-/* $OpenBSD: ec_lcl.h,v 1.7 2016/12/21 15:49:29 jsing Exp $ */
+/* $OpenBSD: ec_lcl.h,v 1.8 2018/07/10 21:55:49 tb Exp $ */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
- /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
- * (default implementations are used if the 'mul' pointer is 0): */
- int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
- size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
+ /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult */
+ int (*mul_generator_ct)(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar, BN_CTX *);
+ int (*mul_single_ct)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ const EC_POINT *point, BN_CTX *);
+ int (*mul_double_nonct)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
+ const BIGNUM *p_scalar, const EC_POINT *point, BN_CTX *);
int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
int (*have_precompute_mult)(const EC_GROUP *group);
int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+int ec_GFp_simple_mul_generator_ct(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar, BN_CTX *);
+int ec_GFp_simple_mul_single_ct(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar,
+ const EC_POINT *point, BN_CTX *);
+int ec_GFp_simple_mul_double_nonct(const EC_GROUP *, EC_POINT *r, const BIGNUM *g_scalar,
+ const BIGNUM *p_scalar, const EC_POINT *point, BN_CTX *);
/* method functions in ecp_mont.c */
-/* $OpenBSD: ec_lib.c,v 1.24 2017/05/02 03:59:44 deraadt Exp $ */
+/* $OpenBSD: ec_lib.c,v 1.25 2018/07/10 21:55:49 tb Exp $ */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
}
-/* Functions for point multiplication.
- *
- * If group->meth->mul is 0, we use the wNAF-based implementations in ec_mult.c;
- * otherwise we dispatch through methods.
- */
-
+/* Functions for point multiplication */
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);
+ /*
+ * The function pointers must be set, and only support num == 0 and
+ * num == 1.
+ */
+ if (group->meth->mul_generator_ct == NULL ||
+ group->meth->mul_single_ct == NULL ||
+ group->meth->mul_double_nonct == NULL ||
+ num > 1) {
+ ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+
+ /* Either bP or aG + bP, this is sane. */
+ if (num == 1 && points != NULL && scalars != NULL)
+ return EC_POINT_mul(group, r, scalar, points[0], scalars[0],
+ ctx);
+
+ /* aG, this is sane */
+ if (scalar != NULL && points == NULL && scalars == NULL)
+ return EC_POINT_mul(group, r, scalar, NULL, NULL, ctx);
+
+ /* anything else is an error */
+ ECerror(ERR_R_EC_LIB);
+ return 0;
}
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];
- const BIGNUM *scalars[1];
-
- points[0] = point;
- scalars[0] = p_scalar;
-
- return EC_POINTs_mul(group, r, g_scalar,
- (point != NULL && p_scalar != NULL),
- points, scalars, ctx);
+ if (group->meth->mul_generator_ct == NULL ||
+ group->meth->mul_single_ct == NULL ||
+ group->meth->mul_double_nonct == NULL) {
+ ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+ if (g_scalar != NULL && point == NULL && p_scalar == NULL) {
+ /*
+ * In this case we want to compute g_scalar * GeneratorPoint:
+ * this codepath is reached most prominently by (ephemeral) key
+ * generation of EC cryptosystems (i.e. ECDSA keygen and sign
+ * setup, ECDH keygen/first half), where the scalar is always
+ * secret. This is why we ignore if BN_FLG_CONSTTIME is actually
+ * set and we always call the constant time version.
+ */
+ return group->meth->mul_generator_ct(group, r, g_scalar, ctx);
+ }
+ if (g_scalar == NULL && point != NULL && p_scalar != NULL) {
+ /* In this case we want to compute p_scalar * GenericPoint:
+ * this codepath is reached most prominently by the second half
+ * of ECDH, where the secret scalar is multiplied by the peer's
+ * public point. To protect the secret scalar, we ignore if
+ * BN_FLG_CONSTTIME is actually set and we always call the
+ * constant time version.
+ */
+ return group->meth->mul_single_ct(group, r, p_scalar, point,
+ ctx);
+ }
+ if (g_scalar != NULL && point != NULL && p_scalar != NULL) {
+ /*
+ * In this case we want to compute
+ * g_scalar * GeneratorPoint + p_scalar * GenericPoint:
+ * this codepath is reached most prominently by ECDSA signature
+ * verification. So we call the non-ct version.
+ */
+ return group->meth->mul_double_nonct(group, r, g_scalar,
+ p_scalar, point, ctx);
+ }
+
+ /* Anything else is an error. */
+ ECerror(ERR_R_EC_LIB);
+ return 0;
}
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);
-
if (group->meth->precompute_mult != 0)
return group->meth->precompute_mult(group, ctx);
else
int
EC_GROUP_have_precompute_mult(const EC_GROUP * group)
{
- if (group->meth->mul == 0)
- /* use default */
- return ec_wNAF_have_precompute_mult(group);
-
if (group->meth->have_precompute_mult != 0)
return group->meth->have_precompute_mult(group);
else
-/* $OpenBSD: ecp_smpl.c,v 1.17 2017/01/29 17:49:23 beck Exp $ */
+/* $OpenBSD: ecp_smpl.c,v 1.18 2018/07/10 21:55:49 tb Exp $ */
/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
* for the OpenSSL project.
* Includes code written by Bodo Moeller for the OpenSSL project.
.point_cmp = ec_GFp_simple_cmp,
.make_affine = ec_GFp_simple_make_affine,
.points_make_affine = ec_GFp_simple_points_make_affine,
+ .mul_generator_ct = ec_GFp_simple_mul_generator_ct,
+ .mul_single_ct = ec_GFp_simple_mul_single_ct,
+ .mul_double_nonct = ec_GFp_simple_mul_double_nonct,
.field_mul = ec_GFp_simple_field_mul,
.field_sqr = ec_GFp_simple_field_sqr
};
{
return BN_mod_sqr(r, a, &group->field, ctx);
}
+
+#define EC_POINT_BN_set_flags(P, flags) do { \
+ BN_set_flags(&(P)->X, (flags)); \
+ BN_set_flags(&(P)->Y, (flags)); \
+ BN_set_flags(&(P)->Z, (flags)); \
+} while(0)
+
+#define EC_POINT_CSWAP(c, a, b, w, t) do { \
+ if (!BN_swap_ct(c, &(a)->X, &(b)->X, w) || \
+ !BN_swap_ct(c, &(a)->Y, &(b)->Y, w) || \
+ !BN_swap_ct(c, &(a)->Z, &(b)->Z, w)) \
+ goto err; \
+ t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
+ (a)->Z_is_one ^= (t); \
+ (b)->Z_is_one ^= (t); \
+} while(0)
+
+/*
+ * This function computes (in constant time) a point multiplication over the
+ * EC group.
+ *
+ * At a high level, it is Montgomery ladder with conditional swaps.
+ *
+ * It performs either a fixed point multiplication
+ * (scalar * generator)
+ * when point is NULL, or a variable point multiplication
+ * (scalar * point)
+ * when point is not NULL.
+ *
+ * scalar should be in the range [0,n) otherwise all constant time bets are off.
+ *
+ * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
+ * which of course are not constant time themselves.
+ *
+ * The product is stored in r.
+ *
+ * Returns 1 on success, 0 otherwise.
+ */
+static int
+ec_GFp_simple_mul_ct(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ const EC_POINT *point, BN_CTX *ctx)
+{
+ int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
+ EC_POINT *s = NULL;
+ BIGNUM *k = NULL;
+ BIGNUM *lambda = NULL;
+ BIGNUM *cardinality = NULL;
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL && (ctx = new_ctx = BN_CTX_new()) == NULL)
+ return 0;
+
+ BN_CTX_start(ctx);
+
+ if ((s = EC_POINT_new(group)) == NULL)
+ goto err;
+
+ if (point == NULL) {
+ if (!EC_POINT_copy(s, group->generator))
+ goto err;
+ } else {
+ if (!EC_POINT_copy(s, point))
+ goto err;
+ }
+
+ EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
+
+ if ((cardinality = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((lambda = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((k = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!BN_mul(cardinality, &group->order, &group->cofactor, ctx))
+ goto err;
+
+ /*
+ * Group cardinalities are often on a word boundary.
+ * So when we pad the scalar, some timing diff might
+ * pop if it needs to be expanded due to carries.
+ * So expand ahead of time.
+ */
+ cardinality_bits = BN_num_bits(cardinality);
+ group_top = cardinality->top;
+ if ((bn_wexpand(k, group_top + 1) == NULL) ||
+ (bn_wexpand(lambda, group_top + 1) == NULL))
+ goto err;
+
+ if (!BN_copy(k, scalar))
+ goto err;
+
+ BN_set_flags(k, BN_FLG_CONSTTIME);
+
+ if (BN_num_bits(k) > cardinality_bits || BN_is_negative(k)) {
+ /*
+ * This is an unusual input, and we don't guarantee
+ * constant-timeness
+ */
+ if (!BN_nnmod(k, k, cardinality, ctx))
+ goto err;
+ }
+
+ if (!BN_add(lambda, k, cardinality))
+ goto err;
+ BN_set_flags(lambda, BN_FLG_CONSTTIME);
+ if (!BN_add(k, lambda, cardinality))
+ goto err;
+ /*
+ * lambda := scalar + cardinality
+ * k := scalar + 2*cardinality
+ */
+ kbit = BN_is_bit_set(lambda, cardinality_bits);
+ if (!BN_swap_ct(kbit, k, lambda, group_top + 1))
+ goto err;
+
+ group_top = group->field.top;
+ if ((bn_wexpand(&s->X, group_top) == NULL) ||
+ (bn_wexpand(&s->Y, group_top) == NULL) ||
+ (bn_wexpand(&s->Z, group_top) == NULL) ||
+ (bn_wexpand(&r->X, group_top) == NULL) ||
+ (bn_wexpand(&r->Y, group_top) == NULL) ||
+ (bn_wexpand(&r->Z, group_top) == NULL))
+ goto err;
+
+ /* top bit is a 1, in a fixed pos */
+ if (!EC_POINT_copy(r, s))
+ goto err;
+
+ EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
+
+ if (!EC_POINT_dbl(group, s, s, ctx))
+ goto err;
+
+ pbit = 0;
+
+ /*
+ * The ladder step, with branches, is
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * Swapping R, S conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: T, U = R, S
+ * k[i] == 1: T, U = S, R
+ *
+ * Then perform the ECC ops.
+ *
+ * U = add(T, U)
+ * T = dbl(T)
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: U = add(R, S), T = dbl(R)
+ * k[i] == 1: U = add(S, R), T = dbl(S)
+ *
+ * Swapping T, U conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: R, S = T, U
+ * k[i] == 1: R, S = U, T
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * So we get the same logic, but instead of a branch it's a
+ * conditional swap, followed by ECC ops, then another conditional swap.
+ *
+ * Optimization: The end of iteration i and start of i-1 looks like
+ *
+ * ...
+ * CSWAP(k[i], R, S)
+ * ECC
+ * CSWAP(k[i], R, S)
+ * (next iteration)
+ * CSWAP(k[i-1], R, S)
+ * ECC
+ * CSWAP(k[i-1], R, S)
+ * ...
+ *
+ * So instead of two contiguous swaps, you can merge the condition
+ * bits and do a single swap.
+ *
+ * k[i] k[i-1] Outcome
+ * 0 0 No Swap
+ * 0 1 Swap
+ * 1 0 Swap
+ * 1 1 No Swap
+ *
+ * This is XOR. pbit tracks the previous bit of k.
+ */
+
+ for (i = cardinality_bits - 1; i >= 0; i--) {
+ kbit = BN_is_bit_set(k, i) ^ pbit;
+ EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
+ if (!EC_POINT_add(group, s, r, s, ctx))
+ goto err;
+ if (!EC_POINT_dbl(group, r, r, ctx))
+ goto err;
+ /*
+ * pbit logic merges this cswap with that of the
+ * next iteration
+ */
+ pbit ^= kbit;
+ }
+ /* one final cswap to move the right value into r */
+ EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
+
+ ret = 1;
+
+ err:
+ EC_POINT_free(s);
+ if (ctx != NULL)
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+
+ return ret;
+}
+
+#undef EC_POINT_BN_set_flags
+#undef EC_POINT_CSWAP
+
+int
+ec_GFp_simple_mul_generator_ct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, BN_CTX *ctx)
+{
+ return ec_GFp_simple_mul_ct(group, r, scalar, NULL, ctx);
+}
+
+int
+ec_GFp_simple_mul_single_ct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
+{
+ return ec_GFp_simple_mul_ct(group, r, scalar, point, ctx);
+}
+
+int
+ec_GFp_simple_mul_double_nonct(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *g_scalar, const BIGNUM *p_scalar, const EC_POINT *point,
+ BN_CTX *ctx)
+{
+ return ec_wNAF_mul(group, r, g_scalar, 1, &point, &p_scalar, ctx);
+}
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