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558 lines
17 KiB
558 lines
17 KiB
/* 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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/* |
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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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|
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#define MONT_WORD /* use the faster word-based algorithm */ |
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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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#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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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if (BN_is_zero(mod)) |
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return 0; |
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|
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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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|
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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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|
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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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|
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mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; |
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|
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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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|
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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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|
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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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|
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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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|
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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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*/ |
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if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) |
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goto err; |
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} |
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#endif |
|
|
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/* setup RR for conversions */ |
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BN_zero(&(mont->RR)); |
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if (!BN_set_bit(&(mont->RR), mont->ri * 2)) |
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goto err; |
|
if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) |
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goto err; |
|
|
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ret = 1; |
|
err: |
|
BN_CTX_end(ctx); |
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return ret; |
|
} |
|
|
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BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) |
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{ |
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if (to == from) |
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return (to); |
|
|
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if (!BN_copy(&(to->RR), &(from->RR))) |
|
return NULL; |
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if (!BN_copy(&(to->N), &(from->N))) |
|
return NULL; |
|
if (!BN_copy(&(to->Ni), &(from->Ni))) |
|
return NULL; |
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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; |
|
}
|
|
|