-/* $OpenBSD: bn_exp.c,v 1.35 2022/11/26 16:08:51 tb Exp $ */
+/* $OpenBSD: bn_exp.c,v 1.36 2023/02/03 05:27:50 jsing Exp $ */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
return (ret);
}
-static int
-BN_mod_exp_internal(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx, int ct)
-{
- int ret;
-
-
- /* For even modulus m = 2^k*m_odd, it might make sense to compute
- * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
- * exponentiation for the odd part), using appropriate exponent
- * reductions, and combine the results using the CRT.
- *
- * For now, we use Montgomery only if the modulus is odd; otherwise,
- * exponentiation using the reciprocal-based quick remaindering
- * algorithm is used.
- *
- * (Timing obtained with expspeed.c [computations a^p mod m
- * where a, p, m are of the same length: 256, 512, 1024, 2048,
- * 4096, 8192 bits], compared to the running time of the
- * standard algorithm:
- *
- * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
- * 55 .. 77 % [UltraSparc processor, but
- * debug-solaris-sparcv8-gcc conf.]
- *
- * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
- * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
- *
- * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
- * at 2048 and more bits, but at 512 and 1024 bits, it was
- * slower even than the standard algorithm!
- *
- * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
- * should be obtained when the new Montgomery reduction code
- * has been integrated into OpenSSL.)
- */
-
- if (BN_is_odd(m)) {
- if (a->top == 1 && !a->neg && !ct) {
- BN_ULONG A = a->d[0];
- ret = BN_mod_exp_mont_word(r, A,p, m,ctx, NULL);
- } else
- ret = BN_mod_exp_mont_ct(r, a,p, m,ctx, NULL);
- } else {
- ret = BN_mod_exp_recp(r, a,p, m, ctx);
- }
-
- return (ret);
-}
-
-int
-BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx)
-{
- return BN_mod_exp_internal(r, a, p, m, ctx,
- (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
-}
-
-int
-BN_mod_exp_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx)
-{
- return BN_mod_exp_internal(r, a, p, m, ctx, 1);
-}
-
-
-int
-BN_mod_exp_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx)
-{
- return BN_mod_exp_internal(r, a, p, m, ctx, 0);
-}
-
-
+/* The old fallback, simple version :-) */
int
-BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx)
{
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
int start = 1;
- BIGNUM *aa;
+ BIGNUM *d;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
- BN_RECP_CTX recp;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
return ret;
}
- BN_RECP_CTX_init(&recp);
-
BN_CTX_start(ctx);
- if ((aa = BN_CTX_get(ctx)) == NULL)
+ if ((d = BN_CTX_get(ctx)) == NULL)
goto err;
if ((val[0] = BN_CTX_get(ctx)) == NULL)
goto err;
- if (m->neg) {
- /* ignore sign of 'm' */
- if (!BN_copy(aa, m))
- goto err;
- aa->neg = 0;
- if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
- goto err;
- } else {
- if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
- goto err;
- }
-
- if (!BN_nnmod(val[0], a, m, ctx))
+ if (!BN_nnmod(val[0],a,m,ctx))
goto err; /* 1 */
if (BN_is_zero(val[0])) {
BN_zero(r);
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
- if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
+ if (!BN_mod_mul(d, val[0], val[0], m, ctx))
goto err; /* 2 */
j = 1 << (window - 1);
for (i = 1; i < j; i++) {
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul_reciprocal(val[i], val[i - 1],
- aa, &recp, ctx))
+ !BN_mod_mul(val[i], val[i - 1], d,m, ctx))
goto err;
}
}
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start)
- if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
- goto err;
- if (wstart == 0)
- break;
- wstart--;
- continue;
- }
- /* We now have wstart on a 'set' bit, we now need to work out
- * how bit a window to do. To do this we need to scan
- * forward until the last set bit before the end of the
- * window */
- j = wstart;
- wvalue = 1;
- wend = 0;
- for (i = 1; i < window; i++) {
- if (wstart - i < 0)
- break;
- if (BN_is_bit_set(p, wstart - i)) {
- wvalue <<= (i - wend);
- wvalue |= 1;
- wend = i;
- }
- }
-
- /* wend is the size of the current window */
- j = wend + 1;
- /* add the 'bytes above' */
- if (!start)
- for (i = 0; i < j; i++) {
- if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
- goto err;
- }
-
- /* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul_reciprocal(r, r,val[wvalue >> 1], &recp, ctx))
- goto err;
-
- /* move the 'window' down further */
- wstart -= wend + 1;
- wvalue = 0;
- start = 0;
- if (wstart < 0)
- break;
- }
- ret = 1;
-
-err:
- BN_CTX_end(ctx);
- BN_RECP_CTX_free(&recp);
- return (ret);
-}
-
-static int
-BN_mod_exp_mont_internal(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx, BN_MONT_CTX *in_mont, int ct)
-{
- int i, j, bits, ret = 0, wstart, wend, window, wvalue;
- int start = 1;
- BIGNUM *d, *r;
- const BIGNUM *aa;
- /* Table of variables obtained from 'ctx' */
- BIGNUM *val[TABLE_SIZE];
- BN_MONT_CTX *mont = NULL;
-
- if (ct) {
- return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
- }
-
-
- if (!BN_is_odd(m)) {
- BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
- return (0);
- }
-
- bits = BN_num_bits(p);
- if (bits == 0) {
- /* x**0 mod 1 is still zero. */
- if (BN_is_one(m)) {
- ret = 1;
- BN_zero(rr);
- } else
- ret = BN_one(rr);
- return ret;
- }
-
- BN_CTX_start(ctx);
- if ((d = BN_CTX_get(ctx)) == NULL)
- goto err;
- if ((r = BN_CTX_get(ctx)) == NULL)
- goto err;
- if ((val[0] = BN_CTX_get(ctx)) == NULL)
- goto err;
-
- /* If this is not done, things will break in the montgomery
- * part */
-
- if (in_mont != NULL)
- mont = in_mont;
- else {
- if ((mont = BN_MONT_CTX_new()) == NULL)
- goto err;
- if (!BN_MONT_CTX_set(mont, m, ctx))
- goto err;
- }
-
- if (a->neg || BN_ucmp(a, m) >= 0) {
- if (!BN_nnmod(val[0], a,m, ctx))
- goto err;
- aa = val[0];
- } else
- aa = a;
- if (BN_is_zero(aa)) {
- BN_zero(rr);
- ret = 1;
- goto err;
- }
- if (!BN_to_montgomery(val[0], aa, mont, ctx))
- goto err; /* 1 */
-
- window = BN_window_bits_for_exponent_size(bits);
- if (window > 1) {
- if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
- goto err; /* 2 */
- j = 1 << (window - 1);
- for (i = 1; i < j; i++) {
- if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul_montgomery(val[i], val[i - 1],
- d, mont, ctx))
- goto err;
- }
- }
-
- start = 1; /* This is used to avoid multiplication etc
- * when there is only the value '1' in the
- * buffer. */
- wvalue = 0; /* The 'value' of the window */
- wstart = bits - 1; /* The top bit of the window */
- wend = 0; /* The bottom bit of the window */
-
- if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
- goto err;
- for (;;) {
- if (BN_is_bit_set(p, wstart) == 0) {
- if (!start) {
- if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ if (!BN_mod_mul(r, r, r, m, ctx))
goto err;
- }
if (wstart == 0)
break;
wstart--;
/* add the 'bytes above' */
if (!start)
for (i = 0; i < j; i++) {
- if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ if (!BN_mod_mul(r, r, r, m, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
+ if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
goto err;
/* move the 'window' down further */
if (wstart < 0)
break;
}
- if (!BN_from_montgomery(rr, r,mont, ctx))
- goto err;
ret = 1;
err:
- if ((in_mont == NULL) && (mont != NULL))
- BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
return (ret);
}
-int
-BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx, BN_MONT_CTX *in_mont)
-{
- return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont,
- (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
-}
-
-int
-BN_mod_exp_mont_ct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx, BN_MONT_CTX *in_mont)
-{
- return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 1);
-}
-
-int
-BN_mod_exp_mont_nonct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx, BN_MONT_CTX *in_mont)
-{
- return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 0);
-}
-
/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
* so that accessing any of these table values shows the same access pattern as far
* as cache lines are concerned. The following functions are used to transfer a BIGNUM
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0,
window))
goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1,
- window))
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1,
+ window))
+ goto err;
+
+ /* If the window size is greater than 1, then calculate
+ * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
+ * (even powers could instead be computed as (a^(i/2))^2
+ * to use the slight performance advantage of sqr over mul).
+ */
+ if (window > 1) {
+ if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
+ goto err;
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf,
+ 2, window))
+ goto err;
+ for (i = 3; i < numPowers; i++) {
+ /* Calculate a^i = a^(i-1) * a */
+ if (!BN_mod_mul_montgomery(&tmp, &am, &tmp,
+ mont, ctx))
+ goto err;
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top,
+ powerbuf, i, window))
+ goto err;
+ }
+ }
+
+ bits--;
+ for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf,
+ wvalue, window))
+ goto err;
+
+ /* Scan the exponent one window at a time starting from the most
+ * significant bits.
+ */
+ while (bits >= 0) {
+ wvalue = 0; /* The 'value' of the window */
+
+ /* Scan the window, squaring the result as we go */
+ for (i = 0; i < window; i++, bits--) {
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp,
+ mont, ctx))
+ goto err;
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+
+ /* Fetch the appropriate pre-computed value from the pre-buf */
+ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf,
+ wvalue, window))
+ goto err;
+
+ /* Multiply the result into the intermediate result */
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
+ goto err;
+ }
+ }
+
+ /* Convert the final result from montgomery to standard format */
+ if (!BN_from_montgomery(rr, &tmp, mont, ctx))
+ goto err;
+ ret = 1;
+
+err:
+ if ((in_mont == NULL) && (mont != NULL))
+ BN_MONT_CTX_free(mont);
+ freezero(powerbufFree, powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
+ BN_CTX_end(ctx);
+ return (ret);
+}
+
+static int
+BN_mod_exp_mont_internal(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx, BN_MONT_CTX *in_mont, int ct)
+{
+ int i, j, bits, ret = 0, wstart, wend, window, wvalue;
+ int start = 1;
+ BIGNUM *d, *r;
+ const BIGNUM *aa;
+ /* Table of variables obtained from 'ctx' */
+ BIGNUM *val[TABLE_SIZE];
+ BN_MONT_CTX *mont = NULL;
+
+ if (ct) {
+ return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
+ }
+
+
+ if (!BN_is_odd(m)) {
+ BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
+ return (0);
+ }
+
+ bits = BN_num_bits(p);
+ if (bits == 0) {
+ /* x**0 mod 1 is still zero. */
+ if (BN_is_one(m)) {
+ ret = 1;
+ BN_zero(rr);
+ } else
+ ret = BN_one(rr);
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+ if ((d = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((r = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((val[0] = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ /* If this is not done, things will break in the montgomery
+ * part */
+
+ if (in_mont != NULL)
+ mont = in_mont;
+ else {
+ if ((mont = BN_MONT_CTX_new()) == NULL)
+ goto err;
+ if (!BN_MONT_CTX_set(mont, m, ctx))
+ goto err;
+ }
+
+ if (a->neg || BN_ucmp(a, m) >= 0) {
+ if (!BN_nnmod(val[0], a,m, ctx))
goto err;
+ aa = val[0];
+ } else
+ aa = a;
+ if (BN_is_zero(aa)) {
+ BN_zero(rr);
+ ret = 1;
+ goto err;
+ }
+ if (!BN_to_montgomery(val[0], aa, mont, ctx))
+ goto err; /* 1 */
- /* If the window size is greater than 1, then calculate
- * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
- * (even powers could instead be computed as (a^(i/2))^2
- * to use the slight performance advantage of sqr over mul).
- */
- if (window > 1) {
- if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
- goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf,
- 2, window))
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1) {
+ if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
+ goto err; /* 2 */
+ j = 1 << (window - 1);
+ for (i = 1; i < j; i++) {
+ if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
+ !BN_mod_mul_montgomery(val[i], val[i - 1],
+ d, mont, ctx))
goto err;
- for (i = 3; i < numPowers; i++) {
- /* Calculate a^i = a^(i-1) * a */
- if (!BN_mod_mul_montgomery(&tmp, &am, &tmp,
- mont, ctx))
- goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top,
- powerbuf, i, window))
- goto err;
- }
}
+ }
- bits--;
- for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
- wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
- if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf,
- wvalue, window))
- goto err;
+ start = 1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue = 0; /* The 'value' of the window */
+ wstart = bits - 1; /* The top bit of the window */
+ wend = 0; /* The bottom bit of the window */
- /* Scan the exponent one window at a time starting from the most
- * significant bits.
- */
- while (bits >= 0) {
- wvalue = 0; /* The 'value' of the window */
+ if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
+ goto err;
+ for (;;) {
+ if (BN_is_bit_set(p, wstart) == 0) {
+ if (!start) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ goto err;
+ }
+ if (wstart == 0)
+ break;
+ wstart--;
+ continue;
+ }
+ /* We now have wstart on a 'set' bit, we now need to work out
+ * how bit a window to do. To do this we need to scan
+ * forward until the last set bit before the end of the
+ * window */
+ j = wstart;
+ wvalue = 1;
+ wend = 0;
+ for (i = 1; i < window; i++) {
+ if (wstart - i < 0)
+ break;
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wend);
+ wvalue |= 1;
+ wend = i;
+ }
+ }
- /* Scan the window, squaring the result as we go */
- for (i = 0; i < window; i++, bits--) {
- if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp,
- mont, ctx))
+ /* wend is the size of the current window */
+ j = wend + 1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i = 0; i < j; i++) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
goto err;
- wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
}
- /* Fetch the appropriate pre-computed value from the pre-buf */
- if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf,
- wvalue, window))
- goto err;
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
+ goto err;
- /* Multiply the result into the intermediate result */
- if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
- goto err;
- }
+ /* move the 'window' down further */
+ wstart -= wend + 1;
+ wvalue = 0;
+ start = 0;
+ if (wstart < 0)
+ break;
}
-
- /* Convert the final result from montgomery to standard format */
- if (!BN_from_montgomery(rr, &tmp, mont, ctx))
+ if (!BN_from_montgomery(rr, r,mont, ctx))
goto err;
ret = 1;
err:
if ((in_mont == NULL) && (mont != NULL))
BN_MONT_CTX_free(mont);
- freezero(powerbufFree, powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
BN_CTX_end(ctx);
return (ret);
}
+int
+BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx, BN_MONT_CTX *in_mont)
+{
+ return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont,
+ (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
+}
+
+int
+BN_mod_exp_mont_ct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx, BN_MONT_CTX *in_mont)
+{
+ return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 1);
+}
+
+int
+BN_mod_exp_mont_nonct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx, BN_MONT_CTX *in_mont)
+{
+ return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 0);
+}
+
int
BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx, BN_MONT_CTX *in_mont)
return (ret);
}
-
-/* The old fallback, simple version :-) */
int
-BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx)
{
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
int start = 1;
- BIGNUM *d;
+ BIGNUM *aa;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
+ BN_RECP_CTX recp;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
return ret;
}
+ BN_RECP_CTX_init(&recp);
+
BN_CTX_start(ctx);
- if ((d = BN_CTX_get(ctx)) == NULL)
+ if ((aa = BN_CTX_get(ctx)) == NULL)
goto err;
if ((val[0] = BN_CTX_get(ctx)) == NULL)
goto err;
- if (!BN_nnmod(val[0],a,m,ctx))
+ if (m->neg) {
+ /* ignore sign of 'm' */
+ if (!BN_copy(aa, m))
+ goto err;
+ aa->neg = 0;
+ if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
+ goto err;
+ } else {
+ if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
+ goto err;
+ }
+
+ if (!BN_nnmod(val[0], a, m, ctx))
goto err; /* 1 */
if (BN_is_zero(val[0])) {
BN_zero(r);
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
- if (!BN_mod_mul(d, val[0], val[0], m, ctx))
+ if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
goto err; /* 2 */
j = 1 << (window - 1);
for (i = 1; i < j; i++) {
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul(val[i], val[i - 1], d,m, ctx))
+ !BN_mod_mul_reciprocal(val[i], val[i - 1],
+ aa, &recp, ctx))
goto err;
}
}
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start)
- if (!BN_mod_mul(r, r, r, m, ctx))
+ if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
goto err;
if (wstart == 0)
break;
/* add the 'bytes above' */
if (!start)
for (i = 0; i < j; i++) {
- if (!BN_mod_mul(r, r, r, m, ctx))
+ if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
+ if (!BN_mod_mul_reciprocal(r, r,val[wvalue >> 1], &recp, ctx))
goto err;
/* move the 'window' down further */
err:
BN_CTX_end(ctx);
+ BN_RECP_CTX_free(&recp);
+ return (ret);
+}
+
+static int
+BN_mod_exp_internal(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx, int ct)
+{
+ int ret;
+
+
+ /* For even modulus m = 2^k*m_odd, it might make sense to compute
+ * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
+ * exponentiation for the odd part), using appropriate exponent
+ * reductions, and combine the results using the CRT.
+ *
+ * For now, we use Montgomery only if the modulus is odd; otherwise,
+ * exponentiation using the reciprocal-based quick remaindering
+ * algorithm is used.
+ *
+ * (Timing obtained with expspeed.c [computations a^p mod m
+ * where a, p, m are of the same length: 256, 512, 1024, 2048,
+ * 4096, 8192 bits], compared to the running time of the
+ * standard algorithm:
+ *
+ * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
+ * 55 .. 77 % [UltraSparc processor, but
+ * debug-solaris-sparcv8-gcc conf.]
+ *
+ * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
+ * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
+ *
+ * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
+ * at 2048 and more bits, but at 512 and 1024 bits, it was
+ * slower even than the standard algorithm!
+ *
+ * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
+ * should be obtained when the new Montgomery reduction code
+ * has been integrated into OpenSSL.)
+ */
+
+ if (BN_is_odd(m)) {
+ if (a->top == 1 && !a->neg && !ct) {
+ BN_ULONG A = a->d[0];
+ ret = BN_mod_exp_mont_word(r, A,p, m,ctx, NULL);
+ } else
+ ret = BN_mod_exp_mont_ct(r, a,p, m,ctx, NULL);
+ } else {
+ ret = BN_mod_exp_recp(r, a,p, m, ctx);
+ }
+
return (ret);
}
+
+int
+BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx)
+{
+ return BN_mod_exp_internal(r, a, p, m, ctx,
+ (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
+}
+
+int
+BN_mod_exp_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx)
+{
+ return BN_mod_exp_internal(r, a, p, m, ctx, 1);
+}
+
+int
+BN_mod_exp_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx)
+{
+ return BN_mod_exp_internal(r, a, p, m, ctx, 0);
+}
projects / openbsd / commitdiff