openssl/crypto/bn/bn_mont.c

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/* crypto/bn/bn_mont.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
/*
* Details about Montgomery multiplication algorithms can be found at
* http://security.ece.orst.edu/publications.html, e.g.
* http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
* sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
*/
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
#define MONT_WORD /* use the faster word-based algorithm */
int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
BN_MONT_CTX *mont, BN_CTX *ctx)
{
BIGNUM *tmp,*tmp2;
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int ret=0;
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
tmp2 = BN_CTX_get(ctx);
if (tmp == NULL || tmp2 == NULL) goto err;
bn_check_top(tmp);
bn_check_top(tmp2);
if (a == b)
{
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#if 1
bn_wexpand(tmp,a->top*2);
bn_wexpand(tmp2,a->top*4);
bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
tmp->top=a->top*2;
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if (tmp->top > 0 && tmp->d[tmp->top-1] == 0)
tmp->top--;
#else
if (!BN_sqr(tmp,a,ctx)) goto err;
#endif
}
else
{
if (!BN_mul(tmp,a,b,ctx)) goto err;
}
/* reduce from aRR to aR */
if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
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ret=1;
err:
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BN_CTX_end(ctx);
return(ret);
}
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int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
BN_CTX *ctx)
{
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int retn=0;
#ifdef MONT_WORD
BIGNUM *n,*r;
BN_ULONG *ap,*np,*rp,n0,v,*nrp;
int al,nl,max,i,x,ri;
BN_CTX_start(ctx);
if ((r = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_copy(r,a)) goto err;
n= &(mont->N);
ap=a->d;
/* mont->ri is the size of mont->N in bits (rounded up
to the word size) */
al=ri=mont->ri/BN_BITS2;
nl=n->top;
if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
max=(nl+al+1); /* allow for overflow (no?) XXX */
if (bn_wexpand(r,max) == NULL) goto err;
if (bn_wexpand(ret,max) == NULL) goto err;
r->neg=a->neg^n->neg;
np=n->d;
rp=r->d;
nrp= &(r->d[nl]);
/* clear the top words of T */
#if 1
for (i=r->top; i<max; i++) /* memset? XXX */
r->d[i]=0;
#else
memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
#endif
r->top=max;
n0=mont->n0;
#ifdef BN_COUNT
printf("word BN_from_montgomery %d * %d\n",nl,nl);
#endif
for (i=0; i<nl; i++)
{
v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
nrp++;
rp++;
if (((nrp[-1]+=v)&BN_MASK2) >= v)
continue;
else
{
if (((++nrp[0])&BN_MASK2) != 0) continue;
if (((++nrp[1])&BN_MASK2) != 0) continue;
for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
}
}
bn_fix_top(r);
/* mont->ri will be a multiple of the word size */
#if 0
BN_rshift(ret,r,mont->ri);
#else
x=ri;
rp=ret->d;
ap= &(r->d[x]);
if (r->top < x)
al=0;
else
al=r->top-x;
ret->top=al;
al-=4;
for (i=0; i<al; i+=4)
{
BN_ULONG t1,t2,t3,t4;
t1=ap[i+0];
t2=ap[i+1];
t3=ap[i+2];
t4=ap[i+3];
rp[i+0]=t1;
rp[i+1]=t2;
rp[i+2]=t3;
rp[i+3]=t4;
}
al+=4;
for (; i<al; i++)
rp[i]=ap[i];
#endif
#else /* !MONT_WORD */
BIGNUM *t1,*t2;
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
t2 = BN_CTX_get(ctx);
if (t1 == NULL || t2 == NULL) goto err;
if (!BN_copy(t1,a)) goto err;
BN_mask_bits(t1,mont->ri);
if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
BN_mask_bits(t2,mont->ri);
if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
if (!BN_add(t2,a,t1)) goto err;
BN_rshift(ret,t2,mont->ri);
#endif /* MONT_WORD */
if (BN_ucmp(ret, &(mont->N)) >= 0)
{
BN_usub(ret,ret,&(mont->N));
}
retn=1;
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err:
BN_CTX_end(ctx);
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return(retn);
}
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BN_MONT_CTX *BN_MONT_CTX_new(void)
{
BN_MONT_CTX *ret;
if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
return(NULL);
BN_MONT_CTX_init(ret);
ret->flags=BN_FLG_MALLOCED;
return(ret);
}
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void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
{
ctx->ri=0;
BN_init(&(ctx->RR));
BN_init(&(ctx->N));
BN_init(&(ctx->Ni));
ctx->flags=0;
}
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void BN_MONT_CTX_free(BN_MONT_CTX *mont)
{
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if(mont == NULL)
return;
BN_free(&(mont->RR));
BN_free(&(mont->N));
BN_free(&(mont->Ni));
if (mont->flags & BN_FLG_MALLOCED)
OPENSSL_free(mont);
}
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
{
BIGNUM Ri,*R;
BN_init(&Ri);
R= &(mont->RR); /* grab RR as a temp */
BN_copy(&(mont->N),mod); /* Set N */
#ifdef MONT_WORD
{
BIGNUM tmod;
BN_ULONG buf[2];
mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
BN_zero(R);
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BN_set_bit(R,BN_BITS2); /* R */
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buf[0]=mod->d[0]; /* tmod = N mod word size */
buf[1]=0;
tmod.d=buf;
tmod.top=1;
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tmod.max=2;
tmod.neg=mod->neg;
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/* Ri = R^-1 mod N*/
if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
goto err;
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BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
if (!BN_is_zero(&Ri))
BN_sub_word(&Ri,1);
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else /* if N mod word size == 1 */
BN_set_word(&Ri,BN_MASK2); /* Ri-- (mod word size) */
BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N,
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* keep only least significant word: */
mont->n0=Ri.d[0];
BN_free(&Ri);
}
#else /* !MONT_WORD */
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{ /* bignum version */
mont->ri=BN_num_bits(mod);
BN_zero(R);
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BN_set_bit(R,mont->ri); /* R = 2^ri */
/* Ri = R^-1 mod N*/
if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
goto err;
BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
BN_sub_word(&Ri,1);
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/* Ni = (R*Ri-1) / N */
BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
BN_free(&Ri);
}
#endif
/* setup RR for conversions */
BN_zero(&(mont->RR));
BN_set_bit(&(mont->RR),mont->ri*2);
BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
return(1);
err:
return(0);
}
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BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
{
if (to == from) return(to);
BN_copy(&(to->RR),&(from->RR));
BN_copy(&(to->N),&(from->N));
BN_copy(&(to->Ni),&(from->Ni));
to->ri=from->ri;
to->n0=from->n0;
return(to);
}