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yuzu/externals/libressl/crypto/bn/bn_exp.c

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early-access version 1255
2020-12-28 19:15:37 +04:00
/* $OpenBSD: bn_exp.c,v 1.31 2017/05/02 03:59:44 deraadt Exp $ */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* 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 the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/* ====================================================================
* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* 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
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include <stdlib.h>
#include <string.h>
#include <openssl/err.h>
#include "bn_lcl.h"
#include "constant_time_locl.h"
/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE 32
/* this one works - simple but works */
int
BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
int i, bits, ret = 0;
BIGNUM *v, *rr;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
BN_CTX_start(ctx);
if ((r == a) || (r == p))
rr = BN_CTX_get(ctx);
else
rr = r;
v = BN_CTX_get(ctx);
if (rr == NULL || v == NULL)
goto err;
if (BN_copy(v, a) == NULL)
goto err;
bits = BN_num_bits(p);
if (BN_is_odd(p)) {
if (BN_copy(rr, a) == NULL)
goto err;
} else {
if (!BN_one(rr))
goto err;
}
for (i = 1; i < bits; i++) {
if (!BN_sqr(v, v, ctx))
goto err;
if (BN_is_bit_set(p, i)) {
if (!BN_mul(rr, rr, v, ctx))
goto err;
}
}
ret = 1;
err:
if (r != rr && rr != NULL)
BN_copy(r, rr);
BN_CTX_end(ctx);
bn_check_top(r);
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;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
/* 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);
}
bn_check_top(r);
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);
}
int
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 *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() */
BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1 is still zero. */
if (BN_is_one(m)) {
ret = 1;
BN_zero(r);
} else
ret = BN_one(r);
return ret;
}
BN_CTX_start(ctx);
if ((aa = BN_CTX_get(ctx)) == NULL)
goto err;
if ((val[0] = BN_CTX_get(ctx)) == NULL)
goto err;
BN_RECP_CTX_init(&recp);
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);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
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_reciprocal(val[i], val[i - 1],
aa, &recp, 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_one(r))
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);
bn_check_top(r);
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);
}
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
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))
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_montgomery(r, r, r, mont, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
goto err;
/* move the 'window' down further */
wstart -= wend + 1;
wvalue = 0;
start = 0;
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);
bn_check_top(rr);
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
* from/to that table. */
static int
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf,
int idx, int window)
{
int i, j;
int width = 1 << window;
BN_ULONG *table = (BN_ULONG *)buf;
if (top > b->top)
top = b->top; /* this works because 'buf' is explicitly zeroed */
for (i = 0, j = idx; i < top; i++, j += width) {
table[j] = b->d[i];
}
return 1;
}
static int
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx,
int window)
{
int i, j;
int width = 1 << window;
volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
if (bn_wexpand(b, top) == NULL)
return 0;
if (window <= 3) {
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < width; j++) {
acc |= table[j] &
((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
}
b->d[i] = acc;
}
} else {
int xstride = 1 << (window - 2);
BN_ULONG y0, y1, y2, y3;
i = idx >> (window - 2); /* equivalent of idx / xstride */
idx &= xstride - 1; /* equivalent of idx % xstride */
y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < xstride; j++) {
acc |= ( (table[j + 0 * xstride] & y0) |
(table[j + 1 * xstride] & y1) |
(table[j + 2 * xstride] & y2) |
(table[j + 3 * xstride] & y3) )
& ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
}
b->d[i] = acc;
}
}
b->top = top;
bn_correct_top(b);
return 1;
}
/* Given a pointer value, compute the next address that is a cache line multiple. */
#define MOD_EXP_CTIME_ALIGN(x_) \
((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
/* This variant of BN_mod_exp_mont() uses fixed windows and the special
* precomputation memory layout to limit data-dependency to a minimum
* to protect secret exponents (cf. the hyper-threading timing attacks
* pointed out by Colin Percival,
* http://www.daemonology.net/hyperthreading-considered-harmful/)
*/
int
BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
int i, bits, ret = 0, window, wvalue;
int top;
BN_MONT_CTX *mont = NULL;
int numPowers;
unsigned char *powerbufFree = NULL;
int powerbufLen = 0;
unsigned char *powerbuf = NULL;
BIGNUM tmp, am;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m)) {
BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
return (0);
}
top = m->top;
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);
/* Allocate a montgomery context if it was not supplied by the caller.
* 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;
}
/* Get the window size to use with size of p. */
window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(OPENSSL_BN_ASM_MONT5)
if (window == 6 && bits <= 1024)
window = 5; /* ~5% improvement of 2048-bit RSA sign */
#endif
/* Allocate a buffer large enough to hold all of the pre-computed
* powers of am, am itself and tmp.
*/
numPowers = 1 << window;
powerbufLen = sizeof(m->d[0]) * (top * numPowers +
((2*top) > numPowers ? (2*top) : numPowers));
if ((powerbufFree = calloc(powerbufLen +
MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH, 1)) == NULL)
goto err;
powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
/* lay down tmp and am right after powers table */
tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
am.d = tmp.d + top;
tmp.top = am.top = 0;
tmp.dmax = am.dmax = top;
tmp.neg = am.neg = 0;
tmp.flags = am.flags = BN_FLG_STATIC_DATA;
/* prepare a^0 in Montgomery domain */
#if 1
if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
goto err;
#else
tmp.d[0] = (0 - m - >d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
for (i = 1; i < top; i++)
tmp.d[i] = (~m->d[i]) & BN_MASK2;
tmp.top = top;
#endif
/* prepare a^1 in Montgomery domain */
if (a->neg || BN_ucmp(a, m) >= 0) {
if (!BN_mod_ct(&am, a,m, ctx))
goto err;
if (!BN_to_montgomery(&am, &am, mont, ctx))
goto err;
} else if (!BN_to_montgomery(&am, a,mont, ctx))
goto err;
#if defined(OPENSSL_BN_ASM_MONT5)
/* This optimization uses ideas from http://eprint.iacr.org/2011/239,
* specifically optimization of cache-timing attack countermeasures
* and pre-computation optimization. */
/* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
* 512-bit RSA is hardly relevant, we omit it to spare size... */
if (window == 5 && top > 1) {
void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
const void *table, const BN_ULONG *np,
const BN_ULONG *n0, int num, int power);
void bn_scatter5(const BN_ULONG *inp, size_t num,
void *table, size_t power);
void bn_gather5(BN_ULONG *out, size_t num,
void *table, size_t power);
BN_ULONG *np = mont->N.d, *n0 = mont->n0;
/* BN_to_montgomery can contaminate words above .top
* [in BN_DEBUG[_DEBUG] build]... */
for (i = am.top; i < top; i++)
am.d[i] = 0;
for (i = tmp.top; i < top; i++)
tmp.d[i] = 0;
bn_scatter5(tmp.d, top, powerbuf, 0);
bn_scatter5(am.d, am.top, powerbuf, 1);
bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, 2);
#if 0
for (i = 3; i < 32; i++) {
/* Calculate a^i = a^(i-1) * a */
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
}
#else
/* same as above, but uses squaring for 1/2 of operations */
for (i = 4; i < 32; i*=2) {
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, i);
}
for (i = 3; i < 8; i += 2) {
int j;
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
for (j = 2 * i; j < 32; j *= 2) {
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, j);
}
}
for (; i < 16; i += 2) {
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, 2*i);
}
for (; i < 32; i += 2) {
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
}
#endif
bits--;
for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
bn_gather5(tmp.d, top, powerbuf, wvalue);
/* Scan the exponent one window at a time starting from the most
* significant bits.
*/
while (bits >= 0) {
for (wvalue = 0, i = 0; i < 5; i++, bits--)
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
}
tmp.top = top;
bn_correct_top(&tmp);
} else
#endif
{
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))
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);
}
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)
{
BN_MONT_CTX *mont = NULL;
int b, bits, ret = 0;
int r_is_one;
BN_ULONG w, next_w;
BIGNUM *d, *r, *t;
BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
(BN_mul_word(r, (w)) && \
(/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
(BN_mod_ct(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
/* BN_MOD_MUL_WORD is only used with 'w' large,
* so the BN_ucmp test is probably more overhead
* than always using BN_mod (which uses BN_copy if
* a similar test returns true). */
/* We can use BN_mod and do not need BN_nnmod because our
* accumulator is never negative (the result of BN_mod does
* not depend on the sign of the modulus).
*/
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m)) {
BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
return (0);
}
if (m->top == 1)
a %= m->d[0]; /* make sure that 'a' is reduced */
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;
}
if (a == 0) {
BN_zero(rr);
ret = 1;
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 ((t = BN_CTX_get(ctx)) == NULL)
goto err;
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;
}
r_is_one = 1; /* except for Montgomery factor */
/* bits-1 >= 0 */
/* The result is accumulated in the product r*w. */
w = a; /* bit 'bits-1' of 'p' is always set */
for (b = bits - 2; b >= 0; b--) {
/* First, square r*w. */
next_w = w * w;
if ((next_w / w) != w) /* overflow */
{
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
next_w = 1;
}
w = next_w;
if (!r_is_one) {
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
goto err;
}
/* Second, multiply r*w by 'a' if exponent bit is set. */
if (BN_is_bit_set(p, b)) {
next_w = w * a;
if ((next_w / a) != w) /* overflow */
{
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
next_w = a;
}
w = next_w;
}
}
/* Finally, set r:=r*w. */
if (w != 1) {
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
}
if (r_is_one) /* can happen only if a == 1*/
{
if (!BN_one(rr))
goto err;
} else {
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);
bn_check_top(rr);
return (ret);
}
/* The old fallback, simple version :-) */
int
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 *d;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1 is still zero. */
if (BN_is_one(m)) {
ret = 1;
BN_zero(r);
} else
ret = BN_one(r);
return ret;
}
BN_CTX_start(ctx);
if ((d = 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))
goto err; /* 1 */
if (BN_is_zero(val[0])) {
BN_zero(r);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
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(val[i], val[i - 1], d,m, 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_one(r))
goto err;
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start)
if (!BN_mod_mul(r, r, r, m, 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(r, r, r, m, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul(r, r, val[wvalue >> 1], m, 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_check_top(r);
return (ret);
}
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