558 lines
17 KiB
C
558 lines
17 KiB
C
/* crypto/bn/bn_mont.c */
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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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/* ====================================================================
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* Copyright (c) 1998-2006 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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/*
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* Details about Montgomery multiplication algorithms can be found at
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* http://security.ece.orst.edu/publications.html, e.g.
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* http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
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* sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
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*/
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#include <stdio.h>
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#include "cryptlib.h"
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#include "bn_lcl.h"
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#define MONT_WORD /* use the faster word-based algorithm */
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#ifdef MONT_WORD
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static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
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#endif
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int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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BN_MONT_CTX *mont, BN_CTX *ctx)
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{
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BIGNUM *tmp;
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int ret = 0;
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#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
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int num = mont->N.top;
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if (num > 1 && a->top == num && b->top == num) {
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if (bn_wexpand(r, num) == NULL)
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return (0);
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if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
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r->neg = a->neg ^ b->neg;
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r->top = num;
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bn_correct_top(r);
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return (1);
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}
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}
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#endif
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BN_CTX_start(ctx);
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tmp = BN_CTX_get(ctx);
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if (tmp == NULL)
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goto err;
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bn_check_top(tmp);
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if (a == b) {
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if (!BN_sqr(tmp, a, ctx))
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goto err;
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} else {
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if (!BN_mul(tmp, a, b, ctx))
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goto err;
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}
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/* reduce from aRR to aR */
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#ifdef MONT_WORD
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if (!BN_from_montgomery_word(r, tmp, mont))
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goto err;
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#else
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if (!BN_from_montgomery(r, tmp, mont, ctx))
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goto err;
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#endif
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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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#ifdef MONT_WORD
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static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
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{
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BIGNUM *n;
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BN_ULONG *ap, *np, *rp, n0, v, carry;
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int nl, max, i;
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n = &(mont->N);
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nl = n->top;
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if (nl == 0) {
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ret->top = 0;
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return (1);
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}
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max = (2 * nl); /* carry is stored separately */
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if (bn_wexpand(r, max) == NULL)
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return (0);
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r->neg ^= n->neg;
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np = n->d;
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rp = r->d;
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/* clear the top words of T */
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# if 1
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for (i = r->top; i < max; i++) /* memset? XXX */
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rp[i] = 0;
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# else
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memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
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# endif
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r->top = max;
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n0 = mont->n0[0];
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# ifdef BN_COUNT
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fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
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# endif
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for (carry = 0, i = 0; i < nl; i++, rp++) {
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# ifdef __TANDEM
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{
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long long t1;
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long long t2;
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long long t3;
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t1 = rp[0] * (n0 & 0177777);
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t2 = 037777600000l;
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t2 = n0 & t2;
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t3 = rp[0] & 0177777;
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t2 = (t3 * t2) & BN_MASK2;
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t1 = t1 + t2;
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v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
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}
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# else
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v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
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# endif
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v = (v + carry + rp[nl]) & BN_MASK2;
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carry |= (v != rp[nl]);
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carry &= (v <= rp[nl]);
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rp[nl] = v;
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}
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if (bn_wexpand(ret, nl) == NULL)
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return (0);
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ret->top = nl;
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ret->neg = r->neg;
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rp = ret->d;
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ap = &(r->d[nl]);
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# define BRANCH_FREE 1
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# if BRANCH_FREE
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{
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BN_ULONG *nrp;
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size_t m;
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v = bn_sub_words(rp, ap, np, nl) - carry;
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/*
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* if subtraction result is real, then trick unconditional memcpy
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* below to perform in-place "refresh" instead of actual copy.
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*/
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m = (0 - (size_t)v);
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nrp =
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(BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
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for (i = 0, nl -= 4; i < nl; i += 4) {
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BN_ULONG t1, t2, t3, t4;
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t1 = nrp[i + 0];
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t2 = nrp[i + 1];
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t3 = nrp[i + 2];
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ap[i + 0] = 0;
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t4 = nrp[i + 3];
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ap[i + 1] = 0;
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rp[i + 0] = t1;
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ap[i + 2] = 0;
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rp[i + 1] = t2;
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ap[i + 3] = 0;
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rp[i + 2] = t3;
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rp[i + 3] = t4;
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}
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for (nl += 4; i < nl; i++)
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rp[i] = nrp[i], ap[i] = 0;
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}
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# else
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if (bn_sub_words(rp, ap, np, nl) - carry)
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memcpy(rp, ap, nl * sizeof(BN_ULONG));
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# endif
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bn_correct_top(r);
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bn_correct_top(ret);
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bn_check_top(ret);
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return (1);
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}
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#endif /* MONT_WORD */
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int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx)
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{
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int retn = 0;
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#ifdef MONT_WORD
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BIGNUM *t;
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BN_CTX_start(ctx);
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if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
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retn = BN_from_montgomery_word(ret, t, mont);
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BN_CTX_end(ctx);
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#else /* !MONT_WORD */
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BIGNUM *t1, *t2;
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BN_CTX_start(ctx);
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t1 = BN_CTX_get(ctx);
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t2 = BN_CTX_get(ctx);
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if (t1 == NULL || t2 == NULL)
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goto err;
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if (!BN_copy(t1, a))
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goto err;
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BN_mask_bits(t1, mont->ri);
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if (!BN_mul(t2, t1, &mont->Ni, ctx))
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goto err;
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BN_mask_bits(t2, mont->ri);
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if (!BN_mul(t1, t2, &mont->N, ctx))
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goto err;
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if (!BN_add(t2, a, t1))
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goto err;
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if (!BN_rshift(ret, t2, mont->ri))
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goto err;
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if (BN_ucmp(ret, &(mont->N)) >= 0) {
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if (!BN_usub(ret, ret, &(mont->N)))
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goto err;
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}
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retn = 1;
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bn_check_top(ret);
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err:
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BN_CTX_end(ctx);
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#endif /* MONT_WORD */
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return (retn);
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}
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BN_MONT_CTX *BN_MONT_CTX_new(void)
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{
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BN_MONT_CTX *ret;
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if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
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return (NULL);
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BN_MONT_CTX_init(ret);
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ret->flags = BN_FLG_MALLOCED;
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return (ret);
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}
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void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
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{
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ctx->ri = 0;
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BN_init(&(ctx->RR));
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BN_init(&(ctx->N));
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BN_init(&(ctx->Ni));
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ctx->n0[0] = ctx->n0[1] = 0;
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ctx->flags = 0;
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}
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void BN_MONT_CTX_free(BN_MONT_CTX *mont)
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{
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if (mont == NULL)
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return;
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BN_clear_free(&(mont->RR));
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BN_clear_free(&(mont->N));
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BN_clear_free(&(mont->Ni));
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if (mont->flags & BN_FLG_MALLOCED)
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OPENSSL_free(mont);
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}
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int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
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{
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int ret = 0;
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BIGNUM *Ri, *R;
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if (BN_is_zero(mod))
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return 0;
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BN_CTX_start(ctx);
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if ((Ri = BN_CTX_get(ctx)) == NULL)
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goto err;
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R = &(mont->RR); /* grab RR as a temp */
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if (!BN_copy(&(mont->N), mod))
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goto err; /* Set N */
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mont->N.neg = 0;
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#ifdef MONT_WORD
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{
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BIGNUM tmod;
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BN_ULONG buf[2];
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BN_init(&tmod);
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tmod.d = buf;
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tmod.dmax = 2;
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tmod.neg = 0;
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mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
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# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
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/*
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* Only certain BN_BITS2<=32 platforms actually make use of n0[1],
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* and we could use the #else case (with a shorter R value) for the
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* others. However, currently only the assembler files do know which
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* is which.
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*/
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BN_zero(R);
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if (!(BN_set_bit(R, 2 * BN_BITS2)))
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goto err;
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tmod.top = 0;
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if ((buf[0] = mod->d[0]))
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tmod.top = 1;
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if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
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tmod.top = 2;
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if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
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goto err; /* R*Ri */
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if (!BN_is_zero(Ri)) {
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if (!BN_sub_word(Ri, 1))
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goto err;
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} else { /* if N mod word size == 1 */
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if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
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goto err;
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/* Ri-- (mod double word size) */
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Ri->neg = 0;
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Ri->d[0] = BN_MASK2;
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Ri->d[1] = BN_MASK2;
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Ri->top = 2;
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}
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if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
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goto err;
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/*
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* Ni = (R*Ri-1)/N, keep only couple of least significant words:
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*/
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mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
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mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
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# else
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BN_zero(R);
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if (!(BN_set_bit(R, BN_BITS2)))
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goto err; /* R */
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buf[0] = mod->d[0]; /* tmod = N mod word size */
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buf[1] = 0;
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tmod.top = buf[0] != 0 ? 1 : 0;
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/* Ri = R^-1 mod N */
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if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, BN_BITS2))
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goto err; /* R*Ri */
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if (!BN_is_zero(Ri)) {
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if (!BN_sub_word(Ri, 1))
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goto err;
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} else { /* if N mod word size == 1 */
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if (!BN_set_word(Ri, BN_MASK2))
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goto err; /* Ri-- (mod word size) */
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}
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if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
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goto err;
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/*
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* Ni = (R*Ri-1)/N, keep only least significant word:
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*/
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mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
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mont->n0[1] = 0;
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# endif
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}
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#else /* !MONT_WORD */
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{ /* bignum version */
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mont->ri = BN_num_bits(&mont->N);
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BN_zero(R);
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if (!BN_set_bit(R, mont->ri))
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goto err; /* R = 2^ri */
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/* Ri = R^-1 mod N */
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if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, mont->ri))
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goto err; /* R*Ri */
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if (!BN_sub_word(Ri, 1))
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goto err;
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/*
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* Ni = (R*Ri-1) / N
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|
*/
|
|
if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
|
|
goto err;
|
|
}
|
|
#endif
|
|
|
|
/* setup RR for conversions */
|
|
BN_zero(&(mont->RR));
|
|
if (!BN_set_bit(&(mont->RR), mont->ri * 2))
|
|
goto err;
|
|
if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
|
|
goto err;
|
|
|
|
ret = 1;
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
|
|
{
|
|
if (to == from)
|
|
return (to);
|
|
|
|
if (!BN_copy(&(to->RR), &(from->RR)))
|
|
return NULL;
|
|
if (!BN_copy(&(to->N), &(from->N)))
|
|
return NULL;
|
|
if (!BN_copy(&(to->Ni), &(from->Ni)))
|
|
return NULL;
|
|
to->ri = from->ri;
|
|
to->n0[0] = from->n0[0];
|
|
to->n0[1] = from->n0[1];
|
|
return (to);
|
|
}
|
|
|
|
BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
|
|
const BIGNUM *mod, BN_CTX *ctx)
|
|
{
|
|
BN_MONT_CTX *ret;
|
|
|
|
CRYPTO_r_lock(lock);
|
|
ret = *pmont;
|
|
CRYPTO_r_unlock(lock);
|
|
if (ret)
|
|
return ret;
|
|
|
|
/*
|
|
* We don't want to serialise globally while doing our lazy-init math in
|
|
* BN_MONT_CTX_set. That punishes threads that are doing independent
|
|
* things. Instead, punish the case where more than one thread tries to
|
|
* lazy-init the same 'pmont', by having each do the lazy-init math work
|
|
* independently and only use the one from the thread that wins the race
|
|
* (the losers throw away the work they've done).
|
|
*/
|
|
ret = BN_MONT_CTX_new();
|
|
if (!ret)
|
|
return NULL;
|
|
if (!BN_MONT_CTX_set(ret, mod, ctx)) {
|
|
BN_MONT_CTX_free(ret);
|
|
return NULL;
|
|
}
|
|
|
|
/* The locked compare-and-set, after the local work is done. */
|
|
CRYPTO_w_lock(lock);
|
|
if (*pmont) {
|
|
BN_MONT_CTX_free(ret);
|
|
ret = *pmont;
|
|
} else
|
|
*pmont = ret;
|
|
CRYPTO_w_unlock(lock);
|
|
return ret;
|
|
}
|