA **p; if (ex_data == NULL) return; - for (p = ex_data; *p != NULL; p = &((*p)->next)) - { - if ((*p)->dup_func == dup_func && (*p)->free_func == free_func && (*p)->clear_free_func == clear_free_func) - { + for (p = ex_data; *p != NULL; p = &((*p)->next)) { + if ((*p)->dup_func == dup_func && + (*p)->free_func == free_func && + (*p)->clear_free_func == clear_free_func) { EC_EXTRA_DATA *next = (*p)->next; (*p)->free_func((*p)->data); free(*p); - + *p = next; return; - } } } +} /* this has 'package' visibility */ -void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **ex_data, - void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)) - { +void +EC_EX_DATA_clear_free_data(EC_EXTRA_DATA ** ex_data, + void *(*dup_func) (void *), + void (*free_func) (void *), + void (*clear_free_func) (void *)) +{ EC_EXTRA_DATA **p; if (ex_data == NULL) return; - for (p = ex_data; *p != NULL; p = &((*p)->next)) - { - if ((*p)->dup_func == dup_func && (*p)->free_func == free_func && (*p)->clear_free_func == clear_free_func) - { + for (p = ex_data; *p != NULL; p = &((*p)->next)) { + if ((*p)->dup_func == dup_func && + (*p)->free_func == free_func && + (*p)->clear_free_func == clear_free_func) { EC_EXTRA_DATA *next = (*p)->next; (*p)->clear_free_func((*p)->data); free(*p); - + *p = next; return; - } } } +} /* this has 'package' visibility */ -void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **ex_data) - { +void +EC_EX_DATA_free_all_data(EC_EXTRA_DATA ** ex_data) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return; d = *ex_data; - while (d) - { + while (d) { EC_EXTRA_DATA *next = d->next; - + d->free_func(d->data); free(d); - + d = next; - } - *ex_data = NULL; } + *ex_data = NULL; +} /* this has 'package' visibility */ -void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **ex_data) - { +void +EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA ** ex_data) +{ EC_EXTRA_DATA *d; if (ex_data == NULL) return; d = *ex_data; - while (d) - { + while (d) { EC_EXTRA_DATA *next = d->next; - + d->clear_free_func(d->data); free(d); - + d = next; - } - *ex_data = NULL; } + *ex_data = NULL; +} /* functions for EC_POINT objects */ -EC_POINT *EC_POINT_new(const EC_GROUP *group) - { +EC_POINT * +EC_POINT_new(const EC_GROUP * group) +{ EC_POINT *ret; - if (group == NULL) - { + if (group == NULL) { ECerr(EC_F_EC_POINT_NEW, ERR_R_PASSED_NULL_PARAMETER); return NULL; - } - if (group->meth->point_init == 0) - { + } + if (group->meth->point_init == 0) { ECerr(EC_F_EC_POINT_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return NULL; - } - + } ret = malloc(sizeof *ret); - if (ret == NULL) - { + if (ret == NULL) { ECerr(EC_F_EC_POINT_NEW, ERR_R_MALLOC_FAILURE); return NULL; - } - + } ret->meth = group->meth; - - if (!ret->meth->point_init(ret)) - { + + if (!ret->meth->point_init(ret)) { free(ret); return NULL; - } - - return ret; } + return ret; +} -void EC_POINT_free(EC_POINT *point) - { - if (!point) return; +void +EC_POINT_free(EC_POINT * point) +{ + if (!point) + return; if (point->meth->point_finish != 0) point->meth->point_finish(point); free(point); - } - +} -void EC_POINT_clear_free(EC_POINT *point) - { - if (!point) return; + +void +EC_POINT_clear_free(EC_POINT * point) +{ + if (!point) + return; if (point->meth->point_clear_finish != 0) point->meth->point_clear_finish(point); @@ -744,301 +763,290 @@ void EC_POINT_clear_free(EC_POINT *point) point->meth->point_finish(point); OPENSSL_cleanse(point, sizeof *point); free(point); - } +} -int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src) - { - if (dest->meth->point_copy == 0) - { +int +EC_POINT_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (dest->meth->point_copy == 0) { ECerr(EC_F_EC_POINT_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (dest->meth != src->meth) - { + } + if (dest->meth != src->meth) { ECerr(EC_F_EC_POINT_COPY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } + } if (dest == src) return 1; return dest->meth->point_copy(dest, src); - } +} -EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group) - { +EC_POINT * +EC_POINT_dup(const EC_POINT * a, const EC_GROUP * group) +{ EC_POINT *t; int r; - if (a == NULL) return NULL; + if (a == NULL) + return NULL; t = EC_POINT_new(group); - if (t == NULL) return(NULL); + if (t == NULL) + return (NULL); r = EC_POINT_copy(t, a); - if (!r) - { + if (!r) { EC_POINT_free(t); return NULL; - } - else return t; - } + } else + return t; +} -const EC_METHOD *EC_POINT_method_of(const EC_POINT *point) - { +const EC_METHOD * +EC_POINT_method_of(const EC_POINT * point) +{ return point->meth; - } +} -int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { - if (group->meth->point_set_to_infinity == 0) - { +int +EC_POINT_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ + if (group->meth->point_set_to_infinity == 0) { ECerr(EC_F_EC_POINT_SET_TO_INFINITY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_TO_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_to_infinity(group, point); } + return group->meth->point_set_to_infinity(group, point); +} -int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) - { - if (group->meth->point_set_Jprojective_coordinates_GFp == 0) - { +int +EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) +{ + if (group->meth->point_set_Jprojective_coordinates_GFp == 0) { ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); } + return group->meth->point_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); +} -int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) - { - if (group->meth->point_get_Jprojective_coordinates_GFp == 0) - { +int +EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) +{ + if (group->meth->point_get_Jprojective_coordinates_GFp == 0) { ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); } + return group->meth->point_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx); +} -int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_set_affine_coordinates == 0) - { +int +EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_set_affine_coordinates == 0) - { +int +EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); +} #endif -int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_get_affine_coordinates == 0) - { +int +EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - if (group->meth->point_get_affine_coordinates == 0) - { +int +EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} #endif -int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - if (group->meth->add == 0) - { +int +EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + if (group->meth->add == 0) { ECerr(EC_F_EC_POINT_ADD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if ((group->meth != r->meth) || (r->meth != a->meth) || (a->meth != b->meth)) - { + } + if ((group->meth != r->meth) || (r->meth != a->meth) || (a->meth != b->meth)) { ECerr(EC_F_EC_POINT_ADD, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->add(group, r, a, b, ctx); } + return group->meth->add(group, r, a, b, ctx); +} -int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { - if (group->meth->dbl == 0) - { +int +EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) +{ + if (group->meth->dbl == 0) { ECerr(EC_F_EC_POINT_DBL, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if ((group->meth != r->meth) || (r->meth != a->meth)) - { + } + if ((group->meth != r->meth) || (r->meth != a->meth)) { ECerr(EC_F_EC_POINT_DBL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->dbl(group, r, a, ctx); } + return group->meth->dbl(group, r, a, ctx); +} -int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) - { - if (group->meth->invert == 0) - { +int +EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) +{ + if (group->meth->invert == 0) { ECerr(EC_F_EC_POINT_INVERT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != a->meth) - { + } + if (group->meth != a->meth) { ECerr(EC_F_EC_POINT_INVERT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->invert(group, a, ctx); } + return group->meth->invert(group, a, ctx); +} -int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { - if (group->meth->is_at_infinity == 0) - { +int +EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ + if (group->meth->is_at_infinity == 0) { ECerr(EC_F_EC_POINT_IS_AT_INFINITY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_IS_AT_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->is_at_infinity(group, point); } + return group->meth->is_at_infinity(group, point); +} -int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { - if (group->meth->is_on_curve == 0) - { +int +EC_POINT_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) +{ + if (group->meth->is_on_curve == 0) { ECerr(EC_F_EC_POINT_IS_ON_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_IS_ON_CURVE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->is_on_curve(group, point, ctx); } + return group->meth->is_on_curve(group, point, ctx); +} -int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - if (group->meth->point_cmp == 0) - { +int +EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, + BN_CTX * ctx) +{ + if (group->meth->point_cmp == 0) { ECerr(EC_F_EC_POINT_CMP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return -1; - } - if ((group->meth != a->meth) || (a->meth != b->meth)) - { + } + if ((group->meth != a->meth) || (a->meth != b->meth)) { ECerr(EC_F_EC_POINT_CMP, EC_R_INCOMPATIBLE_OBJECTS); return -1; - } - return group->meth->point_cmp(group, a, b, ctx); } + return group->meth->point_cmp(group, a, b, ctx); +} -int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { - if (group->meth->make_affine == 0) - { +int +EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ + if (group->meth->make_affine == 0) { ECerr(EC_F_EC_POINT_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - return group->meth->make_affine(group, point, ctx); } + return group->meth->make_affine(group, point, ctx); +} -int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], + BN_CTX *ctx) +{ size_t i; - if (group->meth->points_make_affine == 0) - { + if (group->meth->points_make_affine == 0) { ECerr(EC_F_EC_POINTS_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - for (i = 0; i < num; i++) - { - if (group->meth != points[i]->meth) - { + } + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { ECerr(EC_F_EC_POINTS_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } } - return group->meth->points_make_affine(group, num, points, ctx); } + return group->meth->points_make_affine(group, num, points, ctx); +} /* Functions for point multiplication. @@ -1047,19 +1055,21 @@ int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], * otherwise we dispatch through methods. */ -int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); return group->meth->mul(group, r, scalar, num, points, scalars, ctx); - } +} -int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, - const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) - { +int +EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, + const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) +{ /* just a convenient interface to EC_POINTs_mul() */ const EC_POINT *points[1]; @@ -1068,11 +1078,14 @@ int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, points[0] = point; scalars[0] = p_scalar; - return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx); - } + return EC_POINTs_mul(group, r, g_scalar, + (point != NULL && p_scalar != NULL), + points, scalars, ctx); +} -int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +EC_GROUP_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_precompute_mult(group, ctx); @@ -1080,11 +1093,12 @@ int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (group->meth->precompute_mult != 0) return group->meth->precompute_mult(group, ctx); else - return 1; /* nothing to do, so report success */ - } + return 1; /* nothing to do, so report success */ +} -int EC_GROUP_have_precompute_mult(const EC_GROUP *group) - { +int +EC_GROUP_have_precompute_mult(const EC_GROUP * group) +{ if (group->meth->mul == 0) /* use default */ return ec_wNAF_have_precompute_mult(group); @@ -1092,5 +1106,6 @@ int EC_GROUP_have_precompute_mult(const EC_GROUP *group) if (group->meth->have_precompute_mult != 0) return group->meth->have_precompute_mult(group); else - return 0; /* cannot tell whether precomputation has been performed */ - } + return 0; /* cannot tell whether precomputation has + * been performed */ +} diff --git a/lib/libssl/src/crypto/ec/ec_mult.c b/lib/libssl/src/crypto/ec/ec_mult.c index b48c888048b..c0525c49406 100644 --- a/lib/libssl/src/crypto/ec/ec_mult.c +++ b/lib/libssl/src/crypto/ec/ec_mult.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -80,46 +80,49 @@ /* structure for precomputed multiples of the generator */ typedef struct ec_pre_comp_st { - const EC_GROUP *group; /* parent EC_GROUP object */ - size_t blocksize; /* block size for wNAF splitting */ - size_t numblocks; /* max. number of blocks for which we have precomputation */ - size_t w; /* window size */ - EC_POINT **points; /* array with pre-calculated multiples of generator: - * 'num' pointers to EC_POINT objects followed by a NULL */ - size_t num; /* numblocks * 2^(w-1) */ + const EC_GROUP *group; /* parent EC_GROUP object */ + size_t blocksize; /* block size for wNAF splitting */ + size_t numblocks; /* max. number of blocks for which we have + * precomputation */ + size_t w; /* window size */ + EC_POINT **points; /* array with pre-calculated multiples of + * generator: 'num' pointers to EC_POINT + * objects followed by a NULL */ + size_t num; /* numblocks * 2^(w-1) */ int references; } EC_PRE_COMP; - + /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ static void *ec_pre_comp_dup(void *); static void ec_pre_comp_free(void *); static void ec_pre_comp_clear_free(void *); -static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) - { +static EC_PRE_COMP * +ec_pre_comp_new(const EC_GROUP * group) +{ EC_PRE_COMP *ret = NULL; if (!group) return NULL; - ret = (EC_PRE_COMP *)malloc(sizeof(EC_PRE_COMP)); - if (!ret) - { + ret = (EC_PRE_COMP *) malloc(sizeof(EC_PRE_COMP)); + if (!ret) { ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } ret->group = group; - ret->blocksize = 8; /* default */ + ret->blocksize = 8; /* default */ ret->numblocks = 0; - ret->w = 4; /* default */ + ret->w = 4; /* default */ ret->points = NULL; ret->num = 0; ret->references = 1; return ret; - } +} -static void *ec_pre_comp_dup(void *src_) - { +static void * +ec_pre_comp_dup(void *src_) +{ EC_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ @@ -127,10 +130,11 @@ static void *ec_pre_comp_dup(void *src_) CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void ec_pre_comp_free(void *pre_) - { +static void +ec_pre_comp_free(void *pre_) +{ int i; EC_PRE_COMP *pre = pre_; @@ -141,19 +145,19 @@ static void ec_pre_comp_free(void *pre_) if (i > 0) return; - if (pre->points) - { + if (pre->points) { EC_POINT **p; for (p = pre->points; *p != NULL; p++) EC_POINT_free(*p); free(pre->points); - } - free(pre); } + free(pre); +} -static void ec_pre_comp_clear_free(void *pre_) - { +static void +ec_pre_comp_clear_free(void *pre_) +{ int i; EC_PRE_COMP *pre = pre_; @@ -164,20 +168,18 @@ static void ec_pre_comp_clear_free(void *pre_) if (i > 0) return; - if (pre->points) - { + if (pre->points) { EC_POINT **p; - for (p = pre->points; *p != NULL; p++) - { + for (p = pre->points; *p != NULL; p++) { EC_POINT_clear_free(*p); OPENSSL_cleanse(p, sizeof *p); - } - free(pre->points); } + free(pre->points); + } OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} @@ -190,138 +192,125 @@ static void ec_pre_comp_clear_free(void *pre_) * with the exception that the most significant digit may be only * w-1 zeros away from that next non-zero digit. */ -static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) - { +static signed char * +compute_wNAF(const BIGNUM * scalar, int w, size_t * ret_len) +{ int window_val; int ok = 0; signed char *r = NULL; int sign = 1; int bit, next_bit, mask; size_t len = 0, j; - - if (BN_is_zero(scalar)) - { + + if (BN_is_zero(scalar)) { r = malloc(1); - if (!r) - { + if (!r) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); goto err; - } + } r[0] = 0; *ret_len = 1; return r; - } - - if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ - { + } + if (w <= 0 || w > 7) { + /* 'signed char' can represent integers with + * absolute values less than 2^7 */ ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - bit = 1 << w; /* at most 128 */ - next_bit = bit << 1; /* at most 256 */ - mask = next_bit - 1; /* at most 255 */ + } + bit = 1 << w; /* at most 128 */ + next_bit = bit << 1; /* at most 256 */ + mask = next_bit - 1; /* at most 255 */ - if (BN_is_negative(scalar)) - { + if (BN_is_negative(scalar)) { sign = -1; - } - - if (scalar->d == NULL || scalar->top == 0) - { + } + if (scalar->d == NULL || scalar->top == 0) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - + } len = BN_num_bits(scalar); - r = malloc(len + 1); /* modified wNAF may be one digit longer than binary representation - * (*ret_len will be set to the actual length, i.e. at most - * BN_num_bits(scalar) + 1) */ - if (r == NULL) - { + r = malloc(len + 1); /* modified wNAF may be one digit longer than + * binary representation (*ret_len will be + * set to the actual length, i.e. at most + * BN_num_bits(scalar) + 1) */ + if (r == NULL) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); goto err; - } + } window_val = scalar->d[0] & mask; j = 0; - while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ - { + while ((window_val != 0) || (j + w + 1 < len)) { + /* if j+w+1 >= len, window_val will not increase */ int digit = 0; /* 0 <= window_val <= 2^(w+1) */ - - if (window_val & 1) - { + if (window_val & 1) { /* 0 < window_val < 2^(w+1) */ - - if (window_val & bit) - { - digit = window_val - next_bit; /* -2^w < digit < 0 */ - -#if 1 /* modified wNAF */ - if (j + w + 1 >= len) - { - /* special case for generating modified wNAFs: - * no new bits will be added into window_val, - * so using a positive digit here will decrease - * the total length of the representation */ - - digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ - } -#endif - } - else - { - digit = window_val; /* 0 < digit < 2^w */ + if (window_val & bit) { + digit = window_val - next_bit; /* -2^w < digit < 0 */ + +#if 1 /* modified wNAF */ + if (j + w + 1 >= len) { + /* + * special case for generating + * modified wNAFs: no new bits will + * be added into window_val, so using + * a positive digit here will + * decrease the total length of the + * representation + */ + + digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ } - - if (digit <= -bit || digit >= bit || !(digit & 1)) - { +#endif + } else { + digit = window_val; /* 0 < digit < 2^w */ + } + + if (digit <= -bit || digit >= bit || !(digit & 1)) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } - + } window_val -= digit; - /* now window_val is 0 or 2^(w+1) in standard wNAF generation; - * for modified window NAFs, it may also be 2^w + /* + * now window_val is 0 or 2^(w+1) in standard wNAF + * generation; for modified window NAFs, it may also + * be 2^w */ - if (window_val != 0 && window_val != next_bit && window_val != bit) - { + if (window_val != 0 && window_val != next_bit && window_val != bit) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } } - + } r[j++] = sign * digit; window_val >>= 1; window_val += bit * BN_is_bit_set(scalar, j + w); - if (window_val > next_bit) - { + if (window_val > next_bit) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } } + } - if (j > len + 1) - { + if (j > len + 1) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; - } + } len = j; ok = 1; - err: - if (!ok) - { +err: + if (!ok) { free(r); r = NULL; - } + } if (ok) *ret_len = len; return r; - } +} /* TODO: table should be optimised for the wNAF-based implementation, @@ -343,374 +332,353 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) * scalar*generator * in the addition if scalar != NULL */ -int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_wNAF_mul(const EC_GROUP * group, EC_POINT * r, const BIGNUM * scalar, + size_t num, const EC_POINT * points[], const BIGNUM * scalars[], BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; const EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t totalnum; - size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ + size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ size_t pre_points_per_block = 0; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; - size_t *wsize = NULL; /* individual window sizes */ - signed char **wNAF = NULL; /* individual wNAFs */ + size_t *wsize = NULL; /* individual window sizes */ + signed char **wNAF = NULL; /* individual wNAFs */ size_t *wNAF_len = NULL; size_t max_len = 0; size_t num_val; - EC_POINT **val = NULL; /* precomputation */ + EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; - EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */ + EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or + * 'pre_comp->points' */ const EC_PRE_COMP *pre_comp = NULL; - int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars, - * i.e. precomputation is not available */ + int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be + * treated like other scalars, i.e. + * precomputation is not available */ int ret = 0; - - if (group->meth != r->meth) - { + + if (group->meth != r->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - - if ((scalar == NULL) && (num == 0)) - { + } + if ((scalar == NULL) && (num == 0)) { return EC_POINT_set_to_infinity(group, r); - } - - for (i = 0; i < num; i++) - { - if (group->meth != points[i]->meth) - { + } + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } } + } - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; - } - - if (scalar != NULL) - { + } + if (scalar != NULL) { generator = EC_GROUP_get0_generator(group); - if (generator == NULL) - { + if (generator == NULL) { ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); goto err; - } - + } /* look if we can use precomputed multiples of generator */ pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); - if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) - { + if (pre_comp && pre_comp->numblocks && + (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) { blocksize = pre_comp->blocksize; - /* determine maximum number of blocks that wNAF splitting may yield - * (NB: maximum wNAF length is bit length plus one) */ + /* + * determine maximum number of blocks that wNAF + * splitting may yield (NB: maximum wNAF length is + * bit length plus one) + */ numblocks = (BN_num_bits(scalar) / blocksize) + 1; - /* we cannot use more blocks than we have precomputation for */ + /* + * we cannot use more blocks than we have + * precomputation for + */ if (numblocks > pre_comp->numblocks) numblocks = pre_comp->numblocks; - pre_points_per_block = (size_t)1 << (pre_comp->w - 1); + pre_points_per_block = (size_t) 1 << (pre_comp->w - 1); /* check that pre_comp looks sane */ - if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) - { + if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } } - else - { + } else { /* can't use precomputation */ pre_comp = NULL; numblocks = 1; - num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */ - } + num_scalar = 1; /* treat 'scalar' like 'num'-th + * element of 'scalars' */ } - + } totalnum = num + numblocks; - wsize = malloc(totalnum * sizeof wsize[0]); + wsize = malloc(totalnum * sizeof wsize[0]); wNAF_len = malloc(totalnum * sizeof wNAF_len[0]); - wNAF = malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */ - val_sub = malloc(totalnum * sizeof val_sub[0]); - - if (!wsize || !wNAF_len || !wNAF || !val_sub) - { + wNAF = malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for + * pivot */ + val_sub = malloc(totalnum * sizeof val_sub[0]); + + if (!wsize || !wNAF_len || !wNAF || !val_sub) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - wNAF[0] = NULL; /* preliminary pivot */ + } + wNAF[0] = NULL; /* preliminary pivot */ /* num_val will be the total number of temporarily precomputed points */ num_val = 0; - for (i = 0; i < num + num_scalar; i++) - { + for (i = 0; i < num + num_scalar; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); - num_val += (size_t)1 << (wsize[i] - 1); - wNAF[i + 1] = NULL; /* make sure we always have a pivot */ + num_val += (size_t) 1 << (wsize[i] - 1); + wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); if (wNAF[i] == NULL) goto err; if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; - } + } - if (numblocks) - { + if (numblocks) { /* we go here iff scalar != NULL */ - - if (pre_comp == NULL) - { - if (num_scalar != 1) - { + + if (pre_comp == NULL) { + if (num_scalar != 1) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - /* we have already generated a wNAF for 'scalar' */ } - else - { + /* we have already generated a wNAF for 'scalar' */ + } else { signed char *tmp_wNAF = NULL; size_t tmp_len = 0; - - if (num_scalar != 0) - { + + if (num_scalar != 0) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - - /* use the window size for which we have precomputation */ + } + /* + * use the window size for which we have + * precomputation + */ wsize[num] = pre_comp->w; tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); if (!tmp_wNAF) goto err; - if (tmp_len <= max_len) - { - /* One of the other wNAFs is at least as long - * as the wNAF belonging to the generator, - * so wNAF splitting will not buy us anything. */ + if (tmp_len <= max_len) { + /* + * One of the other wNAFs is at least as long + * as the wNAF belonging to the generator, so + * wNAF splitting will not buy us anything. + */ numblocks = 1; - totalnum = num + 1; /* don't use wNAF splitting */ + totalnum = num + 1; /* don't use wNAF + * splitting */ wNAF[num] = tmp_wNAF; wNAF[num + 1] = NULL; wNAF_len[num] = tmp_len; if (tmp_len > max_len) max_len = tmp_len; - /* pre_comp->points starts with the points that we need here: */ + /* + * pre_comp->points starts with the points + * that we need here: + */ val_sub[num] = pre_comp->points; - } - else - { - /* don't include tmp_wNAF directly into wNAF array - * - use wNAF splitting and include the blocks */ + } else { + /* + * don't include tmp_wNAF directly into wNAF + * array - use wNAF splitting and include the + * blocks + */ signed char *pp; EC_POINT **tmp_points; - - if (tmp_len < numblocks * blocksize) - { - /* possibly we can do with fewer blocks than estimated */ + + if (tmp_len < numblocks * blocksize) { + /* + * possibly we can do with fewer + * blocks than estimated + */ numblocks = (tmp_len + blocksize - 1) / blocksize; - if (numblocks > pre_comp->numblocks) - { + if (numblocks > pre_comp->numblocks) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - totalnum = num + numblocks; } - + totalnum = num + numblocks; + } /* split wNAF in 'numblocks' parts */ pp = tmp_wNAF; tmp_points = pre_comp->points; - for (i = num; i < totalnum; i++) - { - if (i < totalnum - 1) - { + for (i = num; i < totalnum; i++) { + if (i < totalnum - 1) { wNAF_len[i] = blocksize; - if (tmp_len < blocksize) - { + if (tmp_len < blocksize) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - tmp_len -= blocksize; } - else - /* last block gets whatever is left - * (this could be more or less than 'blocksize'!) */ + tmp_len -= blocksize; + } else + /* + * last block gets whatever + * is left (this could be + * more or less than + * 'blocksize'!) + */ wNAF_len[i] = tmp_len; - + wNAF[i + 1] = NULL; wNAF[i] = malloc(wNAF_len[i]); - if (wNAF[i] == NULL) - { + if (wNAF[i] == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); free(tmp_wNAF); goto err; - } + } memcpy(wNAF[i], pp, wNAF_len[i]); if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; - if (*tmp_points == NULL) - { + if (*tmp_points == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); free(tmp_wNAF); goto err; - } + } val_sub[i] = tmp_points; tmp_points += pre_points_per_block; pp += blocksize; - } - free(tmp_wNAF); } + free(tmp_wNAF); } } - - /* All points we precompute now go into a single array 'val'. - * 'val_sub[i]' is a pointer to the subarray for the i-th point, - * or to a subarray of 'pre_comp->points' if we already have precomputation. */ + } + /* + * All points we precompute now go into a single array 'val'. + * 'val_sub[i]' is a pointer to the subarray for the i-th point, or + * to a subarray of 'pre_comp->points' if we already have + * precomputation. + */ val = malloc((num_val + 1) * sizeof val[0]); - if (val == NULL) - { + if (val == NULL) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - val[num_val] = NULL; /* pivot element */ + } + val[num_val] = NULL; /* pivot element */ /* allocate points for precomputation */ v = val; - for (i = 0; i < num + num_scalar; i++) - { + for (i = 0; i < num + num_scalar; i++) { val_sub[i] = v; - for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) - { + for (j = 0; j < ((size_t) 1 << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); - if (*v == NULL) goto err; + if (*v == NULL) + goto err; v++; - } } - if (!(v == val + num_val)) - { + } + if (!(v == val + num_val)) { ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); goto err; - } - + } if (!(tmp = EC_POINT_new(group))) goto err; - /* prepare precomputed values: - * val_sub[i][0] := points[i] - * val_sub[i][1] := 3 * points[i] - * val_sub[i][2] := 5 * points[i] - * ... + /* + * prepare precomputed values: val_sub[i][0] := points[i] + * val_sub[i][1] := 3 * points[i] val_sub[i][2] := 5 * points[i] ... */ - for (i = 0; i < num + num_scalar; i++) - { - if (i < num) - { - if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; - } - else - { - if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; - } + for (i = 0; i < num + num_scalar; i++) { + if (i < num) { + if (!EC_POINT_copy(val_sub[i][0], points[i])) + goto err; + } else { + if (!EC_POINT_copy(val_sub[i][0], generator)) + goto err; + } - if (wsize[i] > 1) - { - if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; - for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) - { - if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; - } + if (wsize[i] > 1) { + if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) + goto err; + for (j = 1; j < ((size_t) 1 << (wsize[i] - 1)); j++) { + if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) + goto err; } } + } -#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ +#if 1 /* optional; EC_window_bits_for_scalar_size + * assumes we do this step */ if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; #endif r_is_at_infinity = 1; - for (k = max_len - 1; k >= 0; k--) - { - if (!r_is_at_infinity) - { - if (!EC_POINT_dbl(group, r, r, ctx)) goto err; - } - - for (i = 0; i < totalnum; i++) - { - if (wNAF_len[i] > (size_t)k) - { + for (k = max_len - 1; k >= 0; k--) { + if (!r_is_at_infinity) { + if (!EC_POINT_dbl(group, r, r, ctx)) + goto err; + } + for (i = 0; i < totalnum; i++) { + if (wNAF_len[i] > (size_t) k) { int digit = wNAF[i][k]; int is_neg; - if (digit) - { + if (digit) { is_neg = digit < 0; if (is_neg) digit = -digit; - if (is_neg != r_is_inverted) - { - if (!r_is_at_infinity) - { - if (!EC_POINT_invert(group, r, ctx)) goto err; - } - r_is_inverted = !r_is_inverted; + if (is_neg != r_is_inverted) { + if (!r_is_at_infinity) { + if (!EC_POINT_invert(group, r, ctx)) + goto err; } - + r_is_inverted = !r_is_inverted; + } /* digit > 0 */ - if (r_is_at_infinity) - { - if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; + if (r_is_at_infinity) { + if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) + goto err; r_is_at_infinity = 0; - } - else - { - if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; - } + } else { + if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) + goto err; } } } } + } - if (r_is_at_infinity) - { - if (!EC_POINT_set_to_infinity(group, r)) goto err; - } - else - { + if (r_is_at_infinity) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { if (r_is_inverted) - if (!EC_POINT_invert(group, r, ctx)) goto err; - } - + if (!EC_POINT_invert(group, r, ctx)) + goto err; + } + ret = 1; - err: +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (tmp != NULL) @@ -719,34 +687,31 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, free(wsize); if (wNAF_len != NULL) free(wNAF_len); - if (wNAF != NULL) - { + if (wNAF != NULL) { signed char **w; - + for (w = wNAF; *w != NULL; w++) free(*w); - + free(wNAF); - } - if (val != NULL) - { + } + if (val != NULL) { for (v = val; *v != NULL; v++) EC_POINT_clear_free(*v); free(val); - } - if (val_sub != NULL) - { + } + if (val_sub != NULL) { free(val_sub); - } - return ret; } + return ret; +} /* ec_wNAF_precompute_mult() * creates an EC_PRE_COMP object with preprecomputed multiples of the generator * for use with wNAF splitting as implemented in ec_wNAF_mul(). - * + * * 'pre_comp->points' is an array of multiples of the generator * of the following form: * points[0] = generator; @@ -762,13 +727,15 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator * points[2^(w-1)*numblocks] = NULL */ -int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_wNAF_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ const EC_POINT *generator; EC_POINT *tmp_point = NULL, *base = NULL, **var; BN_CTX *new_ctx = NULL; BIGNUM *order; - size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; + size_t i, bits, w, pre_points_per_block, blocksize, numblocks, + num; EC_POINT **points = NULL; EC_PRE_COMP *pre_comp; int ret = 0; @@ -780,81 +747,72 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) return 0; generator = EC_GROUP_get0_generator(group); - if (generator == NULL) - { + if (generator == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; - } - + } BN_CTX_start(ctx); order = BN_CTX_get(ctx); - if (order == NULL) goto err; - - if (!EC_GROUP_get_order(group, order, ctx)) goto err; - if (BN_is_zero(order)) - { - ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); + if (order == NULL) goto err; - } + if (!EC_GROUP_get_order(group, order, ctx)) + goto err; + if (BN_is_zero(order)) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); + goto err; + } bits = BN_num_bits(order); - /* The following parameters mean we precompute (approximately) - * one point per bit. - * - * TBD: The combination 8, 4 is perfect for 160 bits; for other - * bit lengths, other parameter combinations might provide better + /* + * The following parameters mean we precompute (approximately) one + * point per bit. + * + * TBD: The combination 8, 4 is perfect for 160 bits; for other bit + * lengths, other parameter combinations might provide better * efficiency. */ blocksize = 8; w = 4; - if (EC_window_bits_for_scalar_size(bits) > w) - { + if (EC_window_bits_for_scalar_size(bits) > w) { /* let's not make the window too small ... */ w = EC_window_bits_for_scalar_size(bits); - } + } + numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks + * to use for wNAF + * splitting */ - numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ - - pre_points_per_block = (size_t)1 << (w - 1); - num = pre_points_per_block * numblocks; /* number of points to compute and store */ + pre_points_per_block = (size_t) 1 << (w - 1); + num = pre_points_per_block * numblocks; /* number of points to + * compute and store */ - points = malloc(sizeof (EC_POINT*)*(num + 1)); - if (!points) - { + points = malloc(sizeof(EC_POINT *) * (num + 1)); + if (!points) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } - + } var = points; - var[num] = NULL; /* pivot */ - for (i = 0; i < num; i++) - { - if ((var[i] = EC_POINT_new(group)) == NULL) - { + var[num] = NULL; /* pivot */ + for (i = 0; i < num; i++) { + if ((var[i] = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } } + } - if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) - { + if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); goto err; - } - + } if (!EC_POINT_copy(base, generator)) goto err; - + /* do the precomputation */ - for (i = 0; i < numblocks; i++) - { + for (i = 0; i < numblocks; i++) { size_t j; if (!EC_POINT_dbl(group, tmp_point, base, ctx)) @@ -863,37 +821,35 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (!EC_POINT_copy(*var++, base)) goto err; - for (j = 1; j < pre_points_per_block; j++, var++) - { + for (j = 1; j < pre_points_per_block; j++, var++) { /* calculate odd multiples of the current base point */ if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) goto err; - } + } - if (i < numblocks - 1) - { - /* get the next base (multiply current one by 2^blocksize) */ + if (i < numblocks - 1) { + /* + * get the next base (multiply current one by + * 2^blocksize) + */ size_t k; - if (blocksize <= 2) - { + if (blocksize <= 2) { ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); goto err; - } - + } if (!EC_POINT_dbl(group, base, tmp_point, ctx)) goto err; - for (k = 2; k < blocksize; k++) - { - if (!EC_POINT_dbl(group,base,base,ctx)) + for (k = 2; k < blocksize; k++) { + if (!EC_POINT_dbl(group, base, base, ctx)) goto err; - } } - } + } + } if (!EC_POINTs_make_affine(group, num, points, ctx)) goto err; - + pre_comp->group = group; pre_comp->blocksize = blocksize; pre_comp->numblocks = numblocks; @@ -908,33 +864,33 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) pre_comp = NULL; ret = 1; - err: +err: if (ctx != NULL) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); if (pre_comp) ec_pre_comp_free(pre_comp); - if (points) - { + if (points) { EC_POINT **p; for (p = points; *p != NULL; p++) EC_POINT_free(*p); free(points); - } + } if (tmp_point) EC_POINT_free(tmp_point); if (base) EC_POINT_free(base); return ret; - } +} -int ec_wNAF_have_precompute_mult(const EC_GROUP *group) - { +int +ec_wNAF_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) return 1; else return 0; - } +} diff --git a/lib/libssl/src/crypto/ec/ec_oct.c b/lib/libssl/src/crypto/ec/ec_oct.c index fd9db0798d3..e0fb62fee2f 100644 --- a/lib/libssl/src/crypto/ec/ec_oct.c +++ b/lib/libssl/src/crypto/ec/ec_oct.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Binary polynomial ECC support in OpenSSL originally developed by + * Binary polynomial ECC support in OpenSSL originally developed by * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. */ @@ -68,132 +68,123 @@ #include "ec_lcl.h" -int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { +int +EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, int y_bit, BN_CTX * ctx) +{ if (group->meth->point_set_compressed_coordinates == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); #endif - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); +} #ifndef OPENSSL_NO_EC2M -int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { +int +EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, int y_bit, BN_CTX * ctx) +{ if (group->meth->point_set_compressed_coordinates == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); else return ec_GF2m_simple_set_compressed_coordinates( - group, point, x, y_bit, ctx); - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + group, point, x, y_bit, ctx); } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); +} #endif -size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) +{ if (group->meth->point2oct == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_point2oct(group, point, - form, buf, len, ctx); + form, buf, len, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_point2oct(group, point, - form, buf, len, ctx); + form, buf, len, ctx); #endif - } - - return group->meth->point2oct(group, point, form, buf, len, ctx); } + return group->meth->point2oct(group, point, form, buf, len, ctx); +} -int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->oct2point == 0 - && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) - { +int +EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ + if (group->meth->oct2point == 0 && + !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; - } - if (group->meth != point->meth) - { + } + if (group->meth != point->meth) { ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); return 0; - } - if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) - { + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { if (group->meth->field_type == NID_X9_62_prime_field) return ec_GFp_simple_oct2point(group, point, - buf, len, ctx); + buf, len, ctx); else #ifdef OPENSSL_NO_EC2M - { + { ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_GF2M_NOT_SUPPORTED); return 0; - } + } #else return ec_GF2m_simple_oct2point(group, point, - buf, len, ctx); + buf, len, ctx); #endif - } - return group->meth->oct2point(group, point, buf, len, ctx); } - + return group->meth->oct2point(group, point, buf, len, ctx); +} diff --git a/lib/libssl/src/crypto/ec/ec_pmeth.c b/lib/libssl/src/crypto/ec/ec_pmeth.c index c970d8c9ca2..28f501070c5 100644 --- a/lib/libssl/src/crypto/ec/ec_pmeth.c +++ b/lib/libssl/src/crypto/ec/ec_pmeth.c @@ -9,7 +9,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -66,16 +66,16 @@ /* EC pkey context structure */ -typedef struct - { +typedef struct { /* Key and paramgen group */ EC_GROUP *gen_group; /* message digest */ const EVP_MD *md; - } EC_PKEY_CTX; +} EC_PKEY_CTX; -static int pkey_ec_init(EVP_PKEY_CTX *ctx) - { +static int +pkey_ec_init(EVP_PKEY_CTX * ctx) +{ EC_PKEY_CTX *dctx; dctx = malloc(sizeof(EC_PKEY_CTX)); if (!dctx) @@ -86,55 +86,52 @@ static int pkey_ec_init(EVP_PKEY_CTX *ctx) ctx->data = dctx; return 1; - } +} -static int pkey_ec_copy(EVP_PKEY_CTX *dst, EVP_PKEY_CTX *src) - { +static int +pkey_ec_copy(EVP_PKEY_CTX * dst, EVP_PKEY_CTX * src) +{ EC_PKEY_CTX *dctx, *sctx; if (!pkey_ec_init(dst)) return 0; - sctx = src->data; + sctx = src->data; dctx = dst->data; - if (sctx->gen_group) - { + if (sctx->gen_group) { dctx->gen_group = EC_GROUP_dup(sctx->gen_group); if (!dctx->gen_group) return 0; - } + } dctx->md = sctx->md; return 1; - } +} -static void pkey_ec_cleanup(EVP_PKEY_CTX *ctx) - { +static void +pkey_ec_cleanup(EVP_PKEY_CTX * ctx) +{ EC_PKEY_CTX *dctx = ctx->data; - if (dctx) - { + if (dctx) { if (dctx->gen_group) EC_GROUP_free(dctx->gen_group); free(dctx); - } } +} -static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, - const unsigned char *tbs, size_t tbslen) - { +static int +pkey_ec_sign(EVP_PKEY_CTX * ctx, unsigned char *sig, size_t * siglen, + const unsigned char *tbs, size_t tbslen) +{ int ret, type; unsigned int sltmp; EC_PKEY_CTX *dctx = ctx->data; EC_KEY *ec = ctx->pkey->pkey.ec; - if (!sig) - { + if (!sig) { *siglen = ECDSA_size(ec); return 1; - } - else if(*siglen < (size_t)ECDSA_size(ec)) - { + } else if (*siglen < (size_t) ECDSA_size(ec)) { ECerr(EC_F_PKEY_EC_SIGN, EC_R_BUFFER_TOO_SMALL); return 0; - } - + } if (dctx->md) type = EVP_MD_type(dctx->md); else @@ -145,14 +142,15 @@ static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, if (ret <= 0) return ret; - *siglen = (size_t)sltmp; + *siglen = (size_t) sltmp; return 1; - } +} -static int pkey_ec_verify(EVP_PKEY_CTX *ctx, - const unsigned char *sig, size_t siglen, - const unsigned char *tbs, size_t tbslen) - { +static int +pkey_ec_verify(EVP_PKEY_CTX * ctx, + const unsigned char *sig, size_t siglen, + const unsigned char *tbs, size_t tbslen) +{ int ret, type; EC_PKEY_CTX *dctx = ctx->data; EC_KEY *ec = ctx->pkey->pkey.ec; @@ -165,116 +163,111 @@ static int pkey_ec_verify(EVP_PKEY_CTX *ctx, ret = ECDSA_verify(type, tbs, tbslen, sig, siglen, ec); return ret; - } +} -static int pkey_ec_derive(EVP_PKEY_CTX *ctx, unsigned char *key, size_t *keylen) - { +static int +pkey_ec_derive(EVP_PKEY_CTX * ctx, unsigned char *key, size_t * keylen) +{ int ret; size_t outlen; const EC_POINT *pubkey = NULL; - if (!ctx->pkey || !ctx->peerkey) - { + if (!ctx->pkey || !ctx->peerkey) { ECerr(EC_F_PKEY_EC_DERIVE, EC_R_KEYS_NOT_SET); return 0; - } - - if (!key) - { + } + if (!key) { const EC_GROUP *group; group = EC_KEY_get0_group(ctx->pkey->pkey.ec); - *keylen = (EC_GROUP_get_degree(group) + 7)/8; + *keylen = (EC_GROUP_get_degree(group) + 7) / 8; return 1; - } - + } pubkey = EC_KEY_get0_public_key(ctx->peerkey->pkey.ec); - /* NB: unlike PKCS#3 DH, if *outlen is less than maximum size this is + /* + * NB: unlike PKCS#3 DH, if *outlen is less than maximum size this is * not an error, the result is truncated. */ outlen = *keylen; - + ret = ECDH_compute_key(key, outlen, pubkey, ctx->pkey->pkey.ec, 0); if (ret < 0) return ret; *keylen = ret; return 1; - } +} -static int pkey_ec_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) - { +static int +pkey_ec_ctrl(EVP_PKEY_CTX * ctx, int type, int p1, void *p2) +{ EC_PKEY_CTX *dctx = ctx->data; EC_GROUP *group; - switch (type) - { - case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: + switch (type) { + case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: group = EC_GROUP_new_by_curve_name(p1); - if (group == NULL) - { + if (group == NULL) { ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_CURVE); return 0; - } + } if (dctx->gen_group) EC_GROUP_free(dctx->gen_group); dctx->gen_group = group; return 1; - case EVP_PKEY_CTRL_MD: - if (EVP_MD_type((const EVP_MD *)p2) != NID_sha1 && - EVP_MD_type((const EVP_MD *)p2) != NID_ecdsa_with_SHA1 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha224 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha256 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha384 && - EVP_MD_type((const EVP_MD *)p2) != NID_sha512) - { + case EVP_PKEY_CTRL_MD: + if (EVP_MD_type((const EVP_MD *) p2) != NID_sha1 && + EVP_MD_type((const EVP_MD *) p2) != NID_ecdsa_with_SHA1 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha224 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha256 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha384 && + EVP_MD_type((const EVP_MD *) p2) != NID_sha512) { ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_DIGEST_TYPE); return 0; - } + } dctx->md = p2; return 1; - case EVP_PKEY_CTRL_PEER_KEY: + case EVP_PKEY_CTRL_PEER_KEY: /* Default behaviour is OK */ - case EVP_PKEY_CTRL_DIGESTINIT: - case EVP_PKEY_CTRL_PKCS7_SIGN: - case EVP_PKEY_CTRL_CMS_SIGN: + case EVP_PKEY_CTRL_DIGESTINIT: + case EVP_PKEY_CTRL_PKCS7_SIGN: + case EVP_PKEY_CTRL_CMS_SIGN: return 1; - default: + default: return -2; - } } - -static int pkey_ec_ctrl_str(EVP_PKEY_CTX *ctx, - const char *type, const char *value) - { - if (!strcmp(type, "ec_paramgen_curve")) - { +} + +static int +pkey_ec_ctrl_str(EVP_PKEY_CTX * ctx, + const char *type, const char *value) +{ + if (!strcmp(type, "ec_paramgen_curve")) { int nid; nid = OBJ_sn2nid(value); if (nid == NID_undef) nid = OBJ_ln2nid(value); - if (nid == NID_undef) - { + if (nid == NID_undef) { ECerr(EC_F_PKEY_EC_CTRL_STR, EC_R_INVALID_CURVE); return 0; - } - return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); } - return -2; + return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); } + return -2; +} -static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) - { +static int +pkey_ec_paramgen(EVP_PKEY_CTX * ctx, EVP_PKEY * pkey) +{ EC_KEY *ec = NULL; EC_PKEY_CTX *dctx = ctx->data; int ret = 0; - if (dctx->gen_group == NULL) - { + if (dctx->gen_group == NULL) { ECerr(EC_F_PKEY_EC_PARAMGEN, EC_R_NO_PARAMETERS_SET); return 0; - } + } ec = EC_KEY_new(); if (!ec) return 0; @@ -284,16 +277,16 @@ static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) else EC_KEY_free(ec); return ret; - } +} -static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) - { +static int +pkey_ec_keygen(EVP_PKEY_CTX * ctx, EVP_PKEY * pkey) +{ EC_KEY *ec = NULL; - if (ctx->pkey == NULL) - { + if (ctx->pkey == NULL) { ECerr(EC_F_PKEY_EC_KEYGEN, EC_R_NO_PARAMETERS_SET); return 0; - } + } ec = EC_KEY_new(); if (!ec) return 0; @@ -302,7 +295,7 @@ static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) if (!EVP_PKEY_copy_parameters(pkey, ctx->pkey)) return 0; return EC_KEY_generate_key(pkey->pkey.ec); - } +} const EVP_PKEY_METHOD ec_pkey_meth = { .pkey_id = EVP_PKEY_EC, diff --git a/lib/libssl/src/crypto/ec/ec_print.c b/lib/libssl/src/crypto/ec/ec_print.c index 1655332c3c5..84a78903b38 100644 --- a/lib/libssl/src/crypto/ec/ec_print.c +++ b/lib/libssl/src/crypto/ec/ec_print.c @@ -7,7 +7,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -56,29 +56,25 @@ #include #include "ec_lcl.h" -BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, - const EC_POINT *point, - point_conversion_form_t form, - BIGNUM *ret, - BN_CTX *ctx) - { - size_t buf_len=0; +BIGNUM * +EC_POINT_point2bn(const EC_GROUP * group, const EC_POINT * point, + point_conversion_form_t form, BIGNUM * ret, BN_CTX * ctx) +{ + size_t buf_len = 0; unsigned char *buf; buf_len = EC_POINT_point2oct(group, point, form, - NULL, 0, ctx); + NULL, 0, ctx); if (buf_len == 0) return NULL; if ((buf = malloc(buf_len)) == NULL) return NULL; - if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) - { + if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) { free(buf); return NULL; - } - + } ret = BN_bin2bn(buf, buf_len, ret); free(buf); @@ -86,103 +82,90 @@ BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, return ret; } -EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, - const BIGNUM *bn, - EC_POINT *point, - BN_CTX *ctx) - { - size_t buf_len=0; +EC_POINT * +EC_POINT_bn2point(const EC_GROUP * group, + const BIGNUM * bn, EC_POINT * point, BN_CTX * ctx) +{ + size_t buf_len = 0; unsigned char *buf; - EC_POINT *ret; + EC_POINT *ret; - if ((buf_len = BN_num_bytes(bn)) == 0) return NULL; + if ((buf_len = BN_num_bytes(bn)) == 0) + return NULL; buf = malloc(buf_len); if (buf == NULL) return NULL; - if (!BN_bn2bin(bn, buf)) - { + if (!BN_bn2bin(bn, buf)) { free(buf); return NULL; - } - - if (point == NULL) - { - if ((ret = EC_POINT_new(group)) == NULL) - { + } + if (point == NULL) { + if ((ret = EC_POINT_new(group)) == NULL) { free(buf); return NULL; - } } - else + } else ret = point; - if (!EC_POINT_oct2point(group, ret, buf, buf_len, ctx)) - { + if (!EC_POINT_oct2point(group, ret, buf, buf_len, ctx)) { if (point == NULL) EC_POINT_clear_free(ret); free(buf); return NULL; - } - + } free(buf); return ret; - } +} static const char *HEX_DIGITS = "0123456789ABCDEF"; /* the return value must be freed (using free()) */ -char *EC_POINT_point2hex(const EC_GROUP *group, - const EC_POINT *point, - point_conversion_form_t form, - BN_CTX *ctx) - { - char *ret, *p; - size_t buf_len=0,i; +char * +EC_POINT_point2hex(const EC_GROUP * group, const EC_POINT * point, + point_conversion_form_t form, BN_CTX * ctx) +{ + char *ret, *p; + size_t buf_len = 0, i; unsigned char *buf, *pbuf; buf_len = EC_POINT_point2oct(group, point, form, - NULL, 0, ctx); + NULL, 0, ctx); if (buf_len == 0) return NULL; if ((buf = malloc(buf_len)) == NULL) return NULL; - if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) - { + if (!EC_POINT_point2oct(group, point, form, buf, buf_len, ctx)) { free(buf); return NULL; - } - - ret = (char *)malloc(buf_len*2+2); - if (ret == NULL) - { + } + ret = (char *) malloc(buf_len * 2 + 2); + if (ret == NULL) { free(buf); return NULL; - } + } p = ret; pbuf = buf; - for (i=buf_len; i > 0; i--) - { - int v = (int) *(pbuf++); - *(p++)=HEX_DIGITS[v>>4]; - *(p++)=HEX_DIGITS[v&0x0F]; - } - *p='\0'; + for (i = buf_len; i > 0; i--) { + int v = (int) *(pbuf++); + *(p++) = HEX_DIGITS[v >> 4]; + *(p++) = HEX_DIGITS[v & 0x0F]; + } + *p = '\0'; free(buf); return ret; - } +} -EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, - const char *buf, - EC_POINT *point, - BN_CTX *ctx) - { - EC_POINT *ret=NULL; - BIGNUM *tmp_bn=NULL; +EC_POINT * +EC_POINT_hex2point(const EC_GROUP * group, const char *buf, + EC_POINT * point, BN_CTX * ctx) +{ + EC_POINT *ret = NULL; + BIGNUM *tmp_bn = NULL; if (!BN_hex2bn(&tmp_bn, buf)) return NULL; @@ -192,4 +175,4 @@ EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, BN_clear_free(tmp_bn); return ret; - } +} diff --git a/lib/libssl/src/crypto/ec/eck_prn.c b/lib/libssl/src/crypto/ec/eck_prn.c index 4e8c748bbc0..86107d51424 100644 --- a/lib/libssl/src/crypto/ec/eck_prn.c +++ b/lib/libssl/src/crypto/ec/eck_prn.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -57,7 +57,7 @@ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * Portions originally developed by SUN MICROSYSTEMS, INC., and + * Portions originally developed by SUN MICROSYSTEMS, INC., and * contributed to the OpenSSL project. */ @@ -68,113 +68,112 @@ #include #ifndef OPENSSL_NO_FP_API -int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off) - { +int +ECPKParameters_print_fp(FILE * fp, const EC_GROUP * x, int off) +{ BIO *b; int ret; - if ((b=BIO_new(BIO_s_file())) == NULL) - { - ECerr(EC_F_ECPKPARAMETERS_PRINT_FP,ERR_R_BUF_LIB); - return(0); - } + if ((b = BIO_new(BIO_s_file())) == NULL) { + ECerr(EC_F_ECPKPARAMETERS_PRINT_FP, ERR_R_BUF_LIB); + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = ECPKParameters_print(b, x, off); BIO_free(b); - return(ret); - } + return (ret); +} -int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off) - { +int +EC_KEY_print_fp(FILE * fp, const EC_KEY * x, int off) +{ BIO *b; int ret; - - if ((b=BIO_new(BIO_s_file())) == NULL) - { + + if ((b = BIO_new(BIO_s_file())) == NULL) { ECerr(EC_F_EC_KEY_PRINT_FP, ERR_R_BIO_LIB); - return(0); - } + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = EC_KEY_print(b, x, off); BIO_free(b); - return(ret); - } + return (ret); +} -int ECParameters_print_fp(FILE *fp, const EC_KEY *x) - { +int +ECParameters_print_fp(FILE * fp, const EC_KEY * x) +{ BIO *b; int ret; - - if ((b=BIO_new(BIO_s_file())) == NULL) - { + + if ((b = BIO_new(BIO_s_file())) == NULL) { ECerr(EC_F_ECPARAMETERS_PRINT_FP, ERR_R_BIO_LIB); - return(0); - } + return (0); + } BIO_set_fp(b, fp, BIO_NOCLOSE); ret = ECParameters_print(b, x); BIO_free(b); - return(ret); - } + return (ret); +} #endif -int EC_KEY_print(BIO *bp, const EC_KEY *x, int off) - { +int +EC_KEY_print(BIO * bp, const EC_KEY * x, int off) +{ EVP_PKEY *pk; int ret; pk = EVP_PKEY_new(); - if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *) x)) return 0; ret = EVP_PKEY_print_private(bp, pk, off, NULL); EVP_PKEY_free(pk); return ret; - } +} -int ECParameters_print(BIO *bp, const EC_KEY *x) - { +int +ECParameters_print(BIO * bp, const EC_KEY * x) +{ EVP_PKEY *pk; int ret; pk = EVP_PKEY_new(); - if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *) x)) return 0; ret = EVP_PKEY_print_params(bp, pk, 4, NULL); EVP_PKEY_free(pk); return ret; - } - -static int print_bin(BIO *fp, const char *str, const unsigned char *num, - size_t len, int off); - -int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) - { - unsigned char *buffer=NULL; - size_t buf_len=0, i; - int ret=0, reason=ERR_R_BIO_LIB; - BN_CTX *ctx=NULL; - const EC_POINT *point=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *gen=NULL, - *order=NULL, *cofactor=NULL; +} + +static int +print_bin(BIO * fp, const char *str, const unsigned char *num, + size_t len, int off); + +int +ECPKParameters_print(BIO * bp, const EC_GROUP * x, int off) +{ + unsigned char *buffer = NULL; + size_t buf_len = 0, i; + int ret = 0, reason = ERR_R_BIO_LIB; + BN_CTX *ctx = NULL; + const EC_POINT *point = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *gen = NULL, *order = NULL, + *cofactor = NULL; const unsigned char *seed; - size_t seed_len=0; - + size_t seed_len = 0; + static const char *gen_compressed = "Generator (compressed):"; static const char *gen_uncompressed = "Generator (uncompressed):"; static const char *gen_hybrid = "Generator (hybrid):"; - - if (!x) - { + + if (!x) { reason = ERR_R_PASSED_NULL_PARAMETER; goto err; - } - + } ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - - if (EC_GROUP_get_asn1_flag(x)) - { + } + if (EC_GROUP_get_asn1_flag(x)) { /* the curve parameter are given by an asn1 OID */ int nid; @@ -189,9 +188,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) goto err; if (BIO_printf(bp, "\n") <= 0) goto err; - } - else - { + } else { /* explicit parameters */ int is_char_two = 0; point_conversion_form_t form; @@ -201,84 +198,71 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) is_char_two = 1; if ((p = BN_new()) == NULL || (a = BN_new()) == NULL || - (b = BN_new()) == NULL || (order = BN_new()) == NULL || - (cofactor = BN_new()) == NULL) - { + (b = BN_new()) == NULL || (order = BN_new()) == NULL || + (cofactor = BN_new()) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } + } #ifndef OPENSSL_NO_EC2M - if (is_char_two) - { - if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) - { + if (is_char_two) { + if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) { reason = ERR_R_EC_LIB; goto err; - } } - else /* prime field */ + } else /* prime field */ #endif - { - if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) - { + { + if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) { reason = ERR_R_EC_LIB; goto err; - } } + } - if ((point = EC_GROUP_get0_generator(x)) == NULL) - { + if ((point = EC_GROUP_get0_generator(x)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - if (!EC_GROUP_get_order(x, order, NULL) || - !EC_GROUP_get_cofactor(x, cofactor, NULL)) - { + } + if (!EC_GROUP_get_order(x, order, NULL) || + !EC_GROUP_get_cofactor(x, cofactor, NULL)) { reason = ERR_R_EC_LIB; goto err; - } - + } form = EC_GROUP_get_point_conversion_form(x); - if ((gen = EC_POINT_point2bn(x, point, - form, NULL, ctx)) == NULL) - { + if ((gen = EC_POINT_point2bn(x, point, + form, NULL, ctx)) == NULL) { reason = ERR_R_EC_LIB; goto err; - } - - buf_len = (size_t)BN_num_bytes(p); - if (buf_len < (i = (size_t)BN_num_bytes(a))) + } + buf_len = (size_t) BN_num_bytes(p); + if (buf_len < (i = (size_t) BN_num_bytes(a))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(b))) + if (buf_len < (i = (size_t) BN_num_bytes(b))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(gen))) + if (buf_len < (i = (size_t) BN_num_bytes(gen))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(order))) + if (buf_len < (i = (size_t) BN_num_bytes(order))) buf_len = i; - if (buf_len < (i = (size_t)BN_num_bytes(cofactor))) + if (buf_len < (i = (size_t) BN_num_bytes(cofactor))) buf_len = i; if ((seed = EC_GROUP_get0_seed(x)) != NULL) seed_len = EC_GROUP_get_seed_len(x); buf_len += 10; - if ((buffer = malloc(buf_len)) == NULL) - { + if ((buffer = malloc(buf_len)) == NULL) { reason = ERR_R_MALLOC_FAILURE; goto err; - } - + } if (!BIO_indent(bp, off, 128)) goto err; /* print the 'short name' of the field type */ if (BIO_printf(bp, "Field Type: %s\n", OBJ_nid2sn(tmp_nid)) - <= 0) - goto err; + <= 0) + goto err; - if (is_char_two) - { + if (is_char_two) { /* print the 'short name' of the base type OID */ int basis_type = EC_GROUP_get_basis_type(x); if (basis_type == 0) @@ -287,7 +271,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) if (!BIO_indent(bp, off, 128)) goto err; - if (BIO_printf(bp, "Basis Type: %s\n", + if (BIO_printf(bp, "Basis Type: %s\n", OBJ_nid2sn(basis_type)) <= 0) goto err; @@ -295,48 +279,43 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) if ((p != NULL) && !ASN1_bn_print(bp, "Polynomial:", p, buffer, off)) goto err; - } - else - { - if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, buffer,off)) + } else { + if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, buffer, off)) goto err; - } - if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, buffer, off)) + } + if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, buffer, off)) goto err; if ((b != NULL) && !ASN1_bn_print(bp, "B: ", b, buffer, off)) goto err; - if (form == POINT_CONVERSION_COMPRESSED) - { + if (form == POINT_CONVERSION_COMPRESSED) { if ((gen != NULL) && !ASN1_bn_print(bp, gen_compressed, gen, buffer, off)) goto err; - } - else if (form == POINT_CONVERSION_UNCOMPRESSED) - { + } else if (form == POINT_CONVERSION_UNCOMPRESSED) { if ((gen != NULL) && !ASN1_bn_print(bp, gen_uncompressed, gen, buffer, off)) goto err; - } - else /* form == POINT_CONVERSION_HYBRID */ - { + } else { /* form == POINT_CONVERSION_HYBRID */ if ((gen != NULL) && !ASN1_bn_print(bp, gen_hybrid, gen, buffer, off)) goto err; - } - if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, - buffer, off)) goto err; - if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, - buffer, off)) goto err; + } + if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, + buffer, off)) + goto err; + if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, + buffer, off)) + goto err; if (seed && !print_bin(bp, "Seed:", seed, seed_len, off)) goto err; - } - ret=1; + } + ret = 1; err: if (!ret) - ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); - if (p) + ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); + if (p) BN_free(p); - if (a) + if (a) BN_free(a); if (b) BN_free(b); @@ -348,45 +327,42 @@ err: BN_free(cofactor); if (ctx) BN_CTX_free(ctx); - if (buffer != NULL) + if (buffer != NULL) free(buffer); - return(ret); - } + return (ret); +} -static int print_bin(BIO *fp, const char *name, const unsigned char *buf, - size_t len, int off) - { +static int +print_bin(BIO * fp, const char *name, const unsigned char *buf, + size_t len, int off) +{ size_t i; char str[128]; if (buf == NULL) return 1; - if (off) - { + if (off) { if (off > 128) - off=128; - memset(str,' ',off); + off = 128; + memset(str, ' ', off); if (BIO_write(fp, str, off) <= 0) return 0; - } - - if (BIO_printf(fp,"%s", name) <= 0) + } + if (BIO_printf(fp, "%s", name) <= 0) return 0; - for (i=0; ifield_data1 = NULL; group->field_data2 = NULL; return ok; - } +} -void ec_GFp_mont_group_finish(EC_GROUP *group) - { - if (group->field_data1 != NULL) - { +void +ec_GFp_mont_group_finish(EC_GROUP * group) +{ + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_free(group->field_data2); group->field_data2 = NULL; - } - ec_GFp_simple_group_finish(group); } + ec_GFp_simple_group_finish(group); +} -void ec_GFp_mont_group_clear_finish(EC_GROUP *group) - { - if (group->field_data1 != NULL) - { +void +ec_GFp_mont_group_clear_finish(EC_GROUP * group) +{ + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_clear_free(group->field_data2); group->field_data2 = NULL; - } - ec_GFp_simple_group_clear_finish(group); } + ec_GFp_simple_group_clear_finish(group); +} -int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { - if (dest->field_data1 != NULL) - { +int +ec_GFp_mont_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ + if (dest->field_data1 != NULL) { BN_MONT_CTX_free(dest->field_data1); dest->field_data1 = NULL; - } - if (dest->field_data2 != NULL) - { + } + if (dest->field_data2 != NULL) { BN_clear_free(dest->field_data2); dest->field_data2 = NULL; - } - - if (!ec_GFp_simple_group_copy(dest, src)) return 0; + } + if (!ec_GFp_simple_group_copy(dest, src)) + return 0; - if (src->field_data1 != NULL) - { + if (src->field_data1 != NULL) { dest->field_data1 = BN_MONT_CTX_new(); - if (dest->field_data1 == NULL) return 0; - if (!BN_MONT_CTX_copy(dest->field_data1, src->field_data1)) goto err; - } - if (src->field_data2 != NULL) - { + if (dest->field_data1 == NULL) + return 0; + if (!BN_MONT_CTX_copy(dest->field_data1, src->field_data1)) + goto err; + } + if (src->field_data2 != NULL) { dest->field_data2 = BN_dup(src->field_data2); - if (dest->field_data2 == NULL) goto err; - } - + if (dest->field_data2 == NULL) + goto err; + } return 1; - err: - if (dest->field_data1 != NULL) - { +err: + if (dest->field_data1 != NULL) { BN_MONT_CTX_free(dest->field_data1); dest->field_data1 = NULL; - } - return 0; } + return 0; +} -int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ BN_CTX *new_ctx = NULL; BN_MONT_CTX *mont = NULL; BIGNUM *one = NULL; int ret = 0; - if (group->field_data1 != NULL) - { + if (group->field_data1 != NULL) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; - } - if (group->field_data2 != NULL) - { + } + if (group->field_data2 != NULL) { BN_free(group->field_data2); group->field_data2 = NULL; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } mont = BN_MONT_CTX_new(); - if (mont == NULL) goto err; - if (!BN_MONT_CTX_set(mont, p, ctx)) - { + if (mont == NULL) + goto err; + if (!BN_MONT_CTX_set(mont, p, ctx)) { ECerr(EC_F_EC_GFP_MONT_GROUP_SET_CURVE, ERR_R_BN_LIB); goto err; - } + } one = BN_new(); - if (one == NULL) goto err; - if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) goto err; + if (one == NULL) + goto err; + if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) + goto err; group->field_data1 = mont; mont = NULL; @@ -238,79 +234,77 @@ int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM * ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); - if (!ret) - { + if (!ret) { BN_MONT_CTX_free(group->field_data1); group->field_data1 = NULL; BN_free(group->field_data2); group->field_data2 = NULL; - } - - err: + } +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (mont != NULL) BN_MONT_CTX_free(mont); return ret; - } +} -int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_MUL, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_mod_mul_montgomery(r, a, b, group->field_data1, ctx); } + return BN_mod_mul_montgomery(r, a, b, group->field_data1, ctx); +} -int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_SQR, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_mod_mul_montgomery(r, a, a, group->field_data1, ctx); } + return BN_mod_mul_montgomery(r, a, a, group->field_data1, ctx); +} -int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_ENCODE, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_to_montgomery(r, a, (BN_MONT_CTX *)group->field_data1, ctx); } + return BN_to_montgomery(r, a, (BN_MONT_CTX *) group->field_data1, ctx); +} -int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { - if (group->field_data1 == NULL) - { +int +ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_DECODE, EC_R_NOT_INITIALIZED); return 0; - } - - return BN_from_montgomery(r, a, group->field_data1, ctx); } + return BN_from_montgomery(r, a, group->field_data1, ctx); +} -int ec_GFp_mont_field_set_to_one(const EC_GROUP *group, BIGNUM *r, BN_CTX *ctx) - { - if (group->field_data2 == NULL) - { +int +ec_GFp_mont_field_set_to_one(const EC_GROUP *group, BIGNUM *r, BN_CTX *ctx) +{ + if (group->field_data2 == NULL) { ECerr(EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE, EC_R_NOT_INITIALIZED); return 0; - } - - if (!BN_copy(r, group->field_data2)) return 0; - return 1; } + if (!BN_copy(r, group->field_data2)) + return 0; + return 1; +} diff --git a/lib/libssl/src/crypto/ec/ecp_nist.c b/lib/libssl/src/crypto/ec/ecp_nist.c index 479cff8fc93..60c4a2d790c 100644 --- a/lib/libssl/src/crypto/ec/ecp_nist.c +++ b/lib/libssl/src/crypto/ec/ecp_nist.c @@ -10,7 +10,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -81,20 +81,20 @@ EC_GFp_nist_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_simple_point_get_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -110,25 +110,29 @@ EC_GFp_nist_method(void) return &ret; } -int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { +int +ec_GFp_nist_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ dest->field_mod_func = src->field_mod_func; return ec_GFp_simple_group_copy(dest, src); - } +} -int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_bn; - + if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); - if ((tmp_bn = BN_CTX_get(ctx)) == NULL) goto err; + if ((tmp_bn = BN_CTX_get(ctx)) == NULL) + goto err; if (BN_ucmp(BN_get0_nist_prime_192(), p) == 0) group->field_mod_func = BN_nist_mod_192; @@ -140,69 +144,72 @@ int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, group->field_mod_func = BN_nist_mod_384; else if (BN_ucmp(BN_get0_nist_prime_521(), p) == 0) group->field_mod_func = BN_nist_mod_521; - else - { + else { ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_NIST_PRIME); goto err; - } + } ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - const BIGNUM *b, BN_CTX *ctx) - { - int ret=0; - BN_CTX *ctx_new=NULL; +int +ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; - if (!group || !r || !a || !b) - { + if (!group || !r || !a || !b) { ECerr(EC_F_EC_GFP_NIST_FIELD_MUL, ERR_R_PASSED_NULL_PARAMETER); goto err; - } + } if (!ctx) - if ((ctx_new = ctx = BN_CTX_new()) == NULL) goto err; + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; - if (!BN_mul(r, a, b, ctx)) goto err; + if (!BN_mul(r, a, b, ctx)) + goto err; if (!group->field_mod_func(r, r, &group->field, ctx)) goto err; - ret=1; + ret = 1; err: if (ctx_new) BN_CTX_free(ctx_new); return ret; - } +} -int ec_GFp_nist_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - BN_CTX *ctx) - { - int ret=0; - BN_CTX *ctx_new=NULL; +int +ec_GFp_nist_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, + BN_CTX * ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; - if (!group || !r || !a) - { + if (!group || !r || !a) { ECerr(EC_F_EC_GFP_NIST_FIELD_SQR, EC_R_PASSED_NULL_PARAMETER); goto err; - } + } if (!ctx) - if ((ctx_new = ctx = BN_CTX_new()) == NULL) goto err; + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; - if (!BN_sqr(r, a, ctx)) goto err; + if (!BN_sqr(r, a, ctx)) + goto err; if (!group->field_mod_func(r, r, &group->field, ctx)) goto err; - ret=1; + ret = 1; err: if (ctx_new) BN_CTX_free(ctx_new); return ret; - } +} diff --git a/lib/libssl/src/crypto/ec/ecp_nistp224.c b/lib/libssl/src/crypto/ec/ecp_nistp224.c index 696024a5495..057670cf048 100644 --- a/lib/libssl/src/crypto/ec/ecp_nistp224.c +++ b/lib/libssl/src/crypto/ec/ecp_nistp224.c @@ -280,37 +280,40 @@ EC_GFp_nistp224_method(void) } /* Helper functions to convert field elements to/from internal representation */ -static void bin28_to_felem(felem out, const u8 in[28]) - { - out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; - out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; - out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; - out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; - } +static void +bin28_to_felem(felem out, const u8 in[28]) +{ + out[0] = *((const uint64_t *) (in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *) (in + 7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *) (in + 14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *) (in + 21))) & 0x00ffffffffffffff; +} -static void felem_to_bin28(u8 out[28], const felem in) - { +static void +felem_to_bin28(u8 out[28], const felem in) +{ unsigned i; - for (i = 0; i < 7; ++i) - { - out[i] = in[0]>>(8*i); - out[i+7] = in[1]>>(8*i); - out[i+14] = in[2]>>(8*i); - out[i+21] = in[3]>>(8*i); - } + for (i = 0; i < 7; ++i) { + out[i] = in[0] >> (8 * i); + out[i + 7] = in[1] >> (8 * i); + out[i + 14] = in[2] >> (8 * i); + out[i + 21] = in[3] >> (8 * i); } +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* From OpenSSL BIGNUM to internal representation */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -318,30 +321,29 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin28_to_felem(out, b_out); return 1; - } +} /* From internal representation to OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { +static BIGNUM * +felem_to_BN(BIGNUM * out, const felem in) +{ felem_bytearray b_in, b_out; felem_to_bin28(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /******************************************************************************/ /* FIELD OPERATIONS @@ -353,55 +355,60 @@ static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) * */ -static void felem_one(felem out) - { +static void +felem_one(felem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; out[3] = 0; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* Sum two field elements: out += in */ -static void felem_sum(felem out, const felem in) - { +static void +felem_sum(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* Get negative value: out = -in */ /* Assumes in[i] < 2^57 */ -static void felem_neg(felem out, const felem in) - { +static void +felem_neg(felem out, const felem in) +{ static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); + (((limb) 1) << 42) - (((limb) 1) << 2); /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ out[0] = two58p2 - in[0]; out[1] = two58m42m2 - in[1]; out[2] = two58m2 - in[2]; out[3] = two58m2 - in[3]; - } +} /* Subtract field elements: out -= in */ /* Assumes in[i] < 2^57 */ -static void felem_diff(felem out, const felem in) - { +static void +felem_diff(felem out, const felem in) +{ static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); + (((limb) 1) << 42) - (((limb) 1) << 2); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two58p2; @@ -413,17 +420,18 @@ static void felem_diff(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* Subtract in unreduced 128-bit mode: out -= in */ /* Assumes in[i] < 2^119 */ -static void widefelem_diff(widefelem out, const widefelem in) - { +static void +widefelem_diff(widefelem out, const widefelem in) +{ static const widelimb two120 = ((widelimb) 1) << 120; static const widelimb two120m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 64); + (((widelimb) 1) << 64); static const widelimb two120m104m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two120; @@ -441,18 +449,19 @@ static void widefelem_diff(widefelem out, const widefelem in) out[4] -= in[4]; out[5] -= in[5]; out[6] -= in[6]; - } +} /* Subtract in mixed mode: out128 -= in64 */ /* in[i] < 2^63 */ -static void felem_diff_128_64(widefelem out, const felem in) - { +static void +felem_diff_128_64(widefelem out, const felem in) +{ static const widelimb two64p8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 8); + (((widelimb) 1) << 8); static const widelimb two64m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 8); + (((widelimb) 1) << 8); static const widelimb two64m48m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two64p8; @@ -464,22 +473,24 @@ static void felem_diff_128_64(widefelem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* Multiply a field element by a scalar: out = out * scalar * The scalars we actually use are small, so results fit without overflow */ -static void felem_scalar(felem out, const limb scalar) - { +static void +felem_scalar(felem out, const limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; out[3] *= scalar; - } +} /* Multiply an unreduced field element by a scalar: out = out * scalar * The scalars we actually use are small, so results fit without overflow */ -static void widefelem_scalar(widefelem out, const widelimb scalar) - { +static void +widefelem_scalar(widefelem out, const widelimb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -487,49 +498,54 @@ static void widefelem_scalar(widefelem out, const widelimb scalar) out[4] *= scalar; out[5] *= scalar; out[6] *= scalar; - } +} /* Square a field element: out = in^2 */ -static void felem_square(widefelem out, const felem in) - { +static void +felem_square(widefelem out, const felem in) +{ limb tmp0, tmp1, tmp2; - tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; + tmp0 = 2 * in[0]; + tmp1 = 2 * in[1]; + tmp2 = 2 * in[2]; out[0] = ((widelimb) in[0]) * in[0]; out[1] = ((widelimb) in[0]) * tmp1; out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; out[3] = ((widelimb) in[3]) * tmp0 + - ((widelimb) in[1]) * tmp2; + ((widelimb) in[1]) * tmp2; out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; out[5] = ((widelimb) in[3]) * tmp2; out[6] = ((widelimb) in[3]) * in[3]; - } +} /* Multiply two field elements: out = in1 * in2 */ -static void felem_mul(widefelem out, const felem in1, const felem in2) - { +static void +felem_mul(widefelem out, const felem in1, const felem in2) +{ out[0] = ((widelimb) in1[0]) * in2[0]; out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + - ((widelimb) in1[2]) * in2[0]; + ((widelimb) in1[2]) * in2[0]; out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + - ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + - ((widelimb) in1[3]) * in2[1]; + ((widelimb) in1[3]) * in2[1]; out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; out[6] = ((widelimb) in1[3]) * in2[3]; - } +} /* Reduce seven 128-bit coefficients to four 64-bit coefficients. * Requires in[i] < 2^126, * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ -static void felem_reduce(felem out, const widefelem in) - { +static void +felem_reduce(felem out, const widefelem in) +{ static const widelimb two127p15 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 15); + (((widelimb) 1) << 15); static const widelimb two127m71 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71); + (((widelimb) 1) << 71); static const widelimb two127m71m55 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); widelimb output[5]; /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ @@ -578,30 +594,34 @@ static void felem_reduce(felem out, const widefelem in) /* output[3] <= 2^56 + 2^16 */ out[2] = output[2] & 0x00ffffffffffffff; - /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, - * out[3] <= 2^56 + 2^16 (due to final carry), - * so out < 2*p */ + /* + * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 + * (due to final carry), so out < 2*p + */ out[3] = output[3]; - } +} -static void felem_square_reduce(felem out, const felem in) - { +static void +felem_square_reduce(felem out, const felem in) +{ widefelem tmp; felem_square(tmp, in); felem_reduce(out, tmp); - } +} -static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { +static void +felem_mul_reduce(felem out, const felem in1, const felem in2) +{ widefelem tmp; felem_mul(tmp, in1, in2); felem_reduce(out, tmp); - } +} /* Reduce to unique minimal representation. * Requires 0 <= in < 2*p (always call felem_reduce first) */ -static void felem_contract(felem out, const felem in) - { +static void +felem_contract(felem out, const felem in) +{ static const int64_t two56 = ((limb) 1) << 56; /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ @@ -615,21 +635,25 @@ static void felem_contract(felem out, const felem in) tmp[0] -= a; tmp[1] += a << 40; tmp[3] &= 0x00ffffffffffffff; - /* Case 2: a = 0 iff p <= in < 2^224, i.e., - * the high 128 bits are all 1 and the lower part is non-zero */ + /* + * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all + * 1 and the lower part is non-zero + */ a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | - (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); a &= 0x00ffffffffffffff; /* turn a into an all-one mask (if a = 0) or an all-zero mask */ a = (a - 1) >> 63; - /* subtract 2^224 - 2^96 + 1 if a is all-one*/ + /* subtract 2^224 - 2^96 + 1 if a is all-one */ tmp[3] &= a ^ 0xffffffffffffffff; tmp[2] &= a ^ 0xffffffffffffffff; tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; tmp[0] -= 1 & a; - /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must - * be non-zero, so we only need one step */ + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] + * must be non-zero, so we only need one step + */ a = tmp[0] >> 63; tmp[0] += two56 & a; tmp[1] -= 1 & a; @@ -646,107 +670,131 @@ static void felem_contract(felem out, const felem in) out[1] = tmp[1]; out[2] = tmp[2]; out[3] = tmp[3]; - } +} /* Zero-check: returns 1 if input is 0, and 0 otherwise. * We know that field elements are reduced to in < 2^225, * so we only need to check three cases: 0, 2^224 - 2^96 + 1, * and 2^225 - 2^97 + 2 */ -static limb felem_is_zero(const felem in) - { +static limb +felem_is_zero(const felem in) +{ limb zero, two224m96p1, two225m97p2; zero = in[0] | in[1] | in[2] | in[3]; - zero = (((int64_t)(zero) - 1) >> 63) & 1; + zero = (((int64_t) (zero) - 1) >> 63) & 1; two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); - two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); - two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; return (zero | two224m96p1 | two225m97p2); - } +} -static limb felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +static limb +felem_is_zero_int(const felem in) +{ + return (int) (felem_is_zero(in) & ((limb) 1)); +} /* Invert a field element */ /* Computation chain copied from djb's code */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2, ftmp3, ftmp4; widefelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ - for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ - for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ - for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ - for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ - for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ - for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ - for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ - { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } - felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp);/* 2^6 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); + felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp);/* 2^126 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp);/* 2^127 - 1 */ + for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); } + felem_mul(tmp, ftmp, ftmp3); + felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ +} /* Copy in constant time: * if icopy == 1, copy in to out, * if icopy == 0, copy out to itself. */ static void copy_conditional(felem out, const felem in, limb icopy) - { +{ unsigned i; /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ const limb copy = -icopy; - for (i = 0; i < 4; ++i) - { + for (i = 0; i < 4; ++i) { const limb tmp = copy & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /******************************************************************************/ /* ELLIPTIC CURVE POINT OPERATIONS @@ -766,8 +814,8 @@ copy_conditional(felem out, const felem in, limb icopy) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ widefelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; @@ -833,7 +881,7 @@ point_double(felem x_out, felem y_out, felem z_out, widefelem_diff(tmp, tmp2); /* tmp[i] < 2^119 + 2^120 < 2^121 */ felem_reduce(y_out, tmp); - } +} /* Add two elliptic curve points: * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where @@ -851,16 +899,16 @@ point_double(felem x_out, felem y_out, felem z_out, * (while not equal to the point at infinity). * This case never happens during single point multiplication, * so there is no timing leak for ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; widefelem tmp, tmp2; limb z1_is_zero, z2_is_zero, x_equal, y_equal; - if (!mixed) - { + if (!mixed) { /* ftmp2 = z2^2 */ felem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -876,9 +924,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp2 = z2^2*x1 */ felem_mul(tmp2, ftmp2, x1); felem_reduce(ftmp2, tmp2); - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* ftmp4 = z2^3*y1 */ @@ -886,7 +932,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp2 = z2^2*x1 */ felem_assign(ftmp2, x1); - } + } /* ftmp = z1^2 */ felem_square(tmp, z1); @@ -914,30 +960,27 @@ static void point_add(felem x3, felem y3, felem z3, /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ felem_reduce(ftmp, tmp); - /* the formulae are incorrect if the points are equal - * so we check for this and do doubling if this happens */ + /* + * the formulae are incorrect if the points are equal so we check for + * this and do doubling if this happens + */ x_equal = felem_is_zero(ftmp); y_equal = felem_is_zero(ftmp3); z1_is_zero = felem_is_zero(z1); z2_is_zero = felem_is_zero(z2); /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* ftmp5 = z1*z2 */ - if (!mixed) - { + if (!mixed) { felem_mul(tmp, z1, z2); felem_reduce(ftmp5, tmp); - } - else - { + } else { /* special case z2 = 0 is handled later */ felem_assign(ftmp5, z1); - } + } /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ felem_mul(tmp, ftmp, ftmp5); @@ -973,8 +1016,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar(ftmp5, 2); /* ftmp5[i] < 2 * 2^57 = 2^58 */ - /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - - 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + /* + * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 + */ felem_diff_128_64(tmp2, ftmp5); /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ felem_reduce(x_out, tmp2); @@ -987,14 +1032,18 @@ static void point_add(felem x3, felem y3, felem z3, felem_mul(tmp2, ftmp3, ftmp2); /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ - /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - - z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + /* + * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - + * x_out) - z2^3*y1*(z1^2*x2 - z2^2*x1)^3 + */ widefelem_diff(tmp2, tmp); /* tmp2[i] < 2^118 + 2^120 < 2^121 */ felem_reduce(y_out, tmp2); - /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is - * the point at infinity, so we need to check for this separately */ + /* + * the result (x_out, y_out, z_out) is incorrect if one of the inputs + * is the point at infinity, so we need to check for this separately + */ /* if point 1 is at infinity, copy point 2 to output, and vice versa */ copy_conditional(x_out, x2, z1_is_zero); @@ -1006,18 +1055,18 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) - { +static void +select_point(const u64 idx, unsigned int size, const felem pre_comp[ /* size */ ][3], felem out[3]) +{ unsigned i, j; limb *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(felem)); - for (i = 0; i < size; i++) - { + for (i = 0; i < size; i++) { const limb *inlimbs = &pre_comp[i][0][0]; u64 mask = i ^ idx; mask |= mask >> 4; @@ -1027,26 +1076,28 @@ static void select_point(const u64 idx, unsigned int size, const felem pre_comp[ mask--; for (j = 0; j < 4 * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, unsigned i) - { +static char +get_bit(const felem_bytearray in, unsigned i) +{ if (i >= 224) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) +{ int i, skip; unsigned num; unsigned gen_mul = (g_scalar != NULL); @@ -1057,20 +1108,20 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (two in each of the last 28 rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (two in each of the last 28 rounds) and + * additions of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 220 : 27); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 27)) - { + if (gen_mul && (i <= 27)) { /* first, look 28 bits upwards */ bits = get_bit(g_scalar, i + 196) << 3; bits |= get_bit(g_scalar, i + 140) << 2; @@ -1079,17 +1130,14 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[1], tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } + } /* second, look at the current position */ bits = get_bit(g_scalar, i + 168) << 3; @@ -1099,16 +1147,13 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[0], tmp); point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1119,58 +1164,58 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add or subtract */ select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_conditional(tmp[1], tmp[3], sign); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /******************************************************************************/ /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP224_PRE_COMP *nistp224_pre_comp_new() - { +static NISTP224_PRE_COMP * +nistp224_pre_comp_new() +{ NISTP224_PRE_COMP *ret = NULL; ret = (NISTP224_PRE_COMP *) malloc(sizeof *ret); - if (!ret) - { + if (!ret) { ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp224_pre_comp_dup(void *src_) - { +static void * +nistp224_pre_comp_dup(void *src_) +{ NISTP224_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp224_pre_comp_free(void *pre_) - { +static void +nistp224_pre_comp_free(void *pre_) +{ int i; NISTP224_PRE_COMP *pre = pre_; @@ -1182,10 +1227,11 @@ static void nistp224_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp224_pre_comp_clear_free(void *pre_) - { +static void +nistp224_pre_comp_clear_free(void *pre_) +{ int i; NISTP224_PRE_COMP *pre = pre_; @@ -1198,43 +1244,46 @@ static void nistp224_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp224_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp224_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp224_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_224; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1242,74 +1291,81 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in, x_out, y_out; widefelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { + if (x != NULL) { if (!felem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { + if (y != NULL) { if (!felem_to_BN(y, y_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - return 1; } + return 1; +} -static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } + num, + points, + sizeof(felem), + tmp_felems, + (void (*) (void *)) felem_one, + (int (*) (const void *)) felem_is_zero_int, + (void (*) (void *, const void *)) felem_assign, + (void (*) (void *, const void *)) felem_square_reduce, + (void (*) (void *, const void *, const void *)) felem_mul_reduce, + (void (*) (void *, const void *)) felem_inv, + (void (*) (void *, const void *)) felem_contract); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp224_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; unsigned i; @@ -1318,7 +1374,7 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; + felem(*pre_comp)[17][3] = NULL; felem *tmp_felems = NULL; felem_bytearray tmp; unsigned num_bytes; @@ -1326,28 +1382,28 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, size_t num_points = num; felem x_in, y_in, z_in, x_out, y_out, z_out; NISTP224_PRE_COMP *pre = NULL; - const felem (*g_pre_comp)[16][3] = NULL; + const felem(*g_pre_comp)[16][3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp224_pre_comp_dup, nistp224_pre_comp_free, - nistp224_pre_comp_clear_free); + nistp224_pre_comp_dup, nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ - g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; + g_pre_comp = (const felem(*)[16][3]) pre->g_pre_comp; else /* try to use the standard precomputation */ g_pre_comp = &gmul[0]; @@ -1356,147 +1412,137 @@ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, goto err; /* get the generator from precomputation */ if (!felem_to_BN(x, g_pre_comp[0][1][0]) || - !felem_to_BN(y, g_pre_comp[0][1][1]) || - !felem_to_BN(z, g_pre_comp[0][1][2])) - { + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points = num_points + 1; - } - - if (num_points > 0) - { - if (num_points >= 3) - { - /* unless we precompute multiples for just one or two points, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two + * points, converting those into affine form is time + * well spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); if (mixed) tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) /* the generator */ - { + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; felem_assign(pre_comp[i][1][0], x_out); felem_assign(pre_comp[i][1][1], y_out); felem_assign(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof g_secret); /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3]) pre_comp, + g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { + (!felem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -1512,10 +1558,11 @@ err: if (tmp_felems != NULL) free(tmp_felems); return ret; - } +} -int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp224_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP224_PRE_COMP *pre = NULL; int i, j; @@ -1526,113 +1573,113 @@ int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free); + nistp224_pre_comp_free, nistp224_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp224_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) + (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) goto err; - /* compute 2^56*G, 2^112*G, 2^168*G for the first table, - * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one + /* + * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, + * 2^84*G, 2^140*G, 2^196*G for the second one */ - for (i = 1; i <= 8; i <<= 1) - { + for (i = 1; i <= 8; i <<= 1) { point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); - for (j = 0; j < 27; ++j) - { + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) { point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - } + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } if (i == 8) break; point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - for (j = 0; j < 27; ++j) - { + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) { point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); - } + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]); } - for (i = 0; i < 2; i++) - { + } + for (i = 0; i < 2; i++) { /* g_pre_comp[i][0] is the point at infinity */ memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); /* the remaining multiples */ /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ point_add( - pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], - pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], - pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ point_add( - pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], - pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ point_add( - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], - pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], - pre->g_pre_comp[i][4][2]); - /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + + * 2^196*G + */ point_add( - pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], - pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], - pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); - for (j = 1; j < 8; ++j) - { + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { /* odd multiples: add G resp. 2^28*G */ point_add( - pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], - pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], - pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], - 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], - pre->g_pre_comp[i][1][2]); - } + pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2], + 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); } + } make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) + nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -1641,18 +1688,19 @@ int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp224_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp224_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free) - != NULL) + nistp224_pre_comp_free, nistp224_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libssl/src/crypto/ec/ecp_nistp256.c b/lib/libssl/src/crypto/ec/ecp_nistp256.c index 132ca0d2507..345f67d5207 100644 --- a/lib/libssl/src/crypto/ec/ecp_nistp256.c +++ b/lib/libssl/src/crypto/ec/ecp_nistp256.c @@ -112,41 +112,45 @@ typedef limb longfelem[NLIMBS * 2]; typedef u64 smallfelem[NLIMBS]; /* This is the value of the prime as four 64-bit words, little-endian. */ -static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; +static const u64 kPrime[4] = {0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul}; static const limb bottom32bits = 0xffffffff; static const u64 bottom63bits = 0x7ffffffffffffffful; /* bin32_to_felem takes a little-endian byte array and converts it into felem * form. This assumes that the CPU is little-endian. */ -static void bin32_to_felem(felem out, const u8 in[32]) - { - out[0] = *((u64*) &in[0]); - out[1] = *((u64*) &in[8]); - out[2] = *((u64*) &in[16]); - out[3] = *((u64*) &in[24]); - } +static void +bin32_to_felem(felem out, const u8 in[32]) +{ + out[0] = *((u64 *) & in[0]); + out[1] = *((u64 *) & in[8]); + out[2] = *((u64 *) & in[16]); + out[3] = *((u64 *) & in[24]); +} /* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, * 32 byte array. This assumes that the CPU is little-endian. */ -static void smallfelem_to_bin32(u8 out[32], const smallfelem in) - { - *((u64*) &out[0]) = in[0]; - *((u64*) &out[8]) = in[1]; - *((u64*) &out[16]) = in[2]; - *((u64*) &out[24]) = in[3]; - } +static void +smallfelem_to_bin32(u8 out[32], const smallfelem in) +{ + *((u64 *) & out[0]) = in[0]; + *((u64 *) & out[8]) = in[1]; + *((u64 *) & out[16]) = in[2]; + *((u64 *) & out[24]) = in[3]; +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -154,89 +158,95 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin32_to_felem(out, b_out); return 1; - } +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ -static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) - { +static BIGNUM * +smallfelem_to_BN(BIGNUM * out, const smallfelem in) +{ felem_bytearray b_in, b_out; smallfelem_to_bin32(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /* Field operations * ---------------- */ -static void smallfelem_one(smallfelem out) - { +static void +smallfelem_one(smallfelem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; out[3] = 0; - } +} -static void smallfelem_assign(smallfelem out, const smallfelem in) - { +static void +smallfelem_assign(smallfelem out, const smallfelem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* felem_sum sets out = out + in. */ -static void felem_sum(felem out, const felem in) - { +static void +felem_sum(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* felem_small_sum sets out = out + in. */ -static void felem_small_sum(felem out, const smallfelem in) - { +static void +felem_small_sum(felem out, const smallfelem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; out[3] += in[3]; - } +} /* felem_scalar sets out = out * scalar */ -static void felem_scalar(felem out, const u64 scalar) - { +static void +felem_scalar(felem out, const u64 scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; out[3] *= scalar; - } +} /* longfelem_scalar sets out = out * scalar */ -static void longfelem_scalar(longfelem out, const u64 scalar) - { +static void +longfelem_scalar(longfelem out, const u64 scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -245,27 +255,28 @@ static void longfelem_scalar(longfelem out, const u64 scalar) out[5] *= scalar; out[6] *= scalar; out[7] *= scalar; - } +} #define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) #define two105 (((limb)1) << 105) #define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) /* zero105 is 0 mod p */ -static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; +static const felem zero105 = {two105m41m9, two105, two105m41p9, two105m41p9}; /* smallfelem_neg sets |out| to |-small| * On exit: * out[i] < out[i] + 2^105 */ -static void smallfelem_neg(felem out, const smallfelem small) - { +static void +smallfelem_neg(felem out, const smallfelem small) +{ /* In order to prevent underflow, we subtract from 0 mod p. */ out[0] = zero105[0] - small[0]; out[1] = zero105[1] - small[1]; out[2] = zero105[2] - small[2]; out[3] = zero105[3] - small[3]; - } +} /* felem_diff subtracts |in| from |out| * On entry: @@ -273,8 +284,9 @@ static void smallfelem_neg(felem out, const smallfelem small) * On exit: * out[i] < out[i] + 2^105 */ -static void felem_diff(felem out, const felem in) - { +static void +felem_diff(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ out[0] += zero105[0]; out[1] += zero105[1]; @@ -285,14 +297,14 @@ static void felem_diff(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} #define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) #define two107 (((limb)1) << 107) #define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) /* zero107 is 0 mod p */ -static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; +static const felem zero107 = {two107m43m11, two107, two107m43p11, two107m43p11}; /* An alternative felem_diff for larger inputs |in| * felem_diff_zero107 subtracts |in| from |out| @@ -301,8 +313,9 @@ static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 * On exit: * out[i] < out[i] + 2^107 */ -static void felem_diff_zero107(felem out, const felem in) - { +static void +felem_diff_zero107(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ out[0] += zero107[0]; out[1] += zero107[1]; @@ -313,7 +326,7 @@ static void felem_diff_zero107(felem out, const felem in) out[1] -= in[1]; out[2] -= in[2]; out[3] -= in[3]; - } +} /* longfelem_diff subtracts |in| from |out| * On entry: @@ -321,13 +334,14 @@ static void felem_diff_zero107(felem out, const felem in) * On exit: * out[i] < out[i] + 2^70 + 2^40 */ -static void longfelem_diff(longfelem out, const longfelem in) - { - static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); - static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); - static const limb two70 = (((limb)1) << 70); - static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); - static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); +static void +longfelem_diff(longfelem out, const longfelem in) +{ + static const limb two70m8p6 = (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); + static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); + static const limb two70 = (((limb) 1) << 70); + static const limb two70m40m38p6 = (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + (((limb) 1) << 6); + static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); /* add 0 mod p to avoid underflow */ out[0] += two70m8p6; @@ -348,7 +362,7 @@ static void longfelem_diff(longfelem out, const longfelem in) out[5] -= in[5]; out[6] -= in[6]; out[7] -= in[7]; - } +} #define two64m0 (((limb)1) << 64) - 1 #define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 @@ -356,7 +370,7 @@ static void longfelem_diff(longfelem out, const longfelem in) #define two64m32 (((limb)1) << 64) - (((limb)1) << 32) /* zero110 is 0 mod p */ -static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; +static const felem zero110 = {two64m0, two110p32m0, two64m46, two64m32}; /* felem_shrink converts an felem into a smallfelem. The result isn't quite * minimal as the value may be greater than p. @@ -366,12 +380,13 @@ static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; * On exit: * out[i] < 2^64 */ -static void felem_shrink(smallfelem out, const felem in) - { +static void +felem_shrink(smallfelem out, const felem in) +{ felem tmp; u64 a, b, mask; s64 high, low; - static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ /* Carry 2->3 */ tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); @@ -382,50 +397,58 @@ static void felem_shrink(smallfelem out, const felem in) tmp[1] = zero110[1] + in[1]; /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ - /* We perform two partial reductions where we eliminate the - * high-word of tmp[3]. We don't update the other words till the end. + /* + * We perform two partial reductions where we eliminate the high-word + * of tmp[3]. We don't update the other words till the end. */ - a = tmp[3] >> 64; /* a < 2^46 */ + a = tmp[3] >> 64; /* a < 2^46 */ tmp[3] = (u64) tmp[3]; tmp[3] -= a; - tmp[3] += ((limb)a) << 32; + tmp[3] += ((limb) a) << 32; /* tmp[3] < 2^79 */ b = a; - a = tmp[3] >> 64; /* a < 2^15 */ - b += a; /* b < 2^46 + 2^15 < 2^47 */ + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ tmp[3] = (u64) tmp[3]; tmp[3] -= a; - tmp[3] += ((limb)a) << 32; + tmp[3] += ((limb) a) << 32; /* tmp[3] < 2^64 + 2^47 */ - /* This adjusts the other two words to complete the two partial - * reductions. */ + /* + * This adjusts the other two words to complete the two partial + * reductions. + */ tmp[0] += b; - tmp[1] -= (((limb)b) << 32); + tmp[1] -= (((limb) b) << 32); - /* In order to make space in tmp[3] for the carry from 2 -> 3, we - * conditionally subtract kPrime if tmp[3] is large enough. */ + /* + * In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. + */ high = tmp[3] >> 64; /* As tmp[3] < 2^65, high is either 1 or 0 */ high <<= 63; high >>= 63; - /* high is: - * all ones if the high word of tmp[3] is 1 - * all zeros if the high word of tmp[3] if 0 */ + /* + * high is: all ones if the high word of tmp[3] is 1 all zeros if + * the high word of tmp[3] if 0 + */ low = tmp[3]; mask = low >> 63; - /* mask is: - * all ones if the MSB of low is 1 - * all zeros if the MSB of low if 0 */ + /* + * mask is: all ones if the MSB of low is 1 all zeros if the MSB + * of low if 0 + */ low &= bottom63bits; low -= kPrime3Test; /* if low was greater than kPrime3Test then the MSB is zero */ low = ~low; low >>= 63; - /* low is: - * all ones if low was > kPrime3Test - * all zeros if low was <= kPrime3Test */ + /* + * low is: all ones if low was > kPrime3Test all zeros if low was + * <= kPrime3Test + */ mask = (mask & low) | high; tmp[0] -= mask & kPrime[0]; tmp[1] -= mask & kPrime[1]; @@ -433,25 +456,29 @@ static void felem_shrink(smallfelem out, const felem in) tmp[3] -= mask & kPrime[3]; /* tmp[3] < 2**64 - 2**32 + 1 */ - tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; - tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; - tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; + tmp[1] += ((u64) (tmp[0] >> 64)); + tmp[0] = (u64) tmp[0]; + tmp[2] += ((u64) (tmp[1] >> 64)); + tmp[1] = (u64) tmp[1]; + tmp[3] += ((u64) (tmp[2] >> 64)); + tmp[2] = (u64) tmp[2]; /* tmp[i] < 2^64 */ out[0] = tmp[0]; out[1] = tmp[1]; out[2] = tmp[2]; out[3] = tmp[3]; - } +} /* smallfelem_expand converts a smallfelem to an felem */ -static void smallfelem_expand(felem out, const smallfelem in) - { +static void +smallfelem_expand(felem out, const smallfelem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; out[3] = in[3]; - } +} /* smallfelem_square sets |out| = |small|^2 * On entry: @@ -459,8 +486,9 @@ static void smallfelem_expand(felem out, const smallfelem in) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void smallfelem_square(longfelem out, const smallfelem small) - { +static void +smallfelem_square(longfelem out, const smallfelem small) +{ limb a; u64 high, low; @@ -529,7 +557,7 @@ static void smallfelem_square(longfelem out, const smallfelem small) high = a >> 64; out[6] += low; out[7] = high; - } +} /* felem_square sets |out| = |in|^2 * On entry: @@ -537,12 +565,13 @@ static void smallfelem_square(longfelem out, const smallfelem small) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_square(longfelem out, const felem in) - { +static void +felem_square(longfelem out, const felem in) +{ u64 small[4]; felem_shrink(small, in); smallfelem_square(out, small); - } +} /* smallfelem_mul sets |out| = |small1| * |small2| * On entry: @@ -551,8 +580,9 @@ static void felem_square(longfelem out, const felem in) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) - { +static void +smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) +{ limb a; u64 high, low; @@ -657,7 +687,7 @@ static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfe high = a >> 64; out[6] += low; out[7] = high; - } +} /* felem_mul sets |out| = |in1| * |in2| * On entry: @@ -666,13 +696,14 @@ static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfe * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_mul(longfelem out, const felem in1, const felem in2) - { +static void +felem_mul(longfelem out, const felem in1, const felem in2) +{ smallfelem small1, small2; felem_shrink(small1, in1); felem_shrink(small2, in2); smallfelem_mul(out, small1, small2); - } +} /* felem_small_mul sets |out| = |small1| * |in2| * On entry: @@ -681,23 +712,24 @@ static void felem_mul(longfelem out, const felem in1, const felem in2) * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) - { +static void +felem_small_mul(longfelem out, const smallfelem small1, const felem in2) +{ smallfelem small2; felem_shrink(small2, in2); smallfelem_mul(out, small1, small2); - } +} #define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) #define two100 (((limb)1) << 100) #define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) /* zero100 is 0 mod p */ -static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; +static const felem zero100 = {two100m36m4, two100, two100m36p4, two100m36p4}; /* Internal function for the different flavours of felem_reduce. * felem_reduce_ reduces the higher coefficients in[4]-in[7]. * On entry: - * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] * out[1] >= in[7] + 2^32*in[4] * out[2] >= in[5] + 2^32*in[5] * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] @@ -707,8 +739,9 @@ static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] * out[3] <= out[3] + 2^32*in[4] + 3*in[7] */ -static void felem_reduce_(felem out, const longfelem in) - { +static void +felem_reduce_(felem out, const longfelem in) +{ int128_t c; /* combine common terms from below */ c = in[4] + (in[5] << 32); @@ -739,7 +772,7 @@ static void felem_reduce_(felem out, const longfelem in) out[0] -= (in[7] << 32); out[2] += (in[7] << 33); out[3] += (in[7] * 3); - } +} /* felem_reduce converts a longfelem into an felem. * To be called directly after felem_square or felem_mul. @@ -749,8 +782,9 @@ static void felem_reduce_(felem out, const longfelem in) * On exit: * out[i] < 2^101 */ -static void felem_reduce(felem out, const longfelem in) - { +static void +felem_reduce(felem out, const longfelem in) +{ out[0] = zero100[0] + in[0]; out[1] = zero100[1] + in[1]; out[2] = zero100[2] + in[2]; @@ -758,17 +792,18 @@ static void felem_reduce(felem out, const longfelem in) felem_reduce_(out, in); - /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 - * out[1] > 2^100 - 2^64 - 7*2^96 > 0 - * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 - * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 - * - * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 - * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 - * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 - * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + /* + * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 out[2] > 2^100 - 2^36 + 2^4 - + * 5*2^64 - 5*2^96 > 0 out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 + * - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 out[1] < 2^100 + + * 3*2^64 + 5*2^64 + 3*2^97 < 2^101 out[2] < 2^100 + 5*2^64 + 2^64 + + * 3*2^65 + 2^97 < 2^101 out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < + * 2^101 */ - } +} /* felem_reduce_zero105 converts a larger longfelem into an felem. * On entry: @@ -776,8 +811,9 @@ static void felem_reduce(felem out, const longfelem in) * On exit: * out[i] < 2^106 */ -static void felem_reduce_zero105(felem out, const longfelem in) - { +static void +felem_reduce_zero105(felem out, const longfelem in) +{ out[0] = zero105[0] + in[0]; out[1] = zero105[1] + in[1]; out[2] = zero105[2] + in[2]; @@ -785,34 +821,36 @@ static void felem_reduce_zero105(felem out, const longfelem in) felem_reduce_(out, in); - /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 - * out[1] > 2^105 - 2^71 - 2^103 > 0 - * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 - * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 - * - * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 - * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + /* + * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 out[2] > 2^105 - 2^41 + 2^9 - + * 2^71 - 2^103 > 0 out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - + * 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 out[1] < 2^105 + 2^71 + + * 2^71 + 2^103 < 2^106 out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < + * 2^106 out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 */ - } +} /* subtract_u64 sets *result = *result - v and *carry to one if the subtraction * underflowed. */ -static void subtract_u64(u64* result, u64* carry, u64 v) - { +static void +subtract_u64(u64 * result, u64 * carry, u64 v) +{ uint128_t r = *result; r -= v; *carry = (r >> 64) & 1; *result = (u64) r; - } +} /* felem_contract converts |in| to its unique, minimal representation. * On entry: * in[i] < 2^109 */ -static void felem_contract(smallfelem out, const felem in) - { +static void +felem_contract(smallfelem out, const felem in) +{ unsigned i; u64 all_equal_so_far = 0, result = 0, carry; @@ -820,20 +858,25 @@ static void felem_contract(smallfelem out, const felem in) /* small is minimal except that the value might be > p */ all_equal_so_far--; - /* We are doing a constant time test if out >= kPrime. We need to + /* + * We are doing a constant time test if out >= kPrime. We need to * compare each u64, from most-significant to least significant. For - * each one, if all words so far have been equal (m is all ones) then a - * non-equal result is the answer. Otherwise we continue. */ - for (i = 3; i < 4; i--) - { + * each one, if all words so far have been equal (m is all ones) then + * a non-equal result is the answer. Otherwise we continue. + */ + for (i = 3; i < 4; i--) { u64 equal; uint128_t a = ((uint128_t) kPrime[i]) - out[i]; - /* if out[i] > kPrime[i] then a will underflow and the high - * 64-bits will all be set. */ + /* + * if out[i] > kPrime[i] then a will underflow and the high + * 64-bits will all be set. + */ result |= all_equal_so_far & ((u64) (a >> 64)); - /* if kPrime[i] == out[i] then |equal| will be all zeros and - * the decrement will make it all ones. */ + /* + * if kPrime[i] == out[i] then |equal| will be all zeros and + * the decrement will make it all ones. + */ equal = kPrime[i] ^ out[i]; equal--; equal &= equal << 32; @@ -845,10 +888,12 @@ static void felem_contract(smallfelem out, const felem in) equal = ((s64) equal) >> 63; all_equal_so_far &= equal; - } + } - /* if all_equal_so_far is still all ones then the two values are equal - * and so out >= kPrime is true. */ + /* + * if all_equal_so_far is still all ones then the two values are + * equal and so out >= kPrime is true. + */ result |= all_equal_so_far; /* if out >= kPrime then we subtract kPrime. */ @@ -865,35 +910,38 @@ static void felem_contract(smallfelem out, const felem in) subtract_u64(&out[3], &carry, carry); subtract_u64(&out[3], &carry, result & kPrime[3]); - } +} -static void smallfelem_square_contract(smallfelem out, const smallfelem in) - { +static void +smallfelem_square_contract(smallfelem out, const smallfelem in) +{ longfelem longtmp; felem tmp; smallfelem_square(longtmp, in); felem_reduce(tmp, longtmp); felem_contract(out, tmp); - } +} -static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) - { +static void +smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) +{ longfelem longtmp; felem tmp; smallfelem_mul(longtmp, in1, in2); felem_reduce(tmp, longtmp); felem_contract(out, tmp); - } +} /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * small[i] < 2^64 */ -static limb smallfelem_is_zero(const smallfelem small) - { +static limb +smallfelem_is_zero(const smallfelem small) +{ limb result; u64 is_p; @@ -908,9 +956,9 @@ static limb smallfelem_is_zero(const smallfelem small) is_zero = ((s64) is_zero) >> 63; is_p = (small[0] ^ kPrime[0]) | - (small[1] ^ kPrime[1]) | - (small[2] ^ kPrime[2]) | - (small[3] ^ kPrime[3]); + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | + (small[3] ^ kPrime[3]); is_p--; is_p &= is_p << 32; is_p &= is_p << 16; @@ -925,12 +973,13 @@ static limb smallfelem_is_zero(const smallfelem small) result = is_zero; result |= ((limb) is_zero) << 64; return result; - } +} -static int smallfelem_is_zero_int(const smallfelem small) - { - return (int) (smallfelem_is_zero(small) & ((limb)1)); - } +static int +smallfelem_is_zero_int(const smallfelem small) +{ + return (int) (smallfelem_is_zero(small) & ((limb) 1)); +} /* felem_inv calculates |out| = |in|^{-1} * @@ -939,77 +988,110 @@ static int smallfelem_is_zero_int(const smallfelem small) * a^{p-1} = 1 (mod p) * a^{p-2} = a^{-1} (mod p) */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2; /* each e_I will hold |in|^{2^I - 1} */ felem e2, e4, e8, e16, e32, e64; longfelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */ felem_assign(e2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); + felem_reduce(ftmp, tmp);/* 2^4 - 2^0 */ felem_assign(e4, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ - felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^5 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^6 - 2^2 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^7 - 2^3 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); + felem_reduce(ftmp, tmp);/* 2^8 - 2^0 */ felem_assign(e8, ftmp); for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^16 - 2^8 */ - felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); + felem_reduce(ftmp, tmp);/* 2^16 - 2^0 */ felem_assign(e16, ftmp); for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^32 - 2^16 */ - felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); + felem_reduce(ftmp, tmp);/* 2^32 - 2^0 */ felem_assign(e32, ftmp); for (i = 0; i < 32; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^64 - 2^32 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ felem_assign(e64, ftmp); - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp);/* 2^64 - 2^32 + 2^0 */ for (i = 0; i < 192; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^256 - 2^224 + 2^192 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ - felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + felem_mul(tmp, e64, e32); + felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^80 - 2^16 */ - felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); + felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^88 - 2^8 */ - felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); + felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ for (i = 0; i < 4; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^92 - 2^4 */ - felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ - felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ - felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ - - felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ - } + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); + felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); + felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ +} -static void smallfelem_inv_contract(smallfelem out, const smallfelem in) - { +static void +smallfelem_inv_contract(smallfelem out, const smallfelem in) +{ felem tmp; smallfelem_expand(tmp, in); felem_inv(tmp, tmp); felem_contract(out, tmp); - } +} /* Group operations * ---------------- @@ -1027,8 +1109,8 @@ static void smallfelem_inv_contract(smallfelem out, const smallfelem in) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ longfelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; smallfelem small1, small2; @@ -1101,14 +1183,14 @@ point_double(felem x_out, felem y_out, felem z_out, /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ felem_reduce_zero105(y_out, tmp); /* y_out[i] < 2^106 */ - } +} /* point_double_small is the same as point_double, except that it operates on * smallfelems */ static void point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, - const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) - { + const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) +{ felem felem_x_out, felem_y_out, felem_z_out; felem felem_x_in, felem_y_in, felem_z_in; @@ -1116,35 +1198,33 @@ point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, smallfelem_expand(felem_y_in, y_in); smallfelem_expand(felem_z_in, z_in); point_double(felem_x_out, felem_y_out, felem_z_out, - felem_x_in, felem_y_in, felem_z_in); + felem_x_in, felem_y_in, felem_z_in); felem_shrink(x_out, felem_x_out); felem_shrink(y_out, felem_y_out); felem_shrink(z_out, felem_z_out); - } +} /* copy_conditional copies in to out iff mask is all ones. */ static void copy_conditional(felem out, const felem in, limb mask) - { +{ unsigned i; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { const limb tmp = mask & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /* copy_small_conditional copies in to out iff mask is all ones. */ static void copy_small_conditional(felem out, const smallfelem in, limb mask) - { +{ unsigned i; const u64 mask64 = mask; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); - } } +} /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) * @@ -1156,10 +1236,11 @@ copy_small_conditional(felem out, const smallfelem in, limb mask) * are equal, (while not equal to the point at infinity). This case never * happens during single point multiplication, so there is no timing leak for * ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; longfelem tmp, tmp2; smallfelem small1, small2, small3, small4, small5; @@ -1176,8 +1257,7 @@ static void point_add(felem x3, felem y3, felem z3, /* ftmp[i] < 2^101 */ felem_shrink(small1, ftmp); - if(!mixed) - { + if (!mixed) { /* ftmp2 = z2z2 = z2**2 */ smallfelem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -1213,9 +1293,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_mul(tmp, y1, ftmp2); felem_reduce(ftmp6, tmp); /* ftmp6[i] < 2^101 */ - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* u1 = ftmp3 = x1*z2z2 */ @@ -1230,7 +1308,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp2 = y1 * z2**3 */ felem_assign(ftmp6, y1); /* ftmp6[i] < 2^106 */ - } + } /* u2 = x2*z1z1 */ smallfelem_mul(tmp, x2, small1); @@ -1258,18 +1336,16 @@ static void point_add(felem x3, felem y3, felem z3, /* r = ftmp5 = (s2 - s1)*2 */ felem_diff_zero107(ftmp5, ftmp6); - /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ + /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ felem_scalar(ftmp5, 2); /* ftmp5[i] < 2^109 */ felem_shrink(small1, ftmp5); y_equal = smallfelem_is_zero(small1); - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* I = ftmp = (2h)**2 */ felem_assign(ftmp, ftmp4); felem_scalar(ftmp, 2); @@ -1316,14 +1392,15 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* point_add_small is the same as point_add, except that it operates on * smallfelems */ -static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, - smallfelem x1, smallfelem y1, smallfelem z1, - smallfelem x2, smallfelem y2, smallfelem z2) - { +static void +point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) +{ felem felem_x3, felem_y3, felem_z3; felem felem_x1, felem_y1, felem_z1; smallfelem_expand(felem_x1, x1); @@ -1333,7 +1410,7 @@ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, felem_shrink(x3, felem_x3); felem_shrink(y3, felem_y3); felem_shrink(z3, felem_z3); - } +} /* Base point pre computation * -------------------------- @@ -1373,113 +1450,113 @@ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, /* gmul is the table of precomputed base points */ static const smallfelem gmul[2][16][3] = {{{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, - {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, - {1, 0, 0, 0}}, - {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, - {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, - {1, 0, 0, 0}}, - {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, - {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, - {1, 0, 0, 0}}, - {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, - {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, - {1, 0, 0, 0}}, - {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, - {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, - {1, 0, 0, 0}}, - {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, - {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, - {1, 0, 0, 0}}, - {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, - {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, - {1, 0, 0, 0}}, - {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, - {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, - {1, 0, 0, 0}}, - {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, - {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, - {1, 0, 0, 0}}, - {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, - {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, - {1, 0, 0, 0}}, - {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, - {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, - {1, 0, 0, 0}}, - {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, - {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, - {1, 0, 0, 0}}, - {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, - {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, - {1, 0, 0, 0}}, - {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, - {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, - {1, 0, 0, 0}}, - {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, - {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, - {1, 0, 0, 0}}}, - {{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, - {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, - {1, 0, 0, 0}}, - {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, - {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, - {1, 0, 0, 0}}, - {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, - {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, - {1, 0, 0, 0}}, - {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, - {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, - {1, 0, 0, 0}}, - {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, - {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, - {1, 0, 0, 0}}, - {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, - {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, - {1, 0, 0, 0}}, - {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, - {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, - {1, 0, 0, 0}}, - {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, - {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, - {1, 0, 0, 0}}, - {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, - {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, - {1, 0, 0, 0}}, - {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, - {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, - {1, 0, 0, 0}}, - {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, - {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, - {1, 0, 0, 0}}, - {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, - {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, - {1, 0, 0, 0}}, - {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, - {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, - {1, 0, 0, 0}}, - {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, - {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, - {1, 0, 0, 0}}, - {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, - {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, - {1, 0, 0, 0}}}}; +{0, 0, 0, 0}, +{0, 0, 0, 0}}, +{{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, +{0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, +{1, 0, 0, 0}}, +{{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, +{0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, +{1, 0, 0, 0}}, +{{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, +{0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, +{1, 0, 0, 0}}, +{{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, +{0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, +{1, 0, 0, 0}}, +{{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, +{0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, +{1, 0, 0, 0}}, +{{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, +{0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, +{1, 0, 0, 0}}, +{{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, +{0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, +{1, 0, 0, 0}}, +{{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, +{0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, +{1, 0, 0, 0}}, +{{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, +{0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, +{1, 0, 0, 0}}, +{{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, +{0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, +{1, 0, 0, 0}}, +{{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, +{0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, +{1, 0, 0, 0}}, +{{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, +{0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, +{1, 0, 0, 0}}, +{{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, +{0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, +{1, 0, 0, 0}}, +{{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, +{0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, +{1, 0, 0, 0}}, +{{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, +{0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, +{1, 0, 0, 0}}}, +{{{0, 0, 0, 0}, +{0, 0, 0, 0}, +{0, 0, 0, 0}}, +{{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, +{0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, +{1, 0, 0, 0}}, +{{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, +{0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, +{1, 0, 0, 0}}, +{{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, +{0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, +{1, 0, 0, 0}}, +{{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, +{0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, +{1, 0, 0, 0}}, +{{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, +{0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, +{1, 0, 0, 0}}, +{{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, +{0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, +{1, 0, 0, 0}}, +{{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, +{0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, +{1, 0, 0, 0}}, +{{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, +{0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, +{1, 0, 0, 0}}, +{{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, +{0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, +{1, 0, 0, 0}}, +{{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, +{0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, +{1, 0, 0, 0}}, +{{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, +{0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, +{1, 0, 0, 0}}, +{{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, +{0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, +{1, 0, 0, 0}}, +{{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, +{0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, +{1, 0, 0, 0}}, +{{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, +{0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, +{1, 0, 0, 0}}, +{{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, +{0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, +{1, 0, 0, 0}}}}; /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) - { +static void +select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) +{ unsigned i, j; u64 *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(smallfelem)); - for (i = 0; i < size; i++) - { - const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; + for (i = 0; i < size; i++) { + const u64 *inlimbs = (u64 *) & pre_comp[i][0][0]; u64 mask = i ^ idx; mask |= mask >> 4; mask |= mask >> 2; @@ -1488,26 +1565,28 @@ static void select_point(const u64 idx, unsigned int size, const smallfelem pre_ mask--; for (j = 0; j < NLIMBS * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, int i) - { +static char +get_bit(const felem_bytearray in, int i) +{ if ((i < 0) || (i >= 256)) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) +{ int i, skip; unsigned num, gen_mul = (g_scalar != NULL); felem nq[3], ftmp; @@ -1518,20 +1597,20 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (two in each of the last 32 rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (two in each of the last 32 rounds) and + * additions of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 255 : 31); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 255 : 31); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 31)) - { + if (gen_mul && (i <= 31)) { /* first, look 32 bits upwards */ bits = get_bit(g_scalar, i + 224) << 3; bits |= get_bit(g_scalar, i + 160) << 2; @@ -1540,19 +1619,16 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[1], tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { smallfelem_expand(nq[0], tmp[0]); smallfelem_expand(nq[1], tmp[1]); smallfelem_expand(nq[2], tmp[2]); skip = 0; - } + } /* second, look at the current position */ bits = get_bit(g_scalar, i + 192) << 3; @@ -1562,16 +1638,13 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp[0], tmp); point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1580,32 +1653,33 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, bits |= get_bit(scalars[num], i - 1); ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - /* select the point to add or subtract, in constant time */ + /* + * select the point to add or subtract, in + * constant time + */ select_point(digit, 17, pre_comp[num], tmp); - smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); felem_contract(tmp[1], ftmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { smallfelem_expand(nq[0], tmp[0]); smallfelem_expand(nq[1], tmp[1]); smallfelem_expand(nq[2], tmp[2]); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /* Precomputation for the group generator. */ typedef struct { @@ -1627,20 +1701,20 @@ EC_GFp_nistp256_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_nistp256_point_get_affine_coordinates, + ec_GFp_nistp256_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -1663,32 +1737,34 @@ EC_GFp_nistp256_method(void) /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP256_PRE_COMP *nistp256_pre_comp_new() - { +static NISTP256_PRE_COMP * +nistp256_pre_comp_new() +{ NISTP256_PRE_COMP *ret = NULL; ret = (NISTP256_PRE_COMP *) malloc(sizeof *ret); - if (!ret) - { + if (!ret) { ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp256_pre_comp_dup(void *src_) - { +static void * +nistp256_pre_comp_dup(void *src_) +{ NISTP256_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp256_pre_comp_free(void *pre_) - { +static void +nistp256_pre_comp_free(void *pre_) +{ int i; NISTP256_PRE_COMP *pre = pre_; @@ -1700,10 +1776,11 @@ static void nistp256_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp256_pre_comp_clear_free(void *pre_) - { +static void +nistp256_pre_comp_clear_free(void *pre_) +{ int i; NISTP256_PRE_COMP *pre = pre_; @@ -1716,43 +1793,46 @@ static void nistp256_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof *pre); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp256_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp256_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp256_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_256; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1760,76 +1840,82 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in; smallfelem x_out, y_out; longfelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { + if (x != NULL) { if (!smallfelem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { - if (!smallfelem_to_BN(y, y_out)) - { + if (y != NULL) { + if (!smallfelem_to_BN(y, y_out)) { ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); + ERR_R_BN_LIB); return 0; - } } - return 1; } + return 1; +} -static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, smallfelem points[ /* num */ ][3], smallfelem tmp_smallfelems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(smallfelem), - tmp_smallfelems, - (void (*)(void *)) smallfelem_one, - (int (*)(const void *)) smallfelem_is_zero_int, - (void (*)(void *, const void *)) smallfelem_assign, - (void (*)(void *, const void *)) smallfelem_square_contract, - (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, - (void (*)(void *, const void *)) smallfelem_inv_contract, - (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); - } + num, + points, + sizeof(smallfelem), + tmp_smallfelems, + (void (*) (void *)) smallfelem_one, + (int (*) (const void *)) smallfelem_is_zero_int, + (void (*) (void *, const void *)) smallfelem_assign, + (void (*) (void *, const void *)) smallfelem_square_contract, + (void (*) (void *, const void *, const void *)) smallfelem_mul_contract, + (void (*) (void *, const void *)) smallfelem_inv_contract, + (void (*) (void *, const void *)) smallfelem_assign /* nothing to contract */ ); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp256_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; int mixed = 0; @@ -1837,7 +1923,7 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - smallfelem (*pre_comp)[17][3] = NULL; + smallfelem(*pre_comp)[17][3] = NULL; smallfelem *tmp_smallfelems = NULL; felem_bytearray tmp; unsigned i, num_bytes; @@ -1846,28 +1932,28 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, smallfelem x_in, y_in, z_in; felem x_out, y_out, z_out; NISTP256_PRE_COMP *pre = NULL; - const smallfelem (*g_pre_comp)[16][3] = NULL; + const smallfelem(*g_pre_comp)[16][3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp256_pre_comp_dup, nistp256_pre_comp_free, - nistp256_pre_comp_clear_free); + nistp256_pre_comp_dup, nistp256_pre_comp_free, + nistp256_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ - g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; + g_pre_comp = (const smallfelem(*)[16][3]) pre->g_pre_comp; else /* try to use the standard precomputation */ g_pre_comp = &gmul[0]; @@ -1876,147 +1962,140 @@ int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, goto err; /* get the generator from precomputation */ if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || - !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || - !smallfelem_to_BN(z, g_pre_comp[0][1][2])) - { + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points++; - } - if (num_points > 0) - { - if (num_points >= 3) - { - /* unless we precompute multiples for just one or two points, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two + * points, converting those into affine form is time + * well spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(smallfelem)); if (mixed) tmp_smallfelems = malloc((num_points * 17 + 1) * sizeof(smallfelem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) - /* we didn't have a valid precomputation, so we pick - * the generator */ - { + /* + * we didn't have a valid precomputation, so + * we pick the generator + */ + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^256 */ - if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; felem_shrink(pre_comp[i][1][0], x_out); felem_shrink(pre_comp[i][1][1], y_out); felem_shrink(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add_small( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double_small( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof(g_secret)); /* reduce scalar to 0 <= scalar < 2^256 */ - if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const smallfelem (*)[17][3]) pre_comp, - g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const smallfelem(*)[17][3]) pre_comp, + g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const smallfelem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || - (!smallfelem_to_BN(z, z_in))) - { + (!smallfelem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -2032,10 +2111,11 @@ err: if (tmp_smallfelems != NULL) free(tmp_smallfelems); return ret; - } +} -int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp256_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP256_PRE_COMP *pre = NULL; int i, j; @@ -2047,106 +2127,106 @@ int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free); + nistp256_pre_comp_free, nistp256_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp256_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(x_tmp, &group->generator->X)) || - (!BN_to_felem(y_tmp, &group->generator->Y)) || - (!BN_to_felem(z_tmp, &group->generator->Z))) + (!BN_to_felem(y_tmp, &group->generator->Y)) || + (!BN_to_felem(z_tmp, &group->generator->Z))) goto err; felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); - /* compute 2^64*G, 2^128*G, 2^192*G for the first table, - * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one + /* + * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, + * 2^96*G, 2^160*G, 2^224*G for the second one */ - for (i = 1; i <= 8; i <<= 1) - { + for (i = 1; i <= 8; i <<= 1) { point_double_small( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); - for (j = 0; j < 31; ++j) - { + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 31; ++j) { point_double_small( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - } + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } if (i == 8) break; point_double_small( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - for (j = 0; j < 31; ++j) - { + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 31; ++j) { point_double_small( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); - } + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]); } - for (i = 0; i < 2; i++) - { + } + for (i = 0; i < 2; i++) { /* g_pre_comp[i][0] is the point at infinity */ memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); /* the remaining multiples */ /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ point_add_small( - pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], - pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ point_add_small( - pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], - pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ point_add_small( - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); - /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); + /* + * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + + * 2^224*G + */ point_add_small( - pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); - for (j = 1; j < 8; ++j) - { + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { /* odd multiples: add G resp. 2^32*G */ point_add_small( - pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], pre->g_pre_comp[i][2*j+1][2], - pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], - pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); - } + pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1], pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2], + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); } + } make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) + nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -2155,17 +2235,18 @@ int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp256_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp256_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free) - != NULL) + nistp256_pre_comp_free, nistp256_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libssl/src/crypto/ec/ecp_nistp521.c b/lib/libssl/src/crypto/ec/ecp_nistp521.c index c34c38b7e83..f5b72a4c0d3 100644 --- a/lib/libssl/src/crypto/ec/ecp_nistp521.c +++ b/lib/libssl/src/crypto/ec/ecp_nistp521.c @@ -133,46 +133,50 @@ static const limb bottom58bits = 0x3ffffffffffffff; /* bin66_to_felem takes a little-endian byte array and converts it into felem * form. This assumes that the CPU is little-endian. */ -static void bin66_to_felem(felem out, const u8 in[66]) - { - out[0] = (*((limb*) &in[0])) & bottom58bits; - out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; - out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; - out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; - out[4] = (*((limb*) &in[29])) & bottom58bits; - out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; - out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; - out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; - out[8] = (*((limb*) &in[58])) & bottom57bits; - } +static void +bin66_to_felem(felem out, const u8 in[66]) +{ + out[0] = (*((limb *) & in[0])) & bottom58bits; + out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits; + out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits; + out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits; + out[4] = (*((limb *) & in[29])) & bottom58bits; + out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits; + out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits; + out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits; + out[8] = (*((limb *) & in[58])) & bottom57bits; +} /* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte * array. This assumes that the CPU is little-endian. */ -static void felem_to_bin66(u8 out[66], const felem in) - { +static void +felem_to_bin66(u8 out[66], const felem in) +{ memset(out, 0, 66); - (*((limb*) &out[0])) = in[0]; - (*((limb*) &out[7])) |= in[1] << 2; - (*((limb*) &out[14])) |= in[2] << 4; - (*((limb*) &out[21])) |= in[3] << 6; - (*((limb*) &out[29])) = in[4]; - (*((limb*) &out[36])) |= in[5] << 2; - (*((limb*) &out[43])) |= in[6] << 4; - (*((limb*) &out[50])) |= in[7] << 6; - (*((limb*) &out[58])) = in[8]; - } + (*((limb *) & out[0])) = in[0]; + (*((limb *) & out[7])) |= in[1] << 2; + (*((limb *) & out[14])) |= in[2] << 4; + (*((limb *) & out[21])) |= in[3] << 6; + (*((limb *) & out[29])) = in[4]; + (*((limb *) & out[36])) |= in[5] << 2; + (*((limb *) & out[43])) |= in[6] << 4; + (*((limb *) & out[50])) |= in[7] << 6; + (*((limb *) & out[58])) = in[8]; +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +static void +flip_endian(u8 * out, const u8 * in, unsigned len) +{ unsigned i; for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } + out[i] = in[len - 1 - i]; +} /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ -static int BN_to_felem(felem out, const BIGNUM *bn) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -180,37 +184,37 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + if (num_bytes > sizeof b_out) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } - if (BN_is_negative(bn)) - { + } + if (BN_is_negative(bn)) { ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); return 0; - } + } num_bytes = BN_bn2bin(bn, b_in); flip_endian(b_out, b_in, num_bytes); bin66_to_felem(out, b_out); return 1; - } +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { +static BIGNUM * +felem_to_BN(BIGNUM * out, const felem in) +{ felem_bytearray b_in, b_out; felem_to_bin66(b_in, in); flip_endian(b_out, b_in, sizeof b_out); return BN_bin2bn(b_out, sizeof b_out, out); - } +} /* Field operations * ---------------- */ -static void felem_one(felem out) - { +static void +felem_one(felem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; @@ -220,10 +224,11 @@ static void felem_one(felem out) out[6] = 0; out[7] = 0; out[8] = 0; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; @@ -233,11 +238,12 @@ static void felem_assign(felem out, const felem in) out[6] = in[6]; out[7] = in[7]; out[8] = in[8]; - } +} /* felem_sum64 sets out = out + in. */ -static void felem_sum64(felem out, const felem in) - { +static void +felem_sum64(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; @@ -247,11 +253,12 @@ static void felem_sum64(felem out, const felem in) out[6] += in[6]; out[7] += in[7]; out[8] += in[8]; - } +} /* felem_scalar sets out = in * scalar */ -static void felem_scalar(felem out, const felem in, limb scalar) - { +static void +felem_scalar(felem out, const felem in, limb scalar) +{ out[0] = in[0] * scalar; out[1] = in[1] * scalar; out[2] = in[2] * scalar; @@ -261,11 +268,12 @@ static void felem_scalar(felem out, const felem in, limb scalar) out[6] = in[6] * scalar; out[7] = in[7] * scalar; out[8] = in[8] * scalar; - } +} /* felem_scalar64 sets out = out * scalar */ -static void felem_scalar64(felem out, limb scalar) - { +static void +felem_scalar64(felem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -275,11 +283,12 @@ static void felem_scalar64(felem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_scalar128 sets out = out * scalar */ -static void felem_scalar128(largefelem out, limb scalar) - { +static void +felem_scalar128(largefelem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -289,7 +298,7 @@ static void felem_scalar128(largefelem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_neg sets |out| to |-in| * On entry: @@ -297,11 +306,12 @@ static void felem_scalar128(largefelem out, limb scalar) * On exit: * out[i] < 2^62 */ -static void felem_neg(felem out, const felem in) - { +static void +felem_neg(felem out, const felem in) +{ /* In order to prevent underflow, we subtract from 0 mod p. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] = two62m3 - in[0]; out[1] = two62m2 - in[1]; @@ -312,7 +322,7 @@ static void felem_neg(felem out, const felem in) out[6] = two62m2 - in[6]; out[7] = two62m2 - in[7]; out[8] = two62m2 - in[8]; - } +} /* felem_diff64 subtracts |in| from |out| * On entry: @@ -320,11 +330,12 @@ static void felem_neg(felem out, const felem in) * On exit: * out[i] < out[i] + 2^62 */ -static void felem_diff64(felem out, const felem in) - { +static void +felem_diff64(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two62m3 - in[0]; out[1] += two62m2 - in[1]; @@ -335,7 +346,7 @@ static void felem_diff64(felem out, const felem in) out[6] += two62m2 - in[6]; out[7] += two62m2 - in[7]; out[8] += two62m2 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -343,11 +354,12 @@ static void felem_diff64(felem out, const felem in) * On exit: * out[i] < out[i] + 2^63 */ -static void felem_diff_128_64(largefelem out, const felem in) - { +static void +felem_diff_128_64(largefelem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two63m6 - in[0]; out[1] += two63m5 - in[1]; @@ -358,7 +370,7 @@ static void felem_diff_128_64(largefelem out, const felem in) out[6] += two63m5 - in[6]; out[7] += two63m5 - in[7]; out[8] += two63m5 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -366,11 +378,12 @@ static void felem_diff_128_64(largefelem out, const felem in) * On exit: * out[i] < out[i] + 2^127 - 2^69 */ -static void felem_diff128(largefelem out, const largefelem in) - { +static void +felem_diff128(largefelem out, const largefelem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); - static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); + static const uint128_t two127m70 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70); + static const uint128_t two127m69 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69); out[0] += (two127m70 - in[0]); out[1] += (two127m69 - in[1]); @@ -381,7 +394,7 @@ static void felem_diff128(largefelem out, const largefelem in) out[6] += (two127m69 - in[6]); out[7] += (two127m69 - in[7]); out[8] += (two127m69 - in[8]); - } +} /* felem_square sets |out| = |in|^2 * On entry: @@ -389,90 +402,92 @@ static void felem_diff128(largefelem out, const largefelem in) * On exit: * out[i] < 17 * max(in[i]) * max(in[i]) */ -static void felem_square(largefelem out, const felem in) - { +static void +felem_square(largefelem out, const felem in) +{ felem inx2, inx4; felem_scalar(inx2, in, 2); felem_scalar(inx4, in, 4); - /* We have many cases were we want to do - * in[x] * in[y] + - * in[y] * in[x] - * This is obviously just - * 2 * in[x] * in[y] - * However, rather than do the doubling on the 128 bit result, we - * double one of the inputs to the multiplication by reading from - * |inx2| */ + /* + * We have many cases were we want to do in[x] * in[y] + in[y] * + * in[x] This is obviously just 2 * in[x] * in[y] However, rather + * than do the doubling on the 128 bit result, we double one of the + * inputs to the multiplication by reading from |inx2| + */ out[0] = ((uint128_t) in[0]) * in[0]; out[1] = ((uint128_t) in[0]) * inx2[1]; out[2] = ((uint128_t) in[0]) * inx2[2] + - ((uint128_t) in[1]) * in[1]; + ((uint128_t) in[1]) * in[1]; out[3] = ((uint128_t) in[0]) * inx2[3] + - ((uint128_t) in[1]) * inx2[2]; + ((uint128_t) in[1]) * inx2[2]; out[4] = ((uint128_t) in[0]) * inx2[4] + - ((uint128_t) in[1]) * inx2[3] + - ((uint128_t) in[2]) * in[2]; + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; out[5] = ((uint128_t) in[0]) * inx2[5] + - ((uint128_t) in[1]) * inx2[4] + - ((uint128_t) in[2]) * inx2[3]; + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; out[6] = ((uint128_t) in[0]) * inx2[6] + - ((uint128_t) in[1]) * inx2[5] + - ((uint128_t) in[2]) * inx2[4] + - ((uint128_t) in[3]) * in[3]; + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; out[7] = ((uint128_t) in[0]) * inx2[7] + - ((uint128_t) in[1]) * inx2[6] + - ((uint128_t) in[2]) * inx2[5] + - ((uint128_t) in[3]) * inx2[4]; + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; out[8] = ((uint128_t) in[0]) * inx2[8] + - ((uint128_t) in[1]) * inx2[7] + - ((uint128_t) in[2]) * inx2[6] + - ((uint128_t) in[3]) * inx2[5] + - ((uint128_t) in[4]) * in[4]; + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; - /* The remaining limbs fall above 2^521, with the first falling at + /* + * The remaining limbs fall above 2^521, with the first falling at * 2^522. They correspond to locations one bit up from the limbs * produced above so we would have to multiply by two to align them. * Again, rather than operate on the 128-bit result, we double one of - * the inputs to the multiplication. If we want to double for both this - * reason, and the reason above, then we end up multiplying by four. */ + * the inputs to the multiplication. If we want to double for both + * this reason, and the reason above, then we end up multiplying by + * four. + */ /* 9 */ out[0] += ((uint128_t) in[1]) * inx4[8] + - ((uint128_t) in[2]) * inx4[7] + - ((uint128_t) in[3]) * inx4[6] + - ((uint128_t) in[4]) * inx4[5]; + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + + ((uint128_t) in[4]) * inx4[5]; /* 10 */ out[1] += ((uint128_t) in[2]) * inx4[8] + - ((uint128_t) in[3]) * inx4[7] + - ((uint128_t) in[4]) * inx4[6] + - ((uint128_t) in[5]) * inx2[5]; + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + + ((uint128_t) in[5]) * inx2[5]; /* 11 */ out[2] += ((uint128_t) in[3]) * inx4[8] + - ((uint128_t) in[4]) * inx4[7] + - ((uint128_t) in[5]) * inx4[6]; + ((uint128_t) in[4]) * inx4[7] + + ((uint128_t) in[5]) * inx4[6]; /* 12 */ out[3] += ((uint128_t) in[4]) * inx4[8] + - ((uint128_t) in[5]) * inx4[7] + - ((uint128_t) in[6]) * inx2[6]; + ((uint128_t) in[5]) * inx4[7] + + ((uint128_t) in[6]) * inx2[6]; /* 13 */ out[4] += ((uint128_t) in[5]) * inx4[8] + - ((uint128_t) in[6]) * inx4[7]; + ((uint128_t) in[6]) * inx4[7]; /* 14 */ out[5] += ((uint128_t) in[6]) * inx4[8] + - ((uint128_t) in[7]) * inx2[7]; + ((uint128_t) in[7]) * inx2[7]; /* 15 */ out[6] += ((uint128_t) in[7]) * inx4[8]; /* 16 */ out[7] += ((uint128_t) in[8]) * inx2[8]; - } +} /* felem_mul sets |out| = |in1| * |in2| * On entry: @@ -481,111 +496,112 @@ static void felem_square(largefelem out, const felem in) * On exit: * out[i] < 17 * max(in1[i]) * max(in2[i]) */ -static void felem_mul(largefelem out, const felem in1, const felem in2) - { +static void +felem_mul(largefelem out, const felem in1, const felem in2) +{ felem in2x2; felem_scalar(in2x2, in2, 2); out[0] = ((uint128_t) in1[0]) * in2[0]; out[1] = ((uint128_t) in1[0]) * in2[1] + - ((uint128_t) in1[1]) * in2[0]; + ((uint128_t) in1[1]) * in2[0]; out[2] = ((uint128_t) in1[0]) * in2[2] + - ((uint128_t) in1[1]) * in2[1] + - ((uint128_t) in1[2]) * in2[0]; + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; out[3] = ((uint128_t) in1[0]) * in2[3] + - ((uint128_t) in1[1]) * in2[2] + - ((uint128_t) in1[2]) * in2[1] + - ((uint128_t) in1[3]) * in2[0]; + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; out[4] = ((uint128_t) in1[0]) * in2[4] + - ((uint128_t) in1[1]) * in2[3] + - ((uint128_t) in1[2]) * in2[2] + - ((uint128_t) in1[3]) * in2[1] + - ((uint128_t) in1[4]) * in2[0]; + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; out[5] = ((uint128_t) in1[0]) * in2[5] + - ((uint128_t) in1[1]) * in2[4] + - ((uint128_t) in1[2]) * in2[3] + - ((uint128_t) in1[3]) * in2[2] + - ((uint128_t) in1[4]) * in2[1] + - ((uint128_t) in1[5]) * in2[0]; + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; out[6] = ((uint128_t) in1[0]) * in2[6] + - ((uint128_t) in1[1]) * in2[5] + - ((uint128_t) in1[2]) * in2[4] + - ((uint128_t) in1[3]) * in2[3] + - ((uint128_t) in1[4]) * in2[2] + - ((uint128_t) in1[5]) * in2[1] + - ((uint128_t) in1[6]) * in2[0]; + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; out[7] = ((uint128_t) in1[0]) * in2[7] + - ((uint128_t) in1[1]) * in2[6] + - ((uint128_t) in1[2]) * in2[5] + - ((uint128_t) in1[3]) * in2[4] + - ((uint128_t) in1[4]) * in2[3] + - ((uint128_t) in1[5]) * in2[2] + - ((uint128_t) in1[6]) * in2[1] + - ((uint128_t) in1[7]) * in2[0]; + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; out[8] = ((uint128_t) in1[0]) * in2[8] + - ((uint128_t) in1[1]) * in2[7] + - ((uint128_t) in1[2]) * in2[6] + - ((uint128_t) in1[3]) * in2[5] + - ((uint128_t) in1[4]) * in2[4] + - ((uint128_t) in1[5]) * in2[3] + - ((uint128_t) in1[6]) * in2[2] + - ((uint128_t) in1[7]) * in2[1] + - ((uint128_t) in1[8]) * in2[0]; + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; /* See comment in felem_square about the use of in2x2 here */ out[0] += ((uint128_t) in1[1]) * in2x2[8] + - ((uint128_t) in1[2]) * in2x2[7] + - ((uint128_t) in1[3]) * in2x2[6] + - ((uint128_t) in1[4]) * in2x2[5] + - ((uint128_t) in1[5]) * in2x2[4] + - ((uint128_t) in1[6]) * in2x2[3] + - ((uint128_t) in1[7]) * in2x2[2] + - ((uint128_t) in1[8]) * in2x2[1]; + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; out[1] += ((uint128_t) in1[2]) * in2x2[8] + - ((uint128_t) in1[3]) * in2x2[7] + - ((uint128_t) in1[4]) * in2x2[6] + - ((uint128_t) in1[5]) * in2x2[5] + - ((uint128_t) in1[6]) * in2x2[4] + - ((uint128_t) in1[7]) * in2x2[3] + - ((uint128_t) in1[8]) * in2x2[2]; + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; out[2] += ((uint128_t) in1[3]) * in2x2[8] + - ((uint128_t) in1[4]) * in2x2[7] + - ((uint128_t) in1[5]) * in2x2[6] + - ((uint128_t) in1[6]) * in2x2[5] + - ((uint128_t) in1[7]) * in2x2[4] + - ((uint128_t) in1[8]) * in2x2[3]; + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; out[3] += ((uint128_t) in1[4]) * in2x2[8] + - ((uint128_t) in1[5]) * in2x2[7] + - ((uint128_t) in1[6]) * in2x2[6] + - ((uint128_t) in1[7]) * in2x2[5] + - ((uint128_t) in1[8]) * in2x2[4]; + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; out[4] += ((uint128_t) in1[5]) * in2x2[8] + - ((uint128_t) in1[6]) * in2x2[7] + - ((uint128_t) in1[7]) * in2x2[6] + - ((uint128_t) in1[8]) * in2x2[5]; + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; out[5] += ((uint128_t) in1[6]) * in2x2[8] + - ((uint128_t) in1[7]) * in2x2[7] + - ((uint128_t) in1[8]) * in2x2[6]; + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; out[6] += ((uint128_t) in1[7]) * in2x2[8] + - ((uint128_t) in1[8]) * in2x2[7]; + ((uint128_t) in1[8]) * in2x2[7]; out[7] += ((uint128_t) in1[8]) * in2x2[8]; - } +} static const limb bottom52bits = 0xfffffffffffff; @@ -595,8 +611,9 @@ static const limb bottom52bits = 0xfffffffffffff; * On exit: * out[i] < 2^59 + 2^14 */ -static void felem_reduce(felem out, const largefelem in) - { +static void +felem_reduce(felem out, const largefelem in) +{ u64 overflow1, overflow2; out[0] = ((limb) in[0]) & bottom58bits; @@ -613,8 +630,9 @@ static void felem_reduce(felem out, const largefelem in) out[1] += ((limb) in[0]) >> 58; out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; - /* out[1] < 2^58 + 2^6 + 2^58 - * = 2^59 + 2^6 */ + /* + * out[1] < 2^58 + 2^6 + 2^58 = 2^59 + 2^6 + */ out[2] += ((limb) (in[0] >> 64)) >> 52; out[2] += ((limb) in[1]) >> 58; @@ -643,39 +661,43 @@ static void felem_reduce(felem out, const largefelem in) out[8] += ((limb) in[7]) >> 58; out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; - /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 - * < 2^59 + 2^13 */ + /* + * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 < 2^59 + 2^13 + */ overflow1 = ((limb) (in[7] >> 64)) >> 52; overflow1 += ((limb) in[8]) >> 58; overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; overflow2 = ((limb) (in[8] >> 64)) >> 52; - overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ - overflow2 <<= 1; /* overflow2 < 2^13 */ + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ - out[0] += overflow1; /* out[0] < 2^60 */ - out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - /* out[0] < 2^58 - * out[1] < 2^59 + 2^6 + 2^13 + 2^2 - * < 2^59 + 2^14 */ - } + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + /* + * out[0] < 2^58 out[1] < 2^59 + 2^6 + 2^13 + 2^2 < 2^59 + 2^14 + */ +} -static void felem_square_reduce(felem out, const felem in) - { +static void +felem_square_reduce(felem out, const felem in) +{ largefelem tmp; felem_square(tmp, in); felem_reduce(out, tmp); - } +} -static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { +static void +felem_mul_reduce(felem out, const felem in1, const felem in2) +{ largefelem tmp; felem_mul(tmp, in1, in2); felem_reduce(out, tmp); - } +} /* felem_inv calculates |out| = |in|^{-1} * @@ -684,117 +706,153 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2) * a^{p-1} = 1 (mod p) * a^{p-2} = a^{-1} (mod p) */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2, ftmp3, ftmp4; largefelem tmp; unsigned i; - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */ felem_assign(ftmp2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^4 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ felem_assign(ftmp2, ftmp3); - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ felem_assign(ftmp4, ftmp3); - felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 8; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 16; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 32; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 64; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + for (i = 0; i < 64; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 128; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + for (i = 0; i < 128; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 256; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + for (i = 0; i < 256; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ - for (i = 0; i < 9; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ - felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ + for (i = 0; i < 9; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); + felem_reduce(out, tmp); /* 2^512 - 3 */ } /* This is 2^521-1, expressed as an felem */ static const felem kPrime = - { +{ 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff - }; +}; /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * in[i] < 2^59 + 2^14 */ -static limb felem_is_zero(const felem in) - { +static limb +felem_is_zero(const felem in) +{ felem ftmp; limb is_zero, is_p; felem_assign(ftmp, in); - ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; + ftmp[0] += ftmp[8] >> 57; + ftmp[8] &= bottom57bits; /* ftmp[8] < 2^57 */ - ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; - ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; - ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; - ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; - ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; - ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; - ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; - ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; + ftmp[1] += ftmp[0] >> 58; + ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; + ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; + ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; + ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; + ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; + ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; + ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; + ftmp[7] &= bottom58bits; /* ftmp[8] < 2^57 + 4 */ - /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is - * greater than our bound for ftmp[8]. Therefore we only have to check - * if the zero is zero or 2^521-1. */ + /* + * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is + * greater than our bound for ftmp[8]. Therefore we only have to + * check if the zero is zero or 2^521-1. + */ is_zero = 0; is_zero |= ftmp[0]; @@ -808,8 +866,10 @@ static limb felem_is_zero(const felem in) is_zero |= ftmp[8]; is_zero--; - /* We know that ftmp[i] < 2^63, therefore the only way that the top bit - * can be set is if is_zero was 0 before the decrement. */ + /* + * We know that ftmp[i] < 2^63, therefore the only way that the top + * bit can be set is if is_zero was 0 before the decrement. + */ is_zero = ((s64) is_zero) >> 63; is_p = ftmp[0] ^ kPrime[0]; @@ -827,41 +887,57 @@ static limb felem_is_zero(const felem in) is_zero |= is_p; return is_zero; - } +} -static int felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +static int +felem_is_zero_int(const felem in) +{ + return (int) (felem_is_zero(in) & ((limb) 1)); +} /* felem_contract converts |in| to its unique, minimal representation. * On entry: * in[i] < 2^59 + 2^14 */ -static void felem_contract(felem out, const felem in) - { +static void +felem_contract(felem out, const felem in) +{ limb is_p, is_greater, sign; - static const limb two58 = ((limb)1) << 58; + static const limb two58 = ((limb) 1) << 58; felem_assign(out, in); - out[0] += out[8] >> 57; out[8] &= bottom57bits; + out[0] += out[8] >> 57; + out[8] &= bottom57bits; /* out[8] < 2^57 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - out[2] += out[1] >> 58; out[1] &= bottom58bits; - out[3] += out[2] >> 58; out[2] &= bottom58bits; - out[4] += out[3] >> 58; out[3] &= bottom58bits; - out[5] += out[4] >> 58; out[4] &= bottom58bits; - out[6] += out[5] >> 58; out[5] &= bottom58bits; - out[7] += out[6] >> 58; out[6] &= bottom58bits; - out[8] += out[7] >> 58; out[7] &= bottom58bits; + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + out[2] += out[1] >> 58; + out[1] &= bottom58bits; + out[3] += out[2] >> 58; + out[2] &= bottom58bits; + out[4] += out[3] >> 58; + out[3] &= bottom58bits; + out[5] += out[4] >> 58; + out[4] &= bottom58bits; + out[6] += out[5] >> 58; + out[5] &= bottom58bits; + out[7] += out[6] >> 58; + out[6] &= bottom58bits; + out[8] += out[7] >> 58; + out[7] &= bottom58bits; /* out[8] < 2^57 + 4 */ - /* If the value is greater than 2^521-1 then we have to subtract + /* + * If the value is greater than 2^521-1 then we have to subtract * 2^521-1 out. See the comments in felem_is_zero regarding why we - * don't test for other multiples of the prime. */ + * don't test for other multiples of the prime. + */ - /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ + /* + * First, if |out| is equal to 2^521-1, we subtract it out to get + * zero. + */ is_p = out[0] ^ kPrime[0]; is_p |= out[1] ^ kPrime[1]; @@ -895,8 +971,10 @@ static void felem_contract(felem out, const felem in) out[7] &= is_p; out[8] &= is_p; - /* In order to test that |out| >= 2^521-1 we need only test if out[8] - * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ + /* + * In order to test that |out| >= 2^521-1 we need only test if out[8] + * >> 57 is greater than zero as (2^521-1) + x >= 2^522 + */ is_greater = out[8] >> 57; is_greater |= is_greater << 32; is_greater |= is_greater << 16; @@ -917,18 +995,40 @@ static void felem_contract(felem out, const felem in) out[8] -= kPrime[8] & is_greater; /* Eliminate negative coefficients */ - sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); - sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); - sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); - sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); - sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); - sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - } + sign = -(out[0] >> 63); + out[0] += (two58 & sign); + out[1] -= (1 & sign); + sign = -(out[1] >> 63); + out[1] += (two58 & sign); + out[2] -= (1 & sign); + sign = -(out[2] >> 63); + out[2] += (two58 & sign); + out[3] -= (1 & sign); + sign = -(out[3] >> 63); + out[3] += (two58 & sign); + out[4] -= (1 & sign); + sign = -(out[4] >> 63); + out[4] += (two58 & sign); + out[5] -= (1 & sign); + sign = -(out[0] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); + sign = -(out[5] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); +} /* Group operations * ---------------- @@ -946,8 +1046,8 @@ static void felem_contract(felem out, const felem in) * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, - const felem x_in, const felem y_in, const felem z_in) - { + const felem x_in, const felem y_in, const felem z_in) +{ largefelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; @@ -956,15 +1056,15 @@ point_double(felem x_out, felem y_out, felem z_out, /* delta = z^2 */ felem_square(tmp, z_in); - felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ /* gamma = y^2 */ felem_square(tmp, y_in); - felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ /* beta = x*gamma */ felem_mul(tmp, x_in, gamma); - felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + felem_reduce(beta, tmp);/* beta[i] < 2^59 + 2^14 */ /* alpha = 3*(x-delta)*(x+delta) */ felem_diff64(ftmp, delta); @@ -974,17 +1074,17 @@ point_double(felem x_out, felem y_out, felem z_out, felem_scalar64(ftmp2, 3); /* ftmp2[i] < 3*2^60 + 3*2^15 */ felem_mul(tmp, ftmp, ftmp2); - /* tmp[i] < 17(3*2^121 + 3*2^76) - * = 61*2^121 + 61*2^76 - * < 64*2^121 + 64*2^76 - * = 2^127 + 2^82 - * < 2^128 */ + /* + * tmp[i] < 17(3*2^121 + 3*2^76) = 61*2^121 + 61*2^76 < 64*2^121 + + * 64*2^76 = 2^127 + 2^82 < 2^128 + */ felem_reduce(alpha, tmp); /* x' = alpha^2 - 8*beta */ felem_square(tmp, alpha); - /* tmp[i] < 17*2^120 - * < 2^125 */ + /* + * tmp[i] < 17*2^120 < 2^125 + */ felem_assign(ftmp, beta); felem_scalar64(ftmp, 8); /* ftmp[i] < 2^62 + 2^17 */ @@ -999,8 +1099,9 @@ point_double(felem x_out, felem y_out, felem z_out, felem_sum64(ftmp, z_in); /* ftmp[i] < 2^60 + 2^15 */ felem_square(tmp, ftmp); - /* tmp[i] < 17(2^122) - * < 2^127 */ + /* + * tmp[i] < 17(2^122) < 2^127 + */ felem_diff_128_64(tmp, delta); /* tmp[i] < 2^127 + 2^63 */ felem_reduce(z_out, tmp); @@ -1011,36 +1112,39 @@ point_double(felem x_out, felem y_out, felem z_out, felem_diff64(beta, x_out); /* beta[i] < 2^61 + 2^60 + 2^16 */ felem_mul(tmp, alpha, beta); - /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) - * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) - * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * < 2^128 */ + /* + * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) = 17*(2^120 + 2^75 + * + 2^119 + 2^74 + 2^75 + 2^30) = 17*(2^120 + 2^119 + 2^76 + 2^74 + + * 2^30) < 2^128 + */ felem_square(tmp2, gamma); - /* tmp2[i] < 17*(2^59 + 2^14)^2 - * = 17*(2^118 + 2^74 + 2^28) */ + /* + * tmp2[i] < 17*(2^59 + 2^14)^2 = 17*(2^118 + 2^74 + 2^28) + */ felem_scalar128(tmp2, 8); - /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) - * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 - * < 2^126 */ + /* + * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) = 2^125 + 2^121 + 2^81 + 2^77 + * + 2^35 + 2^31 < 2^126 + */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + - * 2^74 + 2^69 + 2^34 + 2^30 - * < 2^128 */ + /* + * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) = + * 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + 2^74 + * + 2^69 + 2^34 + 2^30 < 2^128 + */ felem_reduce(y_out, tmp); - } +} /* copy_conditional copies in to out iff mask is all ones. */ static void copy_conditional(felem out, const felem in, limb mask) - { +{ unsigned i; - for (i = 0; i < NLIMBS; ++i) - { + for (i = 0; i < NLIMBS; ++i) { const limb tmp = mask & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) * @@ -1052,10 +1156,11 @@ copy_conditional(felem out, const felem in, limb mask) * are equal (while not equal to the point at infinity). This case never * happens during single point multiplication, so there is no timing leak for * ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; largefelem tmp, tmp2; limb x_equal, y_equal, z1_is_zero, z2_is_zero; @@ -1067,8 +1172,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_square(tmp, z1); felem_reduce(ftmp, tmp); - if (!mixed) - { + if (!mixed) { /* ftmp2 = z2z2 = z2**2 */ felem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -1098,9 +1202,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_mul(tmp, y1, ftmp2); felem_reduce(ftmp6, tmp); - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* u1 = ftmp3 = x1*z2z2 */ @@ -1111,7 +1213,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_assign(ftmp6, y1); - } + } /* u2 = x2*z1z1 */ felem_mul(tmp, x2, ftmp); @@ -1144,12 +1246,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar64(ftmp5, 2); /* ftmp5[i] < 2^61 */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { point_double(x3, y3, z3, x1, y1, z1); return; - } - + } /* I = ftmp = (2h)**2 */ felem_assign(ftmp, ftmp4); felem_scalar64(ftmp, 2); @@ -1180,8 +1280,9 @@ static void point_add(felem x3, felem y3, felem z3, /* y_out = r(V-x_out) - 2 * s1 * J */ felem_diff64(ftmp3, x_out); - /* ftmp3[i] < 2^60 + 2^60 - * = 2^61 */ + /* + * ftmp3[i] < 2^60 + 2^60 = 2^61 + */ felem_mul(tmp, ftmp5, ftmp3); /* tmp[i] < 17*2^122 */ felem_mul(tmp2, ftmp6, ftmp2); @@ -1189,9 +1290,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar128(tmp2, 2); /* tmp2[i] < 17*2^121 */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17*2^122 - * = 2^126 - 2^122 - 2^6 - 2^2 - 1 - * < 2^127 */ + /* + * tmp[i] < 2^127 - 2^69 + 17*2^122 = 2^126 - 2^122 - 2^6 - 2^2 - 1 < + * 2^127 + */ felem_reduce(y_out, tmp); copy_conditional(x_out, x2, z1_is_zero); @@ -1203,7 +1305,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* Base point pre computation * -------------------------- @@ -1240,126 +1342,126 @@ static void point_add(felem x3, felem y3, felem z3, /* gmul is the table of precomputed base points */ static const felem gmul[16][3] = - {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, - 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, - 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, - {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, - 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, - 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, - 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, - 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, - {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, - 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, - 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, - 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, - 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, - {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, - 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, - 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, - 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, - 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, - {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, - 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, - 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, - 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, - 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, - {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, - 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, - 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, - 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, - 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, - {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, - 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, - 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, - 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, - 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, - {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, - 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, - 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, - 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, - 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, - {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, - 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, - 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, - 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, - 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, - {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, - 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, - 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, - 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, - 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, - {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, - 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, - 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, - 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, - 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, - {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, - 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, - 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, - 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, - 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, - {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, - 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, - 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, - 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, - 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, - {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, - 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, - 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, - 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, - 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, - {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, - 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, - 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, - 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, - 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, - {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, - 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, - 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; +{{{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, +0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, +{0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, +0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, +0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, +{0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, +0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, +0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, +{0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, +0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, +0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, +{0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, +0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, +0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, +{0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, +0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, +0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, +{0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, +0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, +0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, +{0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, +0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, +0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, +{0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, +0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, +0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, +{0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, +0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, +0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, +{0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, +0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, +0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, +{0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, +0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, +0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, +{0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, +0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, +0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, +{0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, +0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, +0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, +{0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, +0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, +0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, +{0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, +0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}}; /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], - felem out[3]) - { +static void +select_point(const limb idx, unsigned int size, const felem pre_comp[ /* size */ ][3], + felem out[3]) +{ unsigned i, j; limb *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(felem)); - for (i = 0; i < size; i++) - { + for (i = 0; i < size; i++) { const limb *inlimbs = &pre_comp[i][0][0]; limb mask = i ^ idx; mask |= mask >> 4; @@ -1369,26 +1471,28 @@ static void select_point(const limb idx, unsigned int size, const felem pre_comp mask--; for (j = 0; j < NLIMBS * 3; j++) outlimbs[j] |= inlimbs[j] & mask; - } } +} /* get_bit returns the |i|th bit in |in| */ -static char get_bit(const felem_bytearray in, int i) - { +static char +get_bit(const felem_bytearray in, int i) +{ if (i < 0) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) +{ int i, skip; unsigned num, gen_mul = (g_scalar != NULL); felem nq[3], tmp[4]; @@ -1398,48 +1502,41 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* set nq to the point at infinity */ memset(nq, 0, 3 * sizeof(felem)); - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (last quarter of rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (last quarter of rounds) and additions + * of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 520 : 130); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 520 : 130); i >= 0; --i) { /* double */ if (!skip) point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); /* add multiples of the generator */ - if (gen_mul && (i <= 130)) - { + if (gen_mul && (i <= 130)) { bits = get_bit(g_scalar, i + 390) << 3; - if (i < 130) - { + if (i < 130) { bits |= get_bit(g_scalar, i + 260) << 2; bits |= get_bit(g_scalar, i + 130) << 1; bits |= get_bit(g_scalar, i); - } + } /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp, tmp); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } - + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + for (num = 0; num < num_points; ++num) { bits = get_bit(scalars[num], i + 4) << 5; bits |= get_bit(scalars[num], i + 3) << 4; bits |= get_bit(scalars[num], i + 2) << 3; @@ -1448,29 +1545,30 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, bits |= get_bit(scalars[num], i - 1); ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - /* select the point to add or subtract, in constant time */ + /* + * select the point to add or subtract, in + * constant time + */ select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_conditional(tmp[1], tmp[3], (-(limb) sign)); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /* Precomputation for the group generator. */ @@ -1493,20 +1591,20 @@ EC_GFp_nistp521_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_nistp521_point_get_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -1530,32 +1628,34 @@ EC_GFp_nistp521_method(void) /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP521_PRE_COMP *nistp521_pre_comp_new() - { +static NISTP521_PRE_COMP * +nistp521_pre_comp_new() +{ NISTP521_PRE_COMP *ret = NULL; - ret = (NISTP521_PRE_COMP *)malloc(sizeof(NISTP521_PRE_COMP)); - if (!ret) - { + ret = (NISTP521_PRE_COMP *) malloc(sizeof(NISTP521_PRE_COMP)); + if (!ret) { ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; - } + } memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); ret->references = 1; return ret; - } +} -static void *nistp521_pre_comp_dup(void *src_) - { +static void * +nistp521_pre_comp_dup(void *src_) +{ NISTP521_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp521_pre_comp_free(void *pre_) - { +static void +nistp521_pre_comp_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1567,10 +1667,11 @@ static void nistp521_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp521_pre_comp_clear_free(void *pre_) - { +static void +nistp521_pre_comp_clear_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1583,43 +1684,46 @@ static void nistp521_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof(*pre)); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp521_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp521_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp521_group_set_curve(EC_GROUP * group, const BIGNUM * p, + const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *curve_p, *curve_a, *curve_b; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_521; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1627,74 +1731,79 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns * (X', Y') = (X/Z^2, Y/Z^3) */ -int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in, x_out, y_out; largefelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + EC_R_POINT_AT_INFINITY); return 0; - } + } if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; + (!BN_to_felem(z1, &point->Z))) + return 0; felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { - if (!felem_to_BN(x, x_out)) - { + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); return 0; - } } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { - if (!felem_to_BN(y, y_out)) - { + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); return 0; - } } - return 1; } + return 1; +} -static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } + num, + points, + sizeof(felem), + tmp_felems, + (void (*) (void *)) felem_one, + (int (*) (const void *)) felem_is_zero_int, + (void (*) (void *, const void *)) felem_assign, + (void (*) (void *, const void *)) felem_square_reduce, + (void (*) (void *, const void *, const void *)) felem_mul_reduce, + (void (*) (void *, const void *)) felem_inv, + (void (*) (void *, const void *)) felem_contract); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { +int +ec_GFp_nistp521_points_mul(const EC_GROUP * group, EC_POINT * r, + const BIGNUM * scalar, size_t num, const EC_POINT * points[], + const BIGNUM * scalars[], BN_CTX * ctx) +{ int ret = 0; int j; int mixed = 0; @@ -1702,7 +1811,7 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; + felem(*pre_comp)[17][3] = NULL; felem *tmp_felems = NULL; felem_bytearray tmp; unsigned i, num_bytes; @@ -1710,178 +1819,170 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, size_t num_points = num; felem x_in, y_in, z_in, x_out, y_out, z_out; NISTP521_PRE_COMP *pre = NULL; - felem (*g_pre_comp)[3] = NULL; + felem(*g_pre_comp)[3] = NULL; EC_POINT *generator = NULL; const EC_POINT *p = NULL; const BIGNUM *p_scalar = NULL; if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp521_pre_comp_dup, nistp521_pre_comp_free, - nistp521_pre_comp_clear_free); + nistp521_pre_comp_dup, nistp521_pre_comp_free, + nistp521_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ g_pre_comp = &pre->g_pre_comp[0]; else /* try to use the standard precomputation */ - g_pre_comp = (felem (*)[3]) gmul; + g_pre_comp = (felem(*)[3]) gmul; generator = EC_POINT_new(group); if (generator == NULL) goto err; /* get the generator from precomputation */ if (!felem_to_BN(x, g_pre_comp[1][0]) || - !felem_to_BN(y, g_pre_comp[1][1]) || - !felem_to_BN(z, g_pre_comp[1][2])) - { + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + generator, x, y, z, ctx)) goto err; if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) /* precomputation matches generator */ have_pre_comp = 1; else - /* we don't have valid precomputation: - * treat the generator as a random point */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points++; - } - - if (num_points > 0) - { - if (num_points >= 2) - { - /* unless we precompute multiples for just one point, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 2) { + /* + * unless we precompute multiples for just one point, + * converting those into affine form is time well + * spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); if (mixed) tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) - /* we didn't have a valid precomputation, so we pick - * the generator */ - { + /* + * we didn't have a valid precomputation, so + * we pick the generator + */ + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { + if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we + * don't guarantee constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(p_scalar, tmp); flip_endian(secrets[i], tmp, num_bytes); /* precompute multiples */ if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof(g_secret)); /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { + if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else num_bytes = BN_bn2bin(scalar, tmp); flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - (const felem (*)[3]) g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3]) pre_comp, + (const felem(*)[3]) g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { + (!felem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -1897,10 +1998,11 @@ err: if (tmp_felems != NULL) free(tmp_felems); return ret; - } +} -int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp521_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP521_PRE_COMP *pre = NULL; int i, j; @@ -1911,95 +2013,93 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free); + nistp521_pre_comp_free, nistp521_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; BN_CTX_start(ctx); if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp521_pre_comp_new()) == NULL) goto err; /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) + (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) goto err; /* compute 2^130*G, 2^260*G, 2^390*G */ - for (i = 1; i <= 4; i <<= 1) - { - point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], - pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); - for (j = 0; j < 129; ++j) - { - point_double(pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], - pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2]); - } + for (i = 1; i <= 4; i <<= 1) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) { + point_double(pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2]); } + } /* g_pre_comp[0] is the point at infinity */ memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); /* the remaining multiples */ /* 2^130*G + 2^260*G */ point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], - pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], - pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^130*G + 2^390*G */ point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], - pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], - pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], - pre->g_pre_comp[4][2]); + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); /* 2^130*G + 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], - pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], - pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - for (i = 1; i < 8; ++i) - { + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) { /* odd multiples: add G */ - point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], - pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], - 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], - pre->g_pre_comp[1][2]); - } + point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1], + pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], + 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -2008,18 +2108,19 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp521_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp521_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free) - != NULL) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libssl/src/crypto/ec/ecp_nistputil.c b/lib/libssl/src/crypto/ec/ecp_nistputil.c index c8140c807fb..0312fb16add 100644 --- a/lib/libssl/src/crypto/ec/ecp_nistputil.c +++ b/lib/libssl/src/crypto/ec/ecp_nistputil.c @@ -41,16 +41,17 @@ * tmp_felems needs to point to a temporary array of 'num'+1 field elements * for storage of intermediate values. */ -void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, - size_t felem_size, void *tmp_felems, - void (*felem_one)(void *out), - int (*felem_is_zero)(const void *in), - void (*felem_assign)(void *out, const void *in), - void (*felem_square)(void *out, const void *in), - void (*felem_mul)(void *out, const void *in1, const void *in2), - void (*felem_inv)(void *out, const void *in), - void (*felem_contract)(void *out, const void *in)) - { +void +ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one) (void *out), + int (*felem_is_zero) (const void *in), + void (*felem_assign) (void *out, const void *in), + void (*felem_square) (void *out, const void *in), + void (*felem_mul) (void *out, const void *in1, const void *in2), + void (*felem_inv) (void *out, const void *in), + void (*felem_contract) (void *out, const void *in)) +{ int i = 0; #define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) @@ -62,50 +63,59 @@ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, felem_assign(tmp_felem(0), Z(0)); else felem_one(tmp_felem(0)); - for (i = 1; i < (int)num; i++) - { + for (i = 1; i < (int) num; i++) { if (!felem_is_zero(Z(i))) - felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); + felem_mul(tmp_felem(i), tmp_felem(i - 1), Z(i)); else - felem_assign(tmp_felem(i), tmp_felem(i-1)); - } - /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: - * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ + felem_assign(tmp_felem(i), tmp_felem(i - 1)); + } + /* + * Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any + * zero-valued factors: if Z(i) = 0, we essentially pretend that Z(i) + * = 1 + */ - felem_inv(tmp_felem(num-1), tmp_felem(num-1)); - for (i = num - 1; i >= 0; i--) - { + felem_inv(tmp_felem(num - 1), tmp_felem(num - 1)); + for (i = num - 1; i >= 0; i--) { if (i > 0) - /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), - * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) + /* + * tmp_felem(i-1) is the product of Z(0) .. Z(i-1), + * tmp_felem(i) is the inverse of the product of Z(0) + * .. Z(i) */ - felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ + felem_mul(tmp_felem(num), tmp_felem(i - 1), tmp_felem(i)); /* 1/Z(i) */ else - felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ - if (!felem_is_zero(Z(i))) - { + if (!felem_is_zero(Z(i))) { if (i > 0) - /* For next iteration, replace tmp_felem(i-1) by its inverse */ - felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); + /* + * For next iteration, replace tmp_felem(i-1) + * by its inverse + */ + felem_mul(tmp_felem(i - 1), tmp_felem(i), Z(i)); - /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ - felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ - felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ - felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ - felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + /* + * Convert point (X, Y, Z) into affine form (X/(Z^2), + * Y/(Z^3), 1) + */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ felem_contract(X(i), X(i)); felem_contract(Y(i), Y(i)); felem_one(Z(i)); - } - else - { + } else { if (i > 0) - /* For next iteration, replace tmp_felem(i-1) by its inverse */ - felem_assign(tmp_felem(i-1), tmp_felem(i)); - } + /* + * For next iteration, replace tmp_felem(i-1) + * by its inverse + */ + felem_assign(tmp_felem(i - 1), tmp_felem(i)); } } +} /* * This function looks at 5+1 scalar bits (5 current, 1 adjacent less @@ -180,18 +190,20 @@ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, * has to be b_4 b_3 b_2 b_1 b_0 0. * */ -void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) - { +void +ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) +{ unsigned char s, d; - s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as + * 6-bit value */ d = (1 << 6) - in - 1; d = (d & s) | (in & ~s); d = (d >> 1) + (d & 1); *sign = s & 1; *digit = d; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif diff --git a/lib/libssl/src/crypto/ec/ecp_oct.c b/lib/libssl/src/crypto/ec/ecp_oct.c index a06abbc8cd6..c7719c74132 100644 --- a/lib/libssl/src/crypto/ec/ecp_oct.c +++ b/lib/libssl/src/crypto/ec/ecp_oct.c @@ -1,6 +1,6 @@ /* crypto/ec/ecp_oct.c */ /* Includes code written by Lenka Fibikova - * for the OpenSSL project. + * for the OpenSSL project. * Includes code written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== @@ -11,7 +11,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -66,23 +66,22 @@ #include "ec_lcl.h" -int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { +int +ec_GFp_simple_set_compressed_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x_, int y_bit, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp1, *tmp2, *x, *y; int ret = 0; - /* clear error queue*/ + /* clear error queue */ ERR_clear_error(); - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } y_bit = (y_bit != 0); BN_CTX_start(ctx); @@ -90,114 +89,117 @@ int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *po tmp2 = BN_CTX_get(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - /* Recover y. We have a Weierstrass equation - * y^2 = x^3 + a*x + b, - * so y is one of the square roots of x^3 + a*x + b. + /* + * Recover y. We have a Weierstrass equation y^2 = x^3 + a*x + b, so + * y is one of the square roots of x^3 + a*x + b. */ /* tmp1 := x^3 */ - if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; - if (group->meth->field_decode == 0) - { + if (!BN_nnmod(x, x_, &group->field, ctx)) + goto err; + if (group->meth->field_decode == 0) { /* field_{sqr,mul} work on standard representation */ - if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; - if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; - } - + if (!group->meth->field_sqr(group, tmp2, x_, ctx)) + goto err; + if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) + goto err; + } else { + if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) + goto err; + if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) + goto err; + } + /* tmp1 := tmp1 + a*x */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; - if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; - if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; - } - else - { + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) + goto err; + if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) + goto err; + if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } else { + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) + goto err; + if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) + goto err; + } else { /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; - } - - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) + goto err; } - + + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } + /* tmp1 := tmp1 + b */ - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; - } - - if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) - { + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) + goto err; + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) + goto err; + } else { + if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) + goto err; + } + + if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) { unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) - { + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) { ERR_clear_error(); ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else + } else ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); goto err; - } - - if (y_bit != BN_is_odd(y)) - { - if (BN_is_zero(y)) - { + } + if (y_bit != BN_is_odd(y)) { + if (BN_is_zero(y)) { int kron; kron = BN_kronecker(x, &group->field, ctx); - if (kron == -2) goto err; + if (kron == -2) + goto err; if (kron == 1) ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); else - /* BN_mod_sqrt() should have cought this error (not a square) */ + /* + * BN_mod_sqrt() should have cought this + * error (not a square) + */ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); goto err; - } - if (!BN_usub(y, &group->field, y)) goto err; } - if (y_bit != BN_is_odd(y)) - { + if (!BN_usub(y, &group->field, y)) + goto err; + } + if (y_bit != BN_is_odd(y)) { ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); goto err; - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + } + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { +size_t +ec_GFp_simple_point2oct(const EC_GROUP * group, const EC_POINT * point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX * ctx) +{ size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; @@ -205,125 +207,106 @@ size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, poi size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { + } + if (EC_POINT_is_at_infinity(group, point)) { /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { + if (buf != NULL) { + if (len < 1) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); return 0; - } - buf[0] = 0; } - return 1; + buf[0] = 0; } - - + return 1; + } /* ret := required output buffer length */ field_len = BN_num_bytes(&group->field); - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { + if (buf != NULL) { + if (len < ret) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); goto err; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); used_ctx = 1; x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) buf[0] = form + 1; else buf[0] = form; - + i = 1; - + skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(x, buf + i); i += skip; - if (i != 1 + field_len) - { + if (i != 1 + field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { + } + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { + if (skip > field_len) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } - while (skip > 0) - { + } + while (skip > 0) { buf[i++] = 0; skip--; - } + } skip = BN_bn2bin(y, buf + i); i += skip; - } - - if (i != ret) - { + } + if (i != ret) { ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; - } } - + } if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - err: +err: if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return 0; - } +} -int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { +int +ec_GFp_simple_oct2point(const EC_GROUP * group, EC_POINT * point, + const unsigned char *buf, size_t len, BN_CTX * ctx) +{ point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; @@ -331,102 +314,84 @@ int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, size_t field_len, enc_len; int ret = 0; - if (len == 0) - { + if (len == 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); return 0; - } + } form = buf[0]; y_bit = form & 1; form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (form == 0) - { - if (len != 1) - { + } + if (form == 0) { + if (len != 1) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - return EC_POINT_set_to_infinity(group, point); } - + return EC_POINT_set_to_infinity(group, point); + } field_len = BN_num_bytes(&group->field); - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; - if (len != enc_len) - { + if (len != enc_len) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, &group->field) >= 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { + } + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, &group->field) >= 0) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (y_bit != BN_is_odd(y)) - { + } + if (form == POINT_CONVERSION_HYBRID) { + if (y_bit != BN_is_odd(y)) { ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; - } } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) { /* test required by + * X9.62 */ ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); goto err; - } - + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } - +} diff --git a/lib/libssl/src/crypto/ec/ecp_smpl.c b/lib/libssl/src/crypto/ec/ecp_smpl.c index c99348f08f5..b87410120df 100644 --- a/lib/libssl/src/crypto/ec/ecp_smpl.c +++ b/lib/libssl/src/crypto/ec/ecp_smpl.c @@ -1,6 +1,6 @@ /* crypto/ec/ecp_smpl.c */ /* Includes code written by Lenka Fibikova - * for the OpenSSL project. + * for the OpenSSL project. * Includes code written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== @@ -11,7 +11,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in @@ -80,20 +80,20 @@ EC_GFp_simple_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, - .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, - .point_get_affine_coordinates = - ec_GFp_simple_point_get_affine_coordinates, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + .point_set_affine_coordinates = + ec_GFp_simple_point_set_affine_coordinates, + .point_get_affine_coordinates = + ec_GFp_simple_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -124,212 +124,225 @@ EC_GFp_simple_method(void) */ -int ec_GFp_simple_group_init(EC_GROUP *group) - { +int +ec_GFp_simple_group_init(EC_GROUP * group) +{ BN_init(&group->field); BN_init(&group->a); BN_init(&group->b); group->a_is_minus3 = 0; return 1; - } +} -void ec_GFp_simple_group_finish(EC_GROUP *group) - { +void +ec_GFp_simple_group_finish(EC_GROUP * group) +{ BN_free(&group->field); BN_free(&group->a); BN_free(&group->b); - } +} -void ec_GFp_simple_group_clear_finish(EC_GROUP *group) - { +void +ec_GFp_simple_group_clear_finish(EC_GROUP * group) +{ BN_clear_free(&group->field); BN_clear_free(&group->a); BN_clear_free(&group->b); - } +} -int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) - { - if (!BN_copy(&dest->field, &src->field)) return 0; - if (!BN_copy(&dest->a, &src->a)) return 0; - if (!BN_copy(&dest->b, &src->b)) return 0; +int +ec_GFp_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) +{ + if (!BN_copy(&dest->field, &src->field)) + return 0; + if (!BN_copy(&dest->a, &src->a)) + return 0; + if (!BN_copy(&dest->b, &src->b)) + return 0; dest->a_is_minus3 = src->a_is_minus3; return 1; - } +} -int ec_GFp_simple_group_set_curve(EC_GROUP *group, - const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_group_set_curve(EC_GROUP * group, + const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_a; - + /* p must be a prime > 3 */ - if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) - { + if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); tmp_a = BN_CTX_get(ctx); - if (tmp_a == NULL) goto err; + if (tmp_a == NULL) + goto err; /* group->field */ - if (!BN_copy(&group->field, p)) goto err; + if (!BN_copy(&group->field, p)) + goto err; BN_set_negative(&group->field, 0); /* group->a */ - if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; - if (group->meth->field_encode) - { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; } - else - if (!BN_copy(&group->a, tmp_a)) goto err; - + if (!BN_nnmod(tmp_a, a, p, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) + goto err; + } else if (!BN_copy(&group->a, tmp_a)) + goto err; + /* group->b */ - if (!BN_nnmod(&group->b, b, p, ctx)) goto err; + if (!BN_nnmod(&group->b, b, p, ctx)) + goto err; if (group->meth->field_encode) - if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err; - + if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) + goto err; + /* group->a_is_minus3 */ - if (!BN_add_word(tmp_a, 3)) goto err; + if (!BN_add_word(tmp_a, 3)) + goto err; group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_group_get_curve(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, BIGNUM * b, BN_CTX * ctx) +{ int ret = 0; BN_CTX *new_ctx = NULL; - - if (p != NULL) - { - if (!BN_copy(p, &group->field)) return 0; - } - if (a != NULL || b != NULL) - { - if (group->meth->field_decode) - { - if (ctx == NULL) - { + if (p != NULL) { + if (!BN_copy(p, &group->field)) + return 0; + } + if (a != NULL || b != NULL) { + if (group->meth->field_decode) { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - if (a != NULL) - { - if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; - } - if (b != NULL) - { - if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; - } } - else - { - if (a != NULL) - { - if (!BN_copy(a, &group->a)) goto err; - } - if (b != NULL) - { - if (!BN_copy(b, &group->b)) goto err; - } + if (a != NULL) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + } + if (b != NULL) { + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } + } else { + if (a != NULL) { + if (!BN_copy(a, &group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, &group->b)) + goto err; } } - + } ret = 1; - - err: + +err: if (new_ctx) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_group_get_degree(const EC_GROUP *group) - { +int +ec_GFp_simple_group_get_degree(const EC_GROUP * group) +{ return BN_num_bits(&group->field); - } +} -int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; - BIGNUM *a,*b,*order,*tmp_1,*tmp_2; + BIGNUM *a, *b, *order, *tmp_1, *tmp_2; const BIGNUM *p = &group->field; BN_CTX *new_ctx = NULL; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - { + if (ctx == NULL) { ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; - } } + } BN_CTX_start(ctx); a = BN_CTX_get(ctx); b = BN_CTX_get(ctx); tmp_1 = BN_CTX_get(ctx); tmp_2 = BN_CTX_get(ctx); order = BN_CTX_get(ctx); - if (order == NULL) goto err; + if (order == NULL) + goto err; - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err; - if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; - } - else - { - if (!BN_copy(a, &group->a)) goto err; - if (!BN_copy(b, &group->b)) goto err; - } - - /* check the discriminant: - * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) - * 0 =< a, b < p */ - if (BN_is_zero(a)) - { - if (BN_is_zero(b)) goto err; - } - else if (!BN_is_zero(b)) - { - if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err; - if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err; - if (!BN_lshift(tmp_1, tmp_2, 2)) goto err; + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, a, &group->a, ctx)) + goto err; + if (!group->meth->field_decode(group, b, &group->b, ctx)) + goto err; + } else { + if (!BN_copy(a, &group->a)) + goto err; + if (!BN_copy(b, &group->b)) + goto err; + } + + /* + * check the discriminant: y^2 = x^3 + a*x + b is an elliptic curve + * <=> 4*a^3 + 27*b^2 != 0 (mod p) 0 =< a, b < p + */ + if (BN_is_zero(a)) { + if (BN_is_zero(b)) + goto err; + } else if (!BN_is_zero(b)) { + if (!BN_mod_sqr(tmp_1, a, p, ctx)) + goto err; + if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) + goto err; + if (!BN_lshift(tmp_1, tmp_2, 2)) + goto err; /* tmp_1 = 4*a^3 */ - if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err; - if (!BN_mul_word(tmp_2, 27)) goto err; + if (!BN_mod_sqr(tmp_2, b, p, ctx)) + goto err; + if (!BN_mul_word(tmp_2, 27)) + goto err; /* tmp_2 = 27*b^2 */ - if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err; - if (BN_is_zero(a)) goto err; - } + if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) + goto err; + if (BN_is_zero(a)) + goto err; + } ret = 1; err: @@ -338,325 +351,312 @@ err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_point_init(EC_POINT *point) - { +int +ec_GFp_simple_point_init(EC_POINT * point) +{ BN_init(&point->X); BN_init(&point->Y); BN_init(&point->Z); point->Z_is_one = 0; return 1; - } +} -void ec_GFp_simple_point_finish(EC_POINT *point) - { +void +ec_GFp_simple_point_finish(EC_POINT * point) +{ BN_free(&point->X); BN_free(&point->Y); BN_free(&point->Z); - } +} -void ec_GFp_simple_point_clear_finish(EC_POINT *point) - { +void +ec_GFp_simple_point_clear_finish(EC_POINT * point) +{ BN_clear_free(&point->X); BN_clear_free(&point->Y); BN_clear_free(&point->Z); point->Z_is_one = 0; - } +} -int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) - { - if (!BN_copy(&dest->X, &src->X)) return 0; - if (!BN_copy(&dest->Y, &src->Y)) return 0; - if (!BN_copy(&dest->Z, &src->Z)) return 0; +int +ec_GFp_simple_point_copy(EC_POINT * dest, const EC_POINT * src) +{ + if (!BN_copy(&dest->X, &src->X)) + return 0; + if (!BN_copy(&dest->Y, &src->Y)) + return 0; + if (!BN_copy(&dest->Z, &src->Z)) + return 0; dest->Z_is_one = src->Z_is_one; return 1; - } +} -int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) - { +int +ec_GFp_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) +{ point->Z_is_one = 0; BN_zero(&point->Z); return 1; - } +} -int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) - { +int +ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, const BIGNUM * z, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; - - if (ctx == NULL) - { + + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; + } + if (x != NULL) { + if (!BN_nnmod(&point->X, x, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) + goto err; } - - if (x != NULL) - { - if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err; - if (group->meth->field_encode) - { - if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err; - } - } - - if (y != NULL) - { - if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err; - if (group->meth->field_encode) - { - if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err; - } + } + if (y != NULL) { + if (!BN_nnmod(&point->Y, y, &group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) + goto err; } - - if (z != NULL) - { + } + if (z != NULL) { int Z_is_one; - if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err; + if (!BN_nnmod(&point->Z, z, &group->field, ctx)) + goto err; Z_is_one = BN_is_one(&point->Z); - if (group->meth->field_encode) - { - if (Z_is_one && (group->meth->field_set_to_one != 0)) - { - if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err; - } - else - { - if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err; - } + if (group->meth->field_encode) { + if (Z_is_one && (group->meth->field_set_to_one != 0)) { + if (!group->meth->field_set_to_one(group, &point->Z, ctx)) + goto err; + } else { + if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) + goto err; } - point->Z_is_one = Z_is_one; } - + point->Z_is_one = Z_is_one; + } ret = 1; - - err: + +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) - { +int +ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP * group, const EC_POINT * point, + BIGNUM * x, BIGNUM * y, BIGNUM * z, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; int ret = 0; - - if (group->meth->field_decode != 0) - { - if (ctx == NULL) - { + + if (group->meth->field_decode != 0) { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - - if (x != NULL) - { - if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; - } - if (y != NULL) - { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; - } - if (z != NULL) - { - if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err; - } } - else - { - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; - } - if (z != NULL) - { - if (!BN_copy(z, &point->Z)) goto err; - } + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + if (z != NULL) { + if (!group->meth->field_decode(group, z, &point->Z, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; } - + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; + } + if (z != NULL) { + if (!BN_copy(z, &point->Z)) + goto err; + } + } + ret = 1; - err: +err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - if (x == NULL || y == NULL) - { +int +ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, + const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) +{ + if (x == NULL || y == NULL) { /* unlike for projective coordinates, we do not tolerate this */ ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; - } - - return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); } + return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); +} -int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP * group, const EC_POINT * point, + BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *Z, *Z_1, *Z_2, *Z_3; const BIGNUM *Z_; int ret = 0; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; - } - - if (ctx == NULL) - { + } + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); Z = BN_CTX_get(ctx); Z_1 = BN_CTX_get(ctx); Z_2 = BN_CTX_get(ctx); Z_3 = BN_CTX_get(ctx); - if (Z_3 == NULL) goto err; + if (Z_3 == NULL) + goto err; /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ - - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err; + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, Z, &point->Z, ctx)) + goto err; Z_ = Z; - } - else - { + } else { Z_ = &point->Z; - } - - if (BN_is_one(Z_)) - { - if (group->meth->field_decode) - { - if (x != NULL) - { - if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err; - } - if (y != NULL) - { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err; - } + } + + if (BN_is_one(Z_)) { + if (group->meth->field_decode) { + if (x != NULL) { + if (!group->meth->field_decode(group, x, &point->X, ctx)) + goto err; } - else - { - if (x != NULL) - { - if (!BN_copy(x, &point->X)) goto err; - } - if (y != NULL) - { - if (!BN_copy(y, &point->Y)) goto err; - } + if (y != NULL) { + if (!group->meth->field_decode(group, y, &point->Y, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, &point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, &point->Y)) + goto err; } } - else - { - if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) - { + } else { + if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) { ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); goto err; - } - - if (group->meth->field_encode == 0) - { + } + if (group->meth->field_encode == 0) { /* field_sqr works on standard representation */ - if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err; - } - - if (x != NULL) - { - /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */ - if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err; - } + if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) + goto err; + } - if (y != NULL) - { - if (group->meth->field_encode == 0) - { + if (x != NULL) { + /* + * in the Montgomery case, field_mul will cancel out + * Montgomery factor in X: + */ + if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) + goto err; + } + if (y != NULL) { + if (group->meth->field_encode == 0) { /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err; - } - else - { - if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err; - } - - /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */ - if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err; + if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) + goto err; } + + /* + * in the Montgomery case, field_mul will cancel out + * Montgomery factor in Y: + */ + if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) + goto err; } + } ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_add(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; int ret = 0; - + if (a == b) return EC_POINT_dbl(group, r, a, ctx); if (EC_POINT_is_at_infinity(group, a)) return EC_POINT_copy(r, b); if (EC_POINT_is_at_infinity(group, b)) return EC_POINT_copy(r, a); - + field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); @@ -665,272 +665,321 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con n4 = BN_CTX_get(ctx); n5 = BN_CTX_get(ctx); n6 = BN_CTX_get(ctx); - if (n6 == NULL) goto end; + if (n6 == NULL) + goto end; - /* Note that in this function we must not read components of 'a' or 'b' - * once we have written the corresponding components of 'r'. - * ('r' might be one of 'a' or 'b'.) + /* + * Note that in this function we must not read components of 'a' or + * 'b' once we have written the corresponding components of 'r'. ('r' + * might be one of 'a' or 'b'.) */ /* n1, n2 */ - if (b->Z_is_one) - { - if (!BN_copy(n1, &a->X)) goto end; - if (!BN_copy(n2, &a->Y)) goto end; + if (b->Z_is_one) { + if (!BN_copy(n1, &a->X)) + goto end; + if (!BN_copy(n2, &a->Y)) + goto end; /* n1 = X_a */ /* n2 = Y_a */ - } - else - { - if (!field_sqr(group, n0, &b->Z, ctx)) goto end; - if (!field_mul(group, n1, &a->X, n0, ctx)) goto end; + } else { + if (!field_sqr(group, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n1, &a->X, n0, ctx)) + goto end; /* n1 = X_a * Z_b^2 */ - if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end; - if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end; + if (!field_mul(group, n0, n0, &b->Z, ctx)) + goto end; + if (!field_mul(group, n2, &a->Y, n0, ctx)) + goto end; /* n2 = Y_a * Z_b^3 */ - } + } /* n3, n4 */ - if (a->Z_is_one) - { - if (!BN_copy(n3, &b->X)) goto end; - if (!BN_copy(n4, &b->Y)) goto end; + if (a->Z_is_one) { + if (!BN_copy(n3, &b->X)) + goto end; + if (!BN_copy(n4, &b->Y)) + goto end; /* n3 = X_b */ /* n4 = Y_b */ - } - else - { - if (!field_sqr(group, n0, &a->Z, ctx)) goto end; - if (!field_mul(group, n3, &b->X, n0, ctx)) goto end; + } else { + if (!field_sqr(group, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n3, &b->X, n0, ctx)) + goto end; /* n3 = X_b * Z_a^2 */ - if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end; - if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end; + if (!field_mul(group, n0, n0, &a->Z, ctx)) + goto end; + if (!field_mul(group, n4, &b->Y, n0, ctx)) + goto end; /* n4 = Y_b * Z_a^3 */ - } + } /* n5, n6 */ - if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; - if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; + if (!BN_mod_sub_quick(n5, n1, n3, p)) + goto end; + if (!BN_mod_sub_quick(n6, n2, n4, p)) + goto end; /* n5 = n1 - n3 */ /* n6 = n2 - n4 */ - if (BN_is_zero(n5)) - { - if (BN_is_zero(n6)) - { + if (BN_is_zero(n5)) { + if (BN_is_zero(n6)) { /* a is the same point as b */ BN_CTX_end(ctx); ret = EC_POINT_dbl(group, r, a, ctx); ctx = NULL; goto end; - } - else - { + } else { /* a is the inverse of b */ BN_zero(&r->Z); r->Z_is_one = 0; ret = 1; goto end; - } } - + } /* 'n7', 'n8' */ - if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; - if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; + if (!BN_mod_add_quick(n1, n1, n3, p)) + goto end; + if (!BN_mod_add_quick(n2, n2, n4, p)) + goto end; /* 'n7' = n1 + n3 */ /* 'n8' = n2 + n4 */ /* Z_r */ - if (a->Z_is_one && b->Z_is_one) - { - if (!BN_copy(&r->Z, n5)) goto end; - } - else - { - if (a->Z_is_one) - { if (!BN_copy(n0, &b->Z)) goto end; } - else if (b->Z_is_one) - { if (!BN_copy(n0, &a->Z)) goto end; } - else - { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; } - if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end; + if (a->Z_is_one && b->Z_is_one) { + if (!BN_copy(&r->Z, n5)) + goto end; + } else { + if (a->Z_is_one) { + if (!BN_copy(n0, &b->Z)) + goto end; + } else if (b->Z_is_one) { + if (!BN_copy(n0, &a->Z)) + goto end; + } else { + if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) + goto end; } + if (!field_mul(group, &r->Z, n0, n5, ctx)) + goto end; + } r->Z_is_one = 0; /* Z_r = Z_a * Z_b * n5 */ /* X_r */ - if (!field_sqr(group, n0, n6, ctx)) goto end; - if (!field_sqr(group, n4, n5, ctx)) goto end; - if (!field_mul(group, n3, n1, n4, ctx)) goto end; - if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end; + if (!field_sqr(group, n0, n6, ctx)) + goto end; + if (!field_sqr(group, n4, n5, ctx)) + goto end; + if (!field_mul(group, n3, n1, n4, ctx)) + goto end; + if (!BN_mod_sub_quick(&r->X, n0, n3, p)) + goto end; /* X_r = n6^2 - n5^2 * 'n7' */ - + /* 'n9' */ - if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end; - if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; + if (!BN_mod_lshift1_quick(n0, &r->X, p)) + goto end; + if (!BN_mod_sub_quick(n0, n3, n0, p)) + goto end; /* n9 = n5^2 * 'n7' - 2 * X_r */ /* Y_r */ - if (!field_mul(group, n0, n0, n6, ctx)) goto end; - if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ - if (!field_mul(group, n1, n2, n5, ctx)) goto end; - if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; + if (!field_mul(group, n0, n0, n6, ctx)) + goto end; + if (!field_mul(group, n5, n4, n5, ctx)) + goto end; /* now n5 is n5^3 */ + if (!field_mul(group, n1, n2, n5, ctx)) + goto end; + if (!BN_mod_sub_quick(n0, n0, n1, p)) + goto end; if (BN_is_odd(n0)) - if (!BN_add(n0, n0, p)) goto end; + if (!BN_add(n0, n0, p)) + goto end; /* now 0 <= n0 < 2*p, and n0 is even */ - if (!BN_rshift1(&r->Y, n0)) goto end; + if (!BN_rshift1(&r->Y, n0)) + goto end; /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ ret = 1; - end: - if (ctx) /* otherwise we already called BN_CTX_end */ +end: + if (ctx) /* otherwise we already called BN_CTX_end */ BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_dbl(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3; int ret = 0; - - if (EC_POINT_is_at_infinity(group, a)) - { + + if (EC_POINT_is_at_infinity(group, a)) { BN_zero(&r->Z); r->Z_is_one = 0; return 1; - } - + } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); - if (n3 == NULL) goto err; + if (n3 == NULL) + goto err; - /* Note that in this function we must not read components of 'a' - * once we have written the corresponding components of 'r'. - * ('r' might the same as 'a'.) + /* + * Note that in this function we must not read components of 'a' once + * we have written the corresponding components of 'r'. ('r' might + * the same as 'a'.) */ /* n1 */ - if (a->Z_is_one) - { - if (!field_sqr(group, n0, &a->X, ctx)) goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; - if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err; + if (a->Z_is_one) { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, &group->a, p)) + goto err; /* n1 = 3 * X_a^2 + a_curve */ - } - else if (group->a_is_minus3) - { - if (!field_sqr(group, n1, &a->Z, ctx)) goto err; - if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err; - if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err; - if (!field_mul(group, n1, n0, n2, ctx)) goto err; - if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; - if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; - /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) - * = 3 * X_a^2 - 3 * Z_a^4 */ - } - else - { - if (!field_sqr(group, n0, &a->X, ctx)) goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; - if (!field_sqr(group, n1, &a->Z, ctx)) goto err; - if (!field_sqr(group, n1, n1, ctx)) goto err; - if (!field_mul(group, n1, n1, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; + } else if (group->a_is_minus3) { + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!BN_mod_add_quick(n0, &a->X, n1, p)) + goto err; + if (!BN_mod_sub_quick(n2, &a->X, n1, p)) + goto err; + if (!field_mul(group, n1, n0, n2, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, n1, p)) + goto err; + /* + * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) = 3 * X_a^2 - 3 * + * Z_a^4 + */ + } else { + if (!field_sqr(group, n0, &a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!field_sqr(group, n1, &a->Z, ctx)) + goto err; + if (!field_sqr(group, n1, n1, ctx)) + goto err; + if (!field_mul(group, n1, n1, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(n1, n1, n0, p)) + goto err; /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ - } + } /* Z_r */ - if (a->Z_is_one) - { - if (!BN_copy(n0, &a->Y)) goto err; - } - else - { - if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err; - } - if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err; + if (a->Z_is_one) { + if (!BN_copy(n0, &a->Y)) + goto err; + } else { + if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) + goto err; + } + if (!BN_mod_lshift1_quick(&r->Z, n0, p)) + goto err; r->Z_is_one = 0; /* Z_r = 2 * Y_a * Z_a */ /* n2 */ - if (!field_sqr(group, n3, &a->Y, ctx)) goto err; - if (!field_mul(group, n2, &a->X, n3, ctx)) goto err; - if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; + if (!field_sqr(group, n3, &a->Y, ctx)) + goto err; + if (!field_mul(group, n2, &a->X, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n2, n2, 2, p)) + goto err; /* n2 = 4 * X_a * Y_a^2 */ /* X_r */ - if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; - if (!field_sqr(group, &r->X, n1, ctx)) goto err; - if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err; + if (!BN_mod_lshift1_quick(n0, n2, p)) + goto err; + if (!field_sqr(group, &r->X, n1, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) + goto err; /* X_r = n1^2 - 2 * n2 */ - + /* n3 */ - if (!field_sqr(group, n0, n3, ctx)) goto err; - if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; + if (!field_sqr(group, n0, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n3, n0, 3, p)) + goto err; /* n3 = 8 * Y_a^4 */ - + /* Y_r */ - if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err; - if (!field_mul(group, n0, n1, n0, ctx)) goto err; - if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err; + if (!BN_mod_sub_quick(n0, n2, &r->X, p)) + goto err; + if (!field_mul(group, n0, n1, n0, ctx)) + goto err; + if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) + goto err; /* Y_r = n1 * (n2 - X_r) - n3 */ ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GFp_simple_invert(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) /* point is its own inverse */ return 1; - + return BN_usub(&point->Y, &group->field, &point->Y); - } +} -int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) - { +int +ec_GFp_simple_is_at_infinity(const EC_GROUP * group, const EC_POINT * point) +{ return BN_is_zero(&point->Z); - } +} -int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) - { - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); +int +ec_GFp_simple_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *rh, *tmp, *Z4, *Z6; @@ -938,199 +987,200 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C if (EC_POINT_is_at_infinity(group, point)) return 1; - + field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); rh = BN_CTX_get(ctx); tmp = BN_CTX_get(ctx); Z4 = BN_CTX_get(ctx); Z6 = BN_CTX_get(ctx); - if (Z6 == NULL) goto err; - - /* We have a curve defined by a Weierstrass equation - * y^2 = x^3 + a*x + b. - * The point to consider is given in Jacobian projective coordinates - * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). - * Substituting this and multiplying by Z^6 transforms the above equation into - * Y^2 = X^3 + a*X*Z^4 + b*Z^6. - * To test this, we add up the right-hand side in 'rh'. + if (Z6 == NULL) + goto err; + + /* + * We have a curve defined by a Weierstrass equation y^2 = x^3 + a*x + * + b. The point to consider is given in Jacobian projective + * coordinates where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). + * Substituting this and multiplying by Z^6 transforms the above + * equation into Y^2 = X^3 + a*X*Z^4 + b*Z^6. To test this, we add up + * the right-hand side in 'rh'. */ /* rh := X^2 */ - if (!field_sqr(group, rh, &point->X, ctx)) goto err; + if (!field_sqr(group, rh, &point->X, ctx)) + goto err; - if (!point->Z_is_one) - { - if (!field_sqr(group, tmp, &point->Z, ctx)) goto err; - if (!field_sqr(group, Z4, tmp, ctx)) goto err; - if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; + if (!point->Z_is_one) { + if (!field_sqr(group, tmp, &point->Z, ctx)) + goto err; + if (!field_sqr(group, Z4, tmp, ctx)) + goto err; + if (!field_mul(group, Z6, Z4, tmp, ctx)) + goto err; /* rh := (rh + a*Z^4)*X */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; - if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; - if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; - } - else - { - if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; - } + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp, Z4, p)) + goto err; + if (!BN_mod_add_quick(tmp, tmp, Z4, p)) + goto err; + if (!BN_mod_sub_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } else { + if (!field_mul(group, tmp, Z4, &group->a, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; + } /* rh := rh + b*Z^6 */ - if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; - } - else - { + if (!field_mul(group, tmp, &group->b, Z6, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + } else { /* point->Z_is_one */ /* rh := (rh + a)*X */ - if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; + if (!BN_mod_add_quick(rh, rh, &group->a, p)) + goto err; + if (!field_mul(group, rh, rh, &point->X, ctx)) + goto err; /* rh := rh + b */ - if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; - } + if (!BN_mod_add_quick(rh, rh, &group->b, p)) + goto err; + } /* 'lh' := Y^2 */ - if (!field_sqr(group, tmp, &point->Y, ctx)) goto err; + if (!field_sqr(group, tmp, &point->Y, ctx)) + goto err; ret = (0 == BN_ucmp(tmp, rh)); - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) - { - /* return values: - * -1 error - * 0 equal (in affine coordinates) - * 1 not equal +int +ec_GFp_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) +{ + /* + * return values: -1 error 0 equal (in affine coordinates) 1 + * not equal */ - int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); - int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); BN_CTX *new_ctx = NULL; BIGNUM *tmp1, *tmp2, *Za23, *Zb23; const BIGNUM *tmp1_, *tmp2_; int ret = -1; - - if (EC_POINT_is_at_infinity(group, a)) - { - return EC_POINT_is_at_infinity(group, b) ? 0 : 1; - } + if (EC_POINT_is_at_infinity(group, a)) { + return EC_POINT_is_at_infinity(group, b) ? 0 : 1; + } if (EC_POINT_is_at_infinity(group, b)) return 1; - - if (a->Z_is_one && b->Z_is_one) - { - return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; - } + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; + } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; - } - + } BN_CTX_start(ctx); tmp1 = BN_CTX_get(ctx); tmp2 = BN_CTX_get(ctx); Za23 = BN_CTX_get(ctx); Zb23 = BN_CTX_get(ctx); - if (Zb23 == NULL) goto end; + if (Zb23 == NULL) + goto end; - /* We have to decide whether - * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), - * or equivalently, whether - * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). + /* + * We have to decide whether (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, + * Y_b/Z_b^3), or equivalently, whether (X_a*Z_b^2, Y_a*Z_b^3) = + * (X_b*Z_a^2, Y_b*Z_a^3). */ - if (!b->Z_is_one) - { - if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end; - if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end; + if (!b->Z_is_one) { + if (!field_sqr(group, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) + goto end; tmp1_ = tmp1; - } - else + } else tmp1_ = &a->X; - if (!a->Z_is_one) - { - if (!field_sqr(group, Za23, &a->Z, ctx)) goto end; - if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end; + if (!a->Z_is_one) { + if (!field_sqr(group, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->X, Za23, ctx)) + goto end; tmp2_ = tmp2; - } - else + } else tmp2_ = &b->X; - + /* compare X_a*Z_b^2 with X_b*Z_a^2 */ - if (BN_cmp(tmp1_, tmp2_) != 0) - { - ret = 1; /* points differ */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ goto end; - } - - - if (!b->Z_is_one) - { - if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end; - if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end; + } + if (!b->Z_is_one) { + if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) + goto end; /* tmp1_ = tmp1 */ - } - else + } else tmp1_ = &a->Y; - if (!a->Z_is_one) - { - if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end; - if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end; + if (!a->Z_is_one) { + if (!field_mul(group, Za23, Za23, &a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) + goto end; /* tmp2_ = tmp2 */ - } - else + } else tmp2_ = &b->Y; /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ - if (BN_cmp(tmp1_, tmp2_) != 0) - { - ret = 1; /* points differ */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ goto end; - } - + } /* points are equal */ ret = 0; - end: +end: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) - { +int +ec_GFp_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; @@ -1138,38 +1188,38 @@ int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); - if (y == NULL) goto err; + if (y == NULL) + goto err; - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - if (!point->Z_is_one) - { + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!point->Z_is_one) { ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); goto err; - } - + } ret = 1; - err: +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; - } +} -int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) - { +int +ec_GFp_simple_points_make_affine(const EC_GROUP * group, size_t num, EC_POINT * points[], BN_CTX * ctx) +{ BN_CTX *new_ctx = NULL; BIGNUM *tmp0, *tmp1; size_t pow2 = 0; @@ -1180,171 +1230,179 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT if (num == 0) return 1; - if (ctx == NULL) - { + if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; - } - + } BN_CTX_start(ctx); tmp0 = BN_CTX_get(ctx); tmp1 = BN_CTX_get(ctx); - if (tmp0 == NULL || tmp1 == NULL) goto err; + if (tmp0 == NULL || tmp1 == NULL) + goto err; - /* Before converting the individual points, compute inverses of all Z values. - * Modular inversion is rather slow, but luckily we can do with a single - * explicit inversion, plus about 3 multiplications per input value. + /* + * Before converting the individual points, compute inverses of all Z + * values. Modular inversion is rather slow, but luckily we can do + * with a single explicit inversion, plus about 3 multiplications per + * input value. */ pow2 = 1; while (num > pow2) pow2 <<= 1; - /* Now pow2 is the smallest power of 2 satifsying pow2 >= num. - * We need twice that. */ + /* + * Now pow2 is the smallest power of 2 satifsying pow2 >= num. We + * need twice that. + */ pow2 <<= 1; heap = malloc(pow2 * sizeof heap[0]); - if (heap == NULL) goto err; - - /* The array is used as a binary tree, exactly as in heapsort: - * - * heap[1] - * heap[2] heap[3] - * heap[4] heap[5] heap[6] heap[7] - * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15] - * - * We put the Z's in the last line; - * then we set each other node to the product of its two child-nodes (where - * empty or 0 entries are treated as ones); - * then we invert heap[1]; - * then we invert each other node by replacing it by the product of its - * parent (after inversion) and its sibling (before inversion). + if (heap == NULL) + goto err; + + /* + * The array is used as a binary tree, exactly as in heapsort: + * + * heap[1] heap[2] heap[3] heap[4] heap[5] + * heap[6] heap[7] heap[8]heap[9] heap[10]heap[11] + * heap[12]heap[13] heap[14] heap[15] + * + * We put the Z's in the last line; then we set each other node to the + * product of its two child-nodes (where empty or 0 entries are + * treated as ones); then we invert heap[1]; then we invert each + * other node by replacing it by the product of its parent (after + * inversion) and its sibling (before inversion). */ heap[0] = NULL; - for (i = pow2/2 - 1; i > 0; i--) + for (i = pow2 / 2 - 1; i > 0; i--) heap[i] = NULL; for (i = 0; i < num; i++) - heap[pow2/2 + i] = &points[i]->Z; - for (i = pow2/2 + num; i < pow2; i++) + heap[pow2 / 2 + i] = &points[i]->Z; + for (i = pow2 / 2 + num; i < pow2; i++) heap[i] = NULL; - + /* set each node to the product of its children */ - for (i = pow2/2 - 1; i > 0; i--) - { + for (i = pow2 / 2 - 1; i > 0; i--) { heap[i] = BN_new(); - if (heap[i] == NULL) goto err; - - if (heap[2*i] != NULL) - { - if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1])) - { - if (!BN_copy(heap[i], heap[2*i])) goto err; - } - else - { - if (BN_is_zero(heap[2*i])) - { - if (!BN_copy(heap[i], heap[2*i + 1])) goto err; - } - else - { + if (heap[i] == NULL) + goto err; + + if (heap[2 * i] != NULL) { + if ((heap[2 * i + 1] == NULL) || BN_is_zero(heap[2 * i + 1])) { + if (!BN_copy(heap[i], heap[2 * i])) + goto err; + } else { + if (BN_is_zero(heap[2 * i])) { + if (!BN_copy(heap[i], heap[2 * i + 1])) + goto err; + } else { if (!group->meth->field_mul(group, heap[i], - heap[2*i], heap[2*i + 1], ctx)) goto err; - } + heap[2 * i], heap[2 * i + 1], ctx)) + goto err; } } } + } /* invert heap[1] */ - if (!BN_is_zero(heap[1])) - { - if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) - { + if (!BN_is_zero(heap[1])) { + if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) { ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); goto err; - } } - if (group->meth->field_encode != 0) - { - /* in the Montgomery case, we just turned R*H (representing H) - * into 1/(R*H), but we need R*(1/H) (representing 1/H); - * i.e. we have need to multiply by the Montgomery factor twice */ - if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; - if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err; - } - + } + if (group->meth->field_encode != 0) { + /* + * in the Montgomery case, we just turned R*H (representing + * H) into 1/(R*H), but we need R*(1/H) (representing + * 1/H); i.e. we have need to multiply by the Montgomery + * factor twice + */ + if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) + goto err; + if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) + goto err; + } /* set other heap[i]'s to their inverses */ - for (i = 2; i < pow2/2 + num; i += 2) - { + for (i = 2; i < pow2 / 2 + num; i += 2) { /* i is even */ - if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) - { - if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err; - if (!BN_copy(heap[i], tmp0)) goto err; - if (!BN_copy(heap[i + 1], tmp1)) goto err; - } - else - { - if (!BN_copy(heap[i], heap[i/2])) goto err; - } + if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) { + if (!group->meth->field_mul(group, tmp0, heap[i / 2], heap[i + 1], ctx)) + goto err; + if (!group->meth->field_mul(group, tmp1, heap[i / 2], heap[i], ctx)) + goto err; + if (!BN_copy(heap[i], tmp0)) + goto err; + if (!BN_copy(heap[i + 1], tmp1)) + goto err; + } else { + if (!BN_copy(heap[i], heap[i / 2])) + goto err; } + } - /* we have replaced all non-zero Z's by their inverses, now fix up all the points */ - for (i = 0; i < num; i++) - { + /* + * we have replaced all non-zero Z's by their inverses, now fix up + * all the points + */ + for (i = 0; i < num; i++) { EC_POINT *p = points[i]; - - if (!BN_is_zero(&p->Z)) - { - /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ - if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err; - if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err; + if (!BN_is_zero(&p->Z)) { + /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ - if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err; - if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err; - - if (group->meth->field_set_to_one != 0) - { - if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err; - } - else - { - if (!BN_one(&p->Z)) goto err; - } - p->Z_is_one = 1; + if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) + goto err; + + if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) + goto err; + + if (group->meth->field_set_to_one != 0) { + if (!group->meth->field_set_to_one(group, &p->Z, ctx)) + goto err; + } else { + if (!BN_one(&p->Z)) + goto err; } + p->Z_is_one = 1; } + } ret = 1; - - err: + +err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); - if (heap != NULL) - { - /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */ - for (i = pow2/2 - 1; i > 0; i--) - { + if (heap != NULL) { + /* + * heap[pow2/2] .. heap[pow2-1] have not been allocated + * locally! + */ + for (i = pow2 / 2 - 1; i > 0; i--) { if (heap[i] != NULL) BN_clear_free(heap[i]); - } - free(heap); } - return ret; + free(heap); } + return ret; +} -int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_simple_field_mul(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) +{ return BN_mod_mul(r, a, b, &group->field, ctx); - } +} -int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) - { +int +ec_GFp_simple_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, BN_CTX * ctx) +{ return BN_mod_sqr(r, a, &group->field, ctx); - } +}