530 lines
15 KiB
C
Executable File
530 lines
15 KiB
C
Executable File
#include "bn.h"
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#ifndef WITH_LIBCRYPTO
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//FIXME Not checked on threadsafety yet; after checking please remove this line
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/* crypto/bn/bn_exp.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 license 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 license
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* [including the GNU Public License.]
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*/
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/* ====================================================================
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* Copyright (c) 1998-2000 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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#include <stdio.h>
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#include "bn_lcl.h"
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#define TABLE_SIZE 32
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/* slow but works */
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int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
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{
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BIGNUM *t;
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int r = 0;
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bn_check_top(a);
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bn_check_top(b);
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bn_check_top(m);
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BN_CTX_start(ctx);
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if((t = BN_CTX_get(ctx)) == NULL) { goto err; }
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if(a == b)
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{
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if(!BN_sqr(t, a, ctx)) { goto err; }
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}
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else
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{
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if(!BN_mul(t, a, b, ctx)) { goto err; }
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}
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if(!BN_mod(ret, t, m, ctx)) { goto err; }
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r = 1;
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err:
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BN_CTX_end(ctx);
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return (r);
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}
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int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
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BN_CTX *ctx)
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{
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int ret;
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bn_check_top(a);
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bn_check_top(p);
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bn_check_top(m);
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ret = BN_mod_exp_simple(r, a, p, m, ctx);
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return (ret);
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}
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/* The old fallback, simple version :-) */
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int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
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BN_CTX *ctx)
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{
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int i, j = 0, bits, ret = 0, wstart = 0, wend = 0, window, wvalue = 0, ts = 0;
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int start = 1;
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BIGNUM *d;
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BIGNUM val[TABLE_SIZE];
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bits = BN_num_bits(p);
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if(bits == 0)
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{
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BN_one(r);
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return (1);
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}
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BN_CTX_start(ctx);
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if((d = BN_CTX_get(ctx)) == NULL) { goto err; }
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BN_init(&(val[0]));
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ts = 1;
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if(!BN_mod(&(val[0]), a, m, ctx)) { goto err; } /* 1 */
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window = BN_window_bits_for_exponent_size(bits);
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if(window > 1)
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{
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if(!BN_mod_mul(d, &(val[0]), &(val[0]), m, ctx))
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{ goto err; } /* 2 */
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j = 1 << (window - 1);
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for(i = 1; i < j; i++)
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{
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BN_init(&(val[i]));
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if(!BN_mod_mul(&(val[i]), &(val[i - 1]), d, m, ctx))
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{ goto err; }
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}
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ts = i;
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}
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start = 1; /* This is used to avoid multiplication etc
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* when there is only the value '1' in the
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* buffer. */
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wstart = bits - 1; /* The top bit of the window */
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if(!BN_one(r)) { goto err; }
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for(;;)
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{
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if(BN_is_bit_set(p, wstart) == 0)
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{
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if(!start)
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if(!BN_mod_mul(r, r, r, m, ctx))
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{ goto err; }
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if(wstart == 0) { break; }
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wstart--;
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continue;
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}
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/* We now have wstart on a 'set' bit, we now need to work out
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* how bit a window to do. To do this we need to scan
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* forward until the last set bit before the end of the
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* window */
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j = wstart;
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wvalue = 1;
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wend = 0;
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for(i = 1; i < window; i++)
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{
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if(wstart - i < 0) { break; }
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if(BN_is_bit_set(p, wstart - i))
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{
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wvalue <<= (i - wend);
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wvalue |= 1;
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wend = i;
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}
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}
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/* wend is the size of the current window */
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j = wend + 1;
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/* add the 'bytes above' */
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if(!start)
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for(i = 0; i < j; i++)
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{
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if(!BN_mod_mul(r, r, r, m, ctx))
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{ goto err; }
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}
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/* wvalue will be an odd number < 2^window */
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if(!BN_mod_mul(r, r, &(val[wvalue >> 1]), m, ctx))
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{ goto err; }
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/* move the 'window' down further */
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wstart -= wend + 1;
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wvalue = 0;
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start = 0;
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if(wstart < 0) { break; }
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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for(i = 0; i < ts; i++)
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{ BN_clear_free(&(val[i])); }
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return (ret);
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}
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int
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BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
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{
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/* like BN_mod, but returns non-negative remainder
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* (i.e., 0 <= r < |d| always holds)
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*/
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if (!(BN_mod(r, m, d, ctx)))
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return 0;
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if (!r->neg)
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return 1;
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/* now -|d| < r < 0, so we have to set r : = r + |d| */
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return (d->neg ? BN_sub : BN_add)(r, r, d);
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}
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/* solves ax == 1 (mod n) */
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BIGNUM *
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BN_mod_inverse(BIGNUM *ret, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
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{
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BIGNUM *A, *B, *X, *Y, *M, *D, *T = NULL;
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int sign;
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bn_check_top(a);
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bn_check_top(n);
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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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X = BN_CTX_get(ctx);
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D = BN_CTX_get(ctx);
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M = BN_CTX_get(ctx);
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Y = BN_CTX_get(ctx);
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T = BN_CTX_get(ctx);
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if (T == NULL) goto err;
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if (ret == NULL) goto err;
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BN_one(X);
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BN_zero(Y);
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if (BN_copy(B, a) == NULL) goto err;
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if (BN_copy(A, n) == NULL) goto err;
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A->neg = 0;
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if (B->neg || (BN_ucmp(B, A) >= 0)) {
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if (!BN_nnmod(B, B, A, ctx)) goto err;
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}
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sign = -1;
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/* From B = a mod |n|, A = |n| it follows that
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*
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* 0 <= B < A,
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* -sign*X*a == B (mod |n|),
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* sign*Y*a == A (mod |n|).
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*/
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if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) {
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/* Binary inversion algorithm; requires odd modulus.
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* This is faster than the general algorithm if the modulus
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* is sufficiently small (about 400 .. 500 bits on 32-bit
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* sytems, but much more on 64-bit systems)
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*/
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int shift;
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while (!BN_is_zero(B)) {
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/*
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* 0 < B < |n|,
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* 0 < A <= |n|,
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* (1) -sign*X*a == B (mod |n|),
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* (2) sign*Y*a == A (mod |n|)
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*/
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/* Now divide B by the maximum possible power of two in the integers,
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* and divide X by the same value mod |n|.
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* When we're done, (1) still holds.
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*/
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shift = 0;
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while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ {
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shift++;
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if (BN_is_odd(X)) {
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if (!BN_uadd(X, X, n)) goto err;
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}
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/* now X is even, so we can easily divide it by two */
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if (!BN_rshift1(X, X)) goto err;
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}
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if (shift > 0) {
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if (!BN_rshift(B, B, shift)) goto err;
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}
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/* Same for A and Y. Afterwards, (2) still holds. */
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shift = 0;
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while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ {
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shift++;
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if (BN_is_odd(Y)) {
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if (!BN_uadd(Y, Y, n)) goto err;
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}
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/* now Y is even */
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if (!BN_rshift1(Y, Y)) goto err;
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}
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if (shift > 0) {
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if (!BN_rshift(A, A, shift)) goto err;
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}
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/* We still have (1) and (2).
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* Both A and B are odd.
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* The following computations ensure that
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*
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* 0 <= B < |n|,
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* 0 < A < |n|,
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* (1) -sign*X*a == B (mod |n|),
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* (2) sign*Y*a == A (mod |n|),
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*
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* and that either A or B is even in the next iteration.
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*/
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if (BN_ucmp(B, A) >= 0) {
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/* -sign*(X + Y)*a == B - A (mod |n|) */
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if (!BN_uadd(X, X, Y)) goto err;
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/* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
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* actually makes the algorithm slower
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*/
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if (!BN_usub(B, B, A)) goto err;
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} else {
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/* sign*(X + Y)*a == A - B (mod |n|) */
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if (!BN_uadd(Y, Y, X)) goto err;
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/* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
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if (!BN_usub(A, A, B)) goto err;
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}
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}
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} else {
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/* general inversion algorithm */
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while (!BN_is_zero(B)) {
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BIGNUM *tmp;
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/*
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* 0 < B < A,
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* (*) -sign*X*a == B (mod |n|),
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* sign*Y*a == A (mod |n|)
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*/
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/* (D, M) : = (A/B, A%B) ... */
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if (BN_num_bits(A) == BN_num_bits(B)) {
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if (!BN_one(D)) goto err;
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if (!BN_sub(M, A, B)) goto err;
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} else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
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/* A/B is 1, 2, or 3 */
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if (!BN_lshift1(T, B)) goto err;
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if (BN_ucmp(A, T) < 0) {
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/* A < 2*B, so D = 1 */
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if (!BN_one(D)) goto err;
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if (!BN_sub(M, A, B)) goto err;
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} else {
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/* A >= 2*B, so D = 2 or D = 3 */
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if (!BN_sub(M, A, T)) goto err;
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if (!BN_add(D, T, B)) goto err;
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/* use D ( := 3 * B) as temp */
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if (BN_ucmp(A, D) < 0) {
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/* A < 3*B, so D = 2 */
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if (!BN_set_word(D, 2)) goto err;
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/* M ( = A - 2*B) already has the correct value */
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} else {
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/* only D = 3 remains */
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if (!BN_set_word(D, 3)) goto err;
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/* currently M = A - 2 * B,
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* but we need M = A - 3 * B
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*/
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if (!BN_sub(M, M, B)) goto err;
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}
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}
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} else {
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if (!BN_div(D, M, A, B, ctx)) goto err;
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}
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/* Now
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* A = D*B + M;
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* thus we have
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* (**) sign*Y*a == D*B + M (mod |n|).
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*/
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tmp = A; /* keep the BIGNUM object, the value does not matter */
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/* (A, B) : = (B, A mod B) ... */
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A = B;
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B = M;
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/* ... so we have 0 <= B < A again */
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/* Since the former M is now B and the former B is now A,
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* (**) translates into
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* sign*Y*a == D*A + B (mod |n|),
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* i.e.
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* sign*Y*a - D*A == B (mod |n|).
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* Similarly, (*) translates into
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* -sign*X*a == A (mod |n|).
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*
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* Thus,
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* sign*Y*a + D*sign*X*a == B (mod |n|),
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* i.e.
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* sign*(Y + D*X)*a == B (mod |n|).
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*
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* So if we set (X, Y, sign) : = (Y + D*X, X, -sign), we arrive back at
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* -sign*X*a == B (mod |n|),
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* sign*Y*a == A (mod |n|).
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* Note that X and Y stay non-negative all the time.
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*/
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/* most of the time D is very small, so we can optimize tmp : = D*X+Y */
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if (BN_is_one(D)) {
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if (!BN_add(tmp, X, Y)) goto err;
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} else {
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if (BN_is_word(D, 2)) {
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if (!BN_lshift1(tmp, X)) goto err;
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} else if (BN_is_word(D, 4)) {
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if (!BN_lshift(tmp, X, 2)) goto err;
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} else if (D->top == 1) {
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if (!BN_copy(tmp, X)) goto err;
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if (!BN_mul_word(tmp, D->d[0])) goto err;
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|
} else {
|
|
if (!BN_mul(tmp, D, X, ctx)) goto err;
|
|
}
|
|
if (!BN_add(tmp, tmp, Y)) goto err;
|
|
}
|
|
|
|
M = Y; /* keep the BIGNUM object, the value does not matter */
|
|
Y = X;
|
|
X = tmp;
|
|
sign = -sign;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* The while loop (Euclid's algorithm) ends when
|
|
* A == gcd(a, n);
|
|
* we have
|
|
* sign*Y*a == A (mod |n|),
|
|
* where Y is non-negative.
|
|
*/
|
|
|
|
if (sign < 0) {
|
|
if (!BN_sub(Y, n, Y)) goto err;
|
|
}
|
|
/* Now Y*a == A (mod |n|). */
|
|
|
|
|
|
if (BN_is_one(A)) {
|
|
/* Y*a == 1 (mod |n|) */
|
|
if (!Y->neg && BN_ucmp(Y, n) < 0) {
|
|
if (!BN_copy(ret, Y)) goto err;
|
|
} else {
|
|
if (!BN_nnmod(ret, Y, n, ctx)) goto err;
|
|
}
|
|
} else {
|
|
goto err;
|
|
}
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return (ret);
|
|
}
|
|
|
|
#endif
|