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/* crypto/bn/bn_recp.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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#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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void BN_RECP_CTX_init(BN_RECP_CTX *recp) |
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{ |
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BN_init(&(recp->N)); |
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BN_init(&(recp->Nr)); |
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recp->num_bits = 0; |
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recp->flags = 0; |
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} |
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|
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BN_RECP_CTX *BN_RECP_CTX_new(void) |
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{ |
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BN_RECP_CTX *ret; |
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|
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if ((ret = (BN_RECP_CTX *)OPENSSL_malloc(sizeof(BN_RECP_CTX))) == NULL) |
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return (NULL); |
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|
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BN_RECP_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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|
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void BN_RECP_CTX_free(BN_RECP_CTX *recp) |
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{ |
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if (recp == NULL) |
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return; |
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|
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BN_free(&(recp->N)); |
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BN_free(&(recp->Nr)); |
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if (recp->flags & BN_FLG_MALLOCED) |
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OPENSSL_free(recp); |
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} |
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|
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int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) |
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{ |
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if (!BN_copy(&(recp->N), d)) |
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return 0; |
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BN_zero(&(recp->Nr)); |
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recp->num_bits = BN_num_bits(d); |
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recp->shift = 0; |
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return (1); |
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} |
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|
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int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, |
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BN_RECP_CTX *recp, BN_CTX *ctx) |
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{ |
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int ret = 0; |
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BIGNUM *a; |
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const BIGNUM *ca; |
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|
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BN_CTX_start(ctx); |
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if ((a = BN_CTX_get(ctx)) == NULL) |
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goto err; |
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if (y != NULL) { |
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if (x == y) { |
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if (!BN_sqr(a, x, ctx)) |
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goto err; |
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} else { |
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if (!BN_mul(a, x, y, ctx)) |
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goto err; |
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} |
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ca = a; |
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} else |
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ca = x; /* Just do the mod */ |
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|
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ret = BN_div_recp(NULL, r, ca, recp, ctx); |
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err: |
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BN_CTX_end(ctx); |
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bn_check_top(r); |
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return (ret); |
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} |
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|
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int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, |
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BN_RECP_CTX *recp, BN_CTX *ctx) |
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{ |
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int i, j, ret = 0; |
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BIGNUM *a, *b, *d, *r; |
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|
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BN_CTX_start(ctx); |
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a = BN_CTX_get(ctx); |
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b = BN_CTX_get(ctx); |
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if (dv != NULL) |
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d = dv; |
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else |
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d = BN_CTX_get(ctx); |
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if (rem != NULL) |
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r = rem; |
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else |
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r = BN_CTX_get(ctx); |
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if (a == NULL || b == NULL || d == NULL || r == NULL) |
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goto err; |
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|
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if (BN_ucmp(m, &(recp->N)) < 0) { |
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BN_zero(d); |
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if (!BN_copy(r, m)) { |
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BN_CTX_end(ctx); |
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return 0; |
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} |
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BN_CTX_end(ctx); |
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return (1); |
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} |
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|
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/* |
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* We want the remainder Given input of ABCDEF / ab we need multiply |
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* ABCDEF by 3 digests of the reciprocal of ab |
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*/ |
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|
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/* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */ |
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i = BN_num_bits(m); |
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j = recp->num_bits << 1; |
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if (j > i) |
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i = j; |
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|
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/* Nr := round(2^i / N) */ |
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if (i != recp->shift) |
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recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx); |
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/* BN_reciprocal could have returned -1 for an error */ |
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if (recp->shift == -1) |
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goto err; |
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|
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/*- |
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* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))| |
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* = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))| |
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* <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| |
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* = |m/N| |
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*/ |
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if (!BN_rshift(a, m, recp->num_bits)) |
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goto err; |
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if (!BN_mul(b, a, &(recp->Nr), ctx)) |
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goto err; |
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if (!BN_rshift(d, b, i - recp->num_bits)) |
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goto err; |
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d->neg = 0; |
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|
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if (!BN_mul(b, &(recp->N), d, ctx)) |
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goto err; |
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if (!BN_usub(r, m, b)) |
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goto err; |
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r->neg = 0; |
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|
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#if 1 |
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j = 0; |
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while (BN_ucmp(r, &(recp->N)) >= 0) { |
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if (j++ > 2) { |
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BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL); |
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goto err; |
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} |
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if (!BN_usub(r, r, &(recp->N))) |
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goto err; |
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if (!BN_add_word(d, 1)) |
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goto err; |
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} |
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#endif |
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|
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r->neg = BN_is_zero(r) ? 0 : m->neg; |
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d->neg = m->neg ^ recp->N.neg; |
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ret = 1; |
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err: |
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BN_CTX_end(ctx); |
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bn_check_top(dv); |
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bn_check_top(rem); |
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return (ret); |
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} |
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|
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/* |
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* len is the expected size of the result We actually calculate with an extra |
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* word of precision, so we can do faster division if the remainder is not |
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* required. |
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*/ |
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/* r := 2^len / m */ |
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int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) |
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{ |
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int ret = -1; |
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BIGNUM *t; |
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|
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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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|
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if (!BN_set_bit(t, len)) |
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goto err; |
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|
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if (!BN_div(r, NULL, t, m, ctx)) |
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goto err; |
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|
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ret = len; |
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err: |
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bn_check_top(r); |
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BN_CTX_end(ctx); |
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return (ret); |
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} |