569 lines
13 KiB
C
569 lines
13 KiB
C
/* 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 licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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#include <stdio.h>
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#include "cryptlib.h"
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#include "bn_lcl.h"
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#define TABLE_SIZE 16
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/* slow but works */
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int BN_mod_mul(ret, a, b, m, ctx)
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BIGNUM *ret;
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BIGNUM *a;
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BIGNUM *b;
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BIGNUM *m;
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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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t= &(ctx->bn[ctx->tos++]);
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if (a == b)
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{ if (!BN_sqr(t,a,ctx)) goto err; }
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else
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{ if (!BN_mul(t,a,b,ctx)) goto err; }
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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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ctx->tos--;
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return(r);
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}
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#if 0
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/* this one works - simple but works */
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int BN_mod_exp(r,a,p,m,ctx)
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BIGNUM *r,*a,*p,*m;
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BN_CTX *ctx;
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{
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int i,bits,ret=0;
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BIGNUM *v,*tmp;
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v= &(ctx->bn[ctx->tos++]);
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tmp= &(ctx->bn[ctx->tos++]);
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if (BN_copy(v,a) == NULL) goto err;
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bits=BN_num_bits(p);
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if (BN_is_odd(p))
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{ if (BN_copy(r,a) == NULL) goto err; }
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else { if (BN_one(r)) goto err; }
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for (i=1; i<bits; i++)
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{
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if (!BN_sqr(tmp,v,ctx)) goto err;
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if (!BN_mod(v,tmp,m,ctx)) goto err;
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if (BN_is_bit_set(p,i))
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{
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if (!BN_mul(tmp,r,v,ctx)) goto err;
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if (!BN_mod(r,tmp,m,ctx)) goto err;
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}
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}
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ret=1;
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err:
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ctx->tos-=2;
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return(ret);
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}
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#endif
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/* this one works - simple but works */
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int BN_exp(r,a,p,ctx)
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BIGNUM *r,*a,*p;
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BN_CTX *ctx;
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{
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int i,bits,ret=0;
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BIGNUM *v,*tmp;
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v= &(ctx->bn[ctx->tos++]);
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tmp= &(ctx->bn[ctx->tos++]);
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if (BN_copy(v,a) == NULL) goto err;
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bits=BN_num_bits(p);
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if (BN_is_odd(p))
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{ if (BN_copy(r,a) == NULL) goto err; }
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else { if (BN_one(r)) goto err; }
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for (i=1; i<bits; i++)
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{
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if (!BN_sqr(tmp,v,ctx)) goto err;
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if (BN_is_bit_set(p,i))
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{
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if (!BN_mul(tmp,r,v,ctx)) goto err;
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}
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}
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ret=1;
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err:
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ctx->tos-=2;
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return(ret);
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}
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int BN_mod_exp(r,a,p,m,ctx)
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BIGNUM *r;
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BIGNUM *a;
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BIGNUM *p;
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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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#ifdef MONT_MUL_MOD
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/* I have finally been able to take out this pre-condition of
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* the top bit being set. It was caused by an error in BN_div
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* with negatives. There was also another problem when for a^b%m
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* a >= m. eay 07-May-97 */
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/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
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if (BN_is_odd(m))
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{ ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
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else
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#endif
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#ifdef RECP_MUL_MOD
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{ ret=BN_mod_exp_recp(r,a,p,m,ctx); }
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#else
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{ ret=BN_mod_exp_simple(r,a,p,m,ctx); }
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#endif
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return(ret);
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}
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/* #ifdef RECP_MUL_MOD */
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int BN_mod_exp_recp(r,a,p,m,ctx)
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BIGNUM *r;
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BIGNUM *a;
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BIGNUM *p;
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BIGNUM *m;
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BN_CTX *ctx;
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{
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int i,j,bits,ret=0,wstart,wend,window,wvalue;
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int start=1,ts=0;
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BIGNUM *aa;
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BIGNUM val[TABLE_SIZE];
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BN_RECP_CTX recp;
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aa= &(ctx->bn[ctx->tos++]);
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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_RECP_CTX_init(&recp);
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if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) 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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if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
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goto err; /* 2 */
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if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
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window=1;
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else if (bits >= 256)
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window=5; /* max size of window */
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else if (bits >= 128)
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window=4;
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else
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window=3;
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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_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
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goto err;
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}
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ts=i;
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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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wvalue=0; /* The 'value' of the window */
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wstart=bits-1; /* The top bit of the window */
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wend=0; /* The bottom 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_reciprocal(r,r,r,&recp,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_reciprocal(r,r,r,&recp,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_reciprocal(r,r,&(val[wvalue>>1]),&recp,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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ctx->tos--;
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for (i=0; i<ts; i++)
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BN_clear_free(&(val[i]));
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BN_RECP_CTX_free(&recp);
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return(ret);
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}
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/* #endif */
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/* #ifdef MONT_MUL_MOD */
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int BN_mod_exp_mont(rr,a,p,m,ctx,in_mont)
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BIGNUM *rr;
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BIGNUM *a;
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BIGNUM *p;
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BIGNUM *m;
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BN_CTX *ctx;
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BN_MONT_CTX *in_mont;
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{
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int i,j,bits,ret=0,wstart,wend,window,wvalue;
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int start=1,ts=0;
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BIGNUM *d,*aa,*r;
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BIGNUM val[TABLE_SIZE];
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BN_MONT_CTX *mont=NULL;
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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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if (!(m->d[0] & 1))
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{
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BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
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return(0);
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}
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d= &(ctx->bn[ctx->tos++]);
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r= &(ctx->bn[ctx->tos++]);
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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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/* If this is not done, things will break in the montgomery
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* part */
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#if 1
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if (in_mont != NULL)
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mont=in_mont;
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else
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#endif
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{
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if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
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if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
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}
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BN_init(&val[0]);
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ts=1;
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if (BN_ucmp(a,m) >= 0)
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{
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BN_mod(&(val[0]),a,m,ctx);
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aa= &(val[0]);
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}
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else
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aa=a;
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if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
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if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
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if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
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window=1;
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else if (bits >= 256)
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window=5; /* max size of window */
|
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else if (bits >= 128)
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window=4;
|
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else
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window=3;
|
|
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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_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
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goto err;
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}
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ts=i;
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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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wvalue=0; /* The 'value' of the window */
|
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wstart=bits-1; /* The top bit of the window */
|
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wend=0; /* The bottom bit of the window */
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|
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if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) 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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{
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if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
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goto err;
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}
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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
|
|
* how bit a window to do. To do this we need to scan
|
|
* 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;
|
|
if (BN_is_bit_set(p,wstart-i))
|
|
{
|
|
wvalue<<=(i-wend);
|
|
wvalue|=1;
|
|
wend=i;
|
|
}
|
|
}
|
|
|
|
/* wend is the size of the current window */
|
|
j=wend+1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i=0; i<j; i++)
|
|
{
|
|
if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
|
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goto err;
|
|
}
|
|
|
|
/* wvalue will be an odd number < 2^window */
|
|
if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
|
|
goto err;
|
|
|
|
/* move the 'window' down further */
|
|
wstart-=wend+1;
|
|
wvalue=0;
|
|
start=0;
|
|
if (wstart < 0) break;
|
|
}
|
|
BN_from_montgomery(rr,r,mont,ctx);
|
|
ret=1;
|
|
err:
|
|
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
|
|
ctx->tos-=2;
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
return(ret);
|
|
}
|
|
/* #endif */
|
|
|
|
/* The old fallback, simple version :-) */
|
|
int BN_mod_exp_simple(r,a,p,m,ctx)
|
|
BIGNUM *r;
|
|
BIGNUM *a;
|
|
BIGNUM *p;
|
|
BIGNUM *m;
|
|
BN_CTX *ctx;
|
|
{
|
|
int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
|
|
int start=1;
|
|
BIGNUM *d;
|
|
BIGNUM val[TABLE_SIZE];
|
|
|
|
d= &(ctx->bn[ctx->tos++]);
|
|
bits=BN_num_bits(p);
|
|
|
|
if (bits == 0)
|
|
{
|
|
BN_one(r);
|
|
return(1);
|
|
}
|
|
|
|
BN_init(&(val[0]));
|
|
ts=1;
|
|
if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
|
|
if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
|
|
goto err; /* 2 */
|
|
|
|
if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
|
|
window=1;
|
|
else if (bits >= 256)
|
|
window=5; /* max size of window */
|
|
else if (bits >= 128)
|
|
window=4;
|
|
else
|
|
window=3;
|
|
|
|
j=1<<(window-1);
|
|
for (i=1; i<j; i++)
|
|
{
|
|
BN_init(&(val[i]));
|
|
if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
|
|
goto err;
|
|
}
|
|
ts=i;
|
|
|
|
start=1; /* This is used to avoid multiplication etc
|
|
* when there is only the value '1' in the
|
|
* buffer. */
|
|
wvalue=0; /* The 'value' of the window */
|
|
wstart=bits-1; /* The top bit of the window */
|
|
wend=0; /* The bottom bit of the window */
|
|
|
|
if (!BN_one(r)) goto err;
|
|
|
|
for (;;)
|
|
{
|
|
if (BN_is_bit_set(p,wstart) == 0)
|
|
{
|
|
if (!start)
|
|
if (!BN_mod_mul(r,r,r,m,ctx))
|
|
goto err;
|
|
if (wstart == 0) break;
|
|
wstart--;
|
|
continue;
|
|
}
|
|
/* We now have wstart on a 'set' bit, we now need to work out
|
|
* how bit a window to do. To do this we need to scan
|
|
* forward until the last set bit before the end of the
|
|
* window */
|
|
j=wstart;
|
|
wvalue=1;
|
|
wend=0;
|
|
for (i=1; i<window; i++)
|
|
{
|
|
if (wstart-i < 0) break;
|
|
if (BN_is_bit_set(p,wstart-i))
|
|
{
|
|
wvalue<<=(i-wend);
|
|
wvalue|=1;
|
|
wend=i;
|
|
}
|
|
}
|
|
|
|
/* wend is the size of the current window */
|
|
j=wend+1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i=0; i<j; i++)
|
|
{
|
|
if (!BN_mod_mul(r,r,r,m,ctx))
|
|
goto err;
|
|
}
|
|
|
|
/* wvalue will be an odd number < 2^window */
|
|
if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
|
|
goto err;
|
|
|
|
/* move the 'window' down further */
|
|
wstart-=wend+1;
|
|
wvalue=0;
|
|
start=0;
|
|
if (wstart < 0) break;
|
|
}
|
|
ret=1;
|
|
err:
|
|
ctx->tos--;
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
return(ret);
|
|
}
|
|
|