openssl1.0/crypto/bn/bn_mod.c

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/* crypto/bn/bn_mod.c */
/*
* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
* for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2018 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).
*
*/
/* 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.]
*/
#include "cryptlib.h"
#include "bn_lcl.h"
#if 0 /* now just a #define */
int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
{
return (BN_div(NULL, rem, m, d, ctx));
/* note that rem->neg == m->neg (unless the remainder is zero) */
}
#endif
int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
{
/*
* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
* always holds)
*/
if (!(BN_mod(r, m, d, ctx)))
return 0;
if (!r->neg)
return 1;
/* now -|d| < r < 0, so we have to set r := r + |d| */
return (d->neg ? BN_sub : BN_add) (r, r, d);
}
int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx)
{
if (!BN_add(r, a, b))
return 0;
return BN_nnmod(r, r, m, ctx);
}
/*
* BN_mod_add variant that may be used if both a and b are non-negative and
* less than m. The original algorithm was
*
* if (!BN_uadd(r, a, b))
* return 0;
* if (BN_ucmp(r, m) >= 0)
* return BN_usub(r, r, m);
*
* which is replaced with addition, subtracting modulus, and conditional
* move depending on whether or not subtraction borrowed.
*/
int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m)
{
size_t i, ai, bi, mtop = m->top;
BN_ULONG storage[1024 / BN_BITS2];
BN_ULONG carry, temp, mask, *rp, *tp = storage;
const BN_ULONG *ap, *bp;
if (bn_wexpand(r, m->top) == NULL)
return 0;
if (mtop > sizeof(storage) / sizeof(storage[0])
&& (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
return 0;
ap = a->d != NULL ? a->d : tp;
bp = b->d != NULL ? b->d : tp;
for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
temp = ((ap[ai] & mask) + carry) & BN_MASK2;
carry = (temp < carry);
mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
carry += (tp[i] < temp);
i++;
ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
}
rp = r->d;
carry -= bn_sub_words(rp, tp, m->d, mtop);
for (i = 0; i < mtop; i++) {
rp[i] = (carry & tp[i]) | (~carry & rp[i]);
((volatile BN_ULONG *)tp)[i] = 0;
}
r->top = mtop;
r->flags |= BN_FLG_FIXED_TOP;
r->neg = 0;
if (tp != storage)
OPENSSL_free(tp);
return 1;
}
int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m)
{
int ret = bn_mod_add_fixed_top(r, a, b, m);
if (ret)
bn_correct_top(r);
return ret;
}
int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx)
{
if (!BN_sub(r, a, b))
return 0;
return BN_nnmod(r, r, m, ctx);
}
/*
* BN_mod_sub variant that may be used if both a and b are non-negative,
* a is less than m, while b is of same bit width as m. It's implemented
* as subtraction followed by two conditional additions.
*
* 0 <= a < m
* 0 <= b < 2^w < 2*m
*
* after subtraction
*
* -2*m < r = a - b < m
*
* Thus it takes up to two conditional additions to make |r| positive.
*/
int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m)
{
size_t i, ai, bi, mtop = m->top;
BN_ULONG borrow, carry, ta, tb, mask, *rp;
const BN_ULONG *ap, *bp;
if (bn_wexpand(r, m->top) == NULL)
return 0;
rp = r->d;
ap = a->d != NULL ? a->d : rp;
bp = b->d != NULL ? b->d : rp;
for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
ta = ap[ai] & mask;
mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
tb = bp[bi] & mask;
rp[i] = ta - tb - borrow;
if (ta != tb)
borrow = (ta < tb);
i++;
ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
}
ap = m->d;
for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
ta = ((ap[i] & mask) + carry) & BN_MASK2;
carry = (ta < carry);
rp[i] = (rp[i] + ta) & BN_MASK2;
carry += (rp[i] < ta);
}
borrow -= carry;
for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
ta = ((ap[i] & mask) + carry) & BN_MASK2;
carry = (ta < carry);
rp[i] = (rp[i] + ta) & BN_MASK2;
carry += (rp[i] < ta);
}
r->top = mtop;
r->flags |= BN_FLG_FIXED_TOP;
r->neg = 0;
return 1;
}
/*
* BN_mod_sub variant that may be used if both a and b are non-negative and
* less than m
*/
int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m)
{
if (!BN_sub(r, a, b))
return 0;
if (r->neg)
return BN_add(r, r, m);
return 1;
}
/* slow but works */
int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx)
{
BIGNUM *t;
int ret = 0;
bn_check_top(a);
bn_check_top(b);
bn_check_top(m);
BN_CTX_start(ctx);
if ((t = BN_CTX_get(ctx)) == NULL)
goto err;
if (a == b) {
if (!BN_sqr(t, a, ctx))
goto err;
} else {
if (!BN_mul(t, a, b, ctx))
goto err;
}
if (!BN_nnmod(r, t, m, ctx))
goto err;
bn_check_top(r);
ret = 1;
err:
BN_CTX_end(ctx);
return (ret);
}
int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
{
if (!BN_sqr(r, a, ctx))
return 0;
/* r->neg == 0, thus we don't need BN_nnmod */
return BN_mod(r, r, m, ctx);
}
int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
{
if (!BN_lshift1(r, a))
return 0;
bn_check_top(r);
return BN_nnmod(r, r, m, ctx);
}
/*
* BN_mod_lshift1 variant that may be used if a is non-negative and less than
* m
*/
int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
{
if (!BN_lshift1(r, a))
return 0;
bn_check_top(r);
if (BN_cmp(r, m) >= 0)
return BN_sub(r, r, m);
return 1;
}
int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
BN_CTX *ctx)
{
BIGNUM *abs_m = NULL;
int ret;
if (!BN_nnmod(r, a, m, ctx))
return 0;
if (m->neg) {
abs_m = BN_dup(m);
if (abs_m == NULL)
return 0;
abs_m->neg = 0;
}
ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
bn_check_top(r);
if (abs_m)
BN_free(abs_m);
return ret;
}
/*
* BN_mod_lshift variant that may be used if a is non-negative and less than
* m
*/
int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
{
if (r != a) {
if (BN_copy(r, a) == NULL)
return 0;
}
while (n > 0) {
int max_shift;
/* 0 < r < m */
max_shift = BN_num_bits(m) - BN_num_bits(r);
/* max_shift >= 0 */
if (max_shift < 0) {
BNerr(BN_F_BN_MOD_LSHIFT_QUICK, BN_R_INPUT_NOT_REDUCED);
return 0;
}
if (max_shift > n)
max_shift = n;
if (max_shift) {
if (!BN_lshift(r, r, max_shift))
return 0;
n -= max_shift;
} else {
if (!BN_lshift1(r, r))
return 0;
--n;
}
/* BN_num_bits(r) <= BN_num_bits(m) */
if (BN_cmp(r, m) >= 0) {
if (!BN_sub(r, r, m))
return 0;
}
}
bn_check_top(r);
return 1;
}