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/* 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) 1998-2006 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 <openssl/bn.h>
#include <assert.h>
#include <string.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/thread.h>
#include <openssl/type_check.h>
#include "internal.h"
#include "../../internal.h"
#if !defined(OPENSSL_NO_ASM) && \
(defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
#define OPENSSL_BN_ASM_MONT
#endif
static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
const BIGNUM *b,
const BN_MONT_CTX *mont, BN_CTX *ctx);
BN_MONT_CTX *BN_MONT_CTX_new(void) {
BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
if (ret == NULL) {
return NULL;
}
OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX));
BN_init(&ret->RR);
BN_init(&ret->N);
return ret;
}
void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
if (mont == NULL) {
return;
}
BN_free(&mont->RR);
BN_free(&mont->N);
OPENSSL_free(mont);
}
BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
if (to == from) {
return to;
}
if (!BN_copy(&to->RR, &from->RR) ||
!BN_copy(&to->N, &from->N)) {
return NULL;
}
to->n0[0] = from->n0[0];
to->n0[1] = from->n0[1];
return to;
}
OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2,
BN_MONT_CTX_N0_LIMBS_VALUE_INVALID);
OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS ==
sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch);
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
if (BN_is_zero(mod)) {
OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
return 0;
}
if (!BN_is_odd(mod)) {
OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
return 0;
}
if (BN_is_negative(mod)) {
OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
return 0;
}
// Save the modulus.
if (!BN_copy(&mont->N, mod)) {
OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
return 0;
}
// Find n0 such that n0 * N == -1 (mod r).
//
// Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the
// others, we could use a shorter R value and use faster |BN_ULONG|-based
// math instead of |uint64_t|-based math, which would be double-precision.
// However, currently only the assembler files know which is which.
uint64_t n0 = bn_mont_n0(mod);
mont->n0[0] = (BN_ULONG)n0;
#if BN_MONT_CTX_N0_LIMBS == 2
mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2);
#else
mont->n0[1] = 0;
#endif
// Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R
// > mod. Even though the assembly on some 32-bit platforms works with 64-bit
// values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS *
// BN_BITS2|, is correct because R**2 will still be a multiple of the latter
// as |BN_MONT_CTX_N0_LIMBS| is either one or two.
//
// XXX: This is not constant time with respect to |mont->N|, but it should be.
unsigned lgBigR = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
if (!bn_mod_exp_base_2_vartime(&mont->RR, lgBigR * 2, &mont->N)) {
return 0;
}
return 1;
}
int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
const BIGNUM *mod, BN_CTX *bn_ctx) {
CRYPTO_MUTEX_lock_read(lock);
BN_MONT_CTX *ctx = *pmont;
CRYPTO_MUTEX_unlock_read(lock);
if (ctx) {
return 1;
}
CRYPTO_MUTEX_lock_write(lock);
ctx = *pmont;
if (ctx) {
goto out;
}
ctx = BN_MONT_CTX_new();
if (ctx == NULL) {
goto out;
}
if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) {
BN_MONT_CTX_free(ctx);
ctx = NULL;
goto out;
}
*pmont = ctx;
out:
CRYPTO_MUTEX_unlock_write(lock);
return ctx != NULL;
}
int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
BN_CTX *ctx) {
return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
}
static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a,
size_t num_a, const BN_MONT_CTX *mont) {
const BN_ULONG *n = mont->N.d;
size_t num_n = mont->N.top;
if (num_r != num_n || num_a != 2 * num_n) {
OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
// Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
// input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
// includes |carry| which is stored separately.
BN_ULONG n0 = mont->n0[0];
BN_ULONG carry = 0;
for (size_t i = 0; i < num_n; i++) {
BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0);
v += carry + a[i + num_n];
carry |= (v != a[i + num_n]);
carry &= (v <= a[i + num_n]);
a[i + num_n] = v;
}
// Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a|
// includes |carry| which is stored separately.
a += num_n;
// |a| thus requires at most one additional subtraction |n| to be reduced.
// Subtract |n| and select the answer in constant time.
OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
crypto_word_t_too_small);
BN_ULONG v = bn_sub_words(r, a, n, num_n) - carry;
// |v| is one if |a| - |n| underflowed or zero if it did not. Note |v| cannot
// be -1. That would imply the subtraction did not fit in |num_n| words, and
// we know at most one subtraction is needed.
v = 0u - v;
for (size_t i = 0; i < num_n; i++) {
r[i] = constant_time_select_w(v, a[i], r[i]);
a[i] = 0;
}
return 1;
}
static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
const BN_MONT_CTX *mont) {
const BIGNUM *n = &mont->N;
if (n->top == 0) {
ret->top = 0;
return 1;
}
int max = (2 * n->top); // carry is stored separately
if (!bn_wexpand(r, max) ||
!bn_wexpand(ret, n->top)) {
return 0;
}
// Clear the top words of |r|.
if (max > r->top) {
OPENSSL_memset(r->d + r->top, 0, (max - r->top) * sizeof(BN_ULONG));
}
r->top = max;
ret->top = n->top;
if (!bn_from_montgomery_in_place(ret->d, ret->top, r->d, r->top, mont)) {
return 0;
}
ret->neg = r->neg;
bn_correct_top(r);
bn_correct_top(ret);
return 1;
}
int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont,
BN_CTX *ctx) {
int ret = 0;
BIGNUM *t;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
if (t == NULL ||
!BN_copy(t, a)) {
goto err;
}
ret = BN_from_montgomery_word(r, t, mont);
err:
BN_CTX_end(ctx);
return ret;
}
int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BN_MONT_CTX *mont, BN_CTX *ctx) {
#if !defined(OPENSSL_BN_ASM_MONT)
return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
#else
int num = mont->N.top;
// |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
if (num < (128 / BN_BITS2) ||
a->top != num ||
b->top != num) {
return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
}
if (!bn_wexpand(r, num)) {
return 0;
}
if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
// The check above ensures this won't happen.
assert(0);
OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
return 0;
}
r->neg = a->neg ^ b->neg;
r->top = num;
bn_correct_top(r);
return 1;
#endif
}
static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
const BIGNUM *b,
const BN_MONT_CTX *mont,
BN_CTX *ctx) {
int ret = 0;
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
if (tmp == NULL) {
goto err;
}
if (a == b) {
if (!BN_sqr(tmp, a, ctx)) {
goto err;
}
} else {
if (!BN_mul(tmp, a, b, ctx)) {
goto err;
}
}
// reduce from aRR to aR
if (!BN_from_montgomery_word(r, tmp, mont)) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}