437 lines
14 KiB
C
437 lines
14 KiB
C
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/* crypto/bn/bn_mod.c */
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/*
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* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
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* for the OpenSSL project.
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*/
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/* ====================================================================
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* Copyright (c) 1998-2018 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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#include "cryptlib.h"
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#include "bn_lcl.h"
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#if 0 /* now just a #define */
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int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
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{
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return (BN_div(NULL, rem, m, d, ctx));
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/* note that rem->neg == m->neg (unless the remainder is zero) */
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}
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#endif
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int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
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{
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/*
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* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
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* always holds)
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*/
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if (!(BN_mod(r, m, d, ctx)))
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return 0;
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if (!r->neg)
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return 1;
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/* now -|d| < r < 0, so we have to set r := r + |d| */
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return (d->neg ? BN_sub : BN_add) (r, r, d);
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}
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int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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if (!BN_add(r, a, b))
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return 0;
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return BN_nnmod(r, r, m, ctx);
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}
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/*
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* BN_mod_add variant that may be used if both a and b are non-negative and
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* less than m. The original algorithm was
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*
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* if (!BN_uadd(r, a, b))
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* return 0;
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* if (BN_ucmp(r, m) >= 0)
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* return BN_usub(r, r, m);
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*
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* which is replaced with addition, subtracting modulus, and conditional
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* move depending on whether or not subtraction borrowed.
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*/
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int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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size_t i, ai, bi, mtop = m->top;
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BN_ULONG storage[1024 / BN_BITS2];
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BN_ULONG carry, temp, mask, *rp, *tp = storage;
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const BN_ULONG *ap, *bp;
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if (bn_wexpand(r, m->top) == NULL)
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return 0;
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if (mtop > sizeof(storage) / sizeof(storage[0])
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&& (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
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return 0;
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ap = a->d != NULL ? a->d : tp;
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bp = b->d != NULL ? b->d : tp;
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for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
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mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
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temp = ((ap[ai] & mask) + carry) & BN_MASK2;
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carry = (temp < carry);
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mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
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tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
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carry += (tp[i] < temp);
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i++;
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ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
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bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
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}
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rp = r->d;
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carry -= bn_sub_words(rp, tp, m->d, mtop);
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for (i = 0; i < mtop; i++) {
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rp[i] = (carry & tp[i]) | (~carry & rp[i]);
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((volatile BN_ULONG *)tp)[i] = 0;
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}
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r->top = mtop;
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r->flags |= BN_FLG_FIXED_TOP;
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r->neg = 0;
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if (tp != storage)
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OPENSSL_free(tp);
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return 1;
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}
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int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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int ret = bn_mod_add_fixed_top(r, a, b, m);
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if (ret)
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bn_correct_top(r);
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return ret;
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}
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int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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if (!BN_sub(r, a, b))
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return 0;
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return BN_nnmod(r, r, m, ctx);
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}
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/*
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* BN_mod_sub variant that may be used if both a and b are non-negative,
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* a is less than m, while b is of same bit width as m. It's implemented
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* as subtraction followed by two conditional additions.
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*
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* 0 <= a < m
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* 0 <= b < 2^w < 2*m
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*
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* after subtraction
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*
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* -2*m < r = a - b < m
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*
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* Thus it takes up to two conditional additions to make |r| positive.
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*/
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int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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size_t i, ai, bi, mtop = m->top;
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BN_ULONG borrow, carry, ta, tb, mask, *rp;
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const BN_ULONG *ap, *bp;
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if (bn_wexpand(r, m->top) == NULL)
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return 0;
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rp = r->d;
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ap = a->d != NULL ? a->d : rp;
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bp = b->d != NULL ? b->d : rp;
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for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
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mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
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ta = ap[ai] & mask;
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mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
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tb = bp[bi] & mask;
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rp[i] = ta - tb - borrow;
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if (ta != tb)
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borrow = (ta < tb);
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i++;
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ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
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bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
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}
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ap = m->d;
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for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
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ta = ((ap[i] & mask) + carry) & BN_MASK2;
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carry = (ta < carry);
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rp[i] = (rp[i] + ta) & BN_MASK2;
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carry += (rp[i] < ta);
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}
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borrow -= carry;
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for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
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ta = ((ap[i] & mask) + carry) & BN_MASK2;
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carry = (ta < carry);
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rp[i] = (rp[i] + ta) & BN_MASK2;
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carry += (rp[i] < ta);
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}
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r->top = mtop;
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r->flags |= BN_FLG_FIXED_TOP;
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r->neg = 0;
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return 1;
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}
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/*
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* BN_mod_sub variant that may be used if both a and b are non-negative and
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* less than m
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*/
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int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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if (!BN_sub(r, a, b))
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return 0;
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if (r->neg)
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return BN_add(r, r, m);
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return 1;
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}
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/* slow but works */
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int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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BIGNUM *t;
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int ret = 0;
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bn_check_top(a);
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bn_check_top(b);
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bn_check_top(m);
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BN_CTX_start(ctx);
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if ((t = BN_CTX_get(ctx)) == NULL)
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goto err;
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if (a == b) {
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if (!BN_sqr(t, a, ctx))
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goto err;
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} else {
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if (!BN_mul(t, a, b, ctx))
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goto err;
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}
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if (!BN_nnmod(r, t, m, ctx))
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goto err;
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bn_check_top(r);
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return (ret);
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}
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int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
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{
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if (!BN_sqr(r, a, ctx))
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return 0;
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/* r->neg == 0, thus we don't need BN_nnmod */
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return BN_mod(r, r, m, ctx);
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}
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int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
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{
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if (!BN_lshift1(r, a))
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return 0;
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bn_check_top(r);
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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;
|
||
|
|
}
|