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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 */
- #ifdef MONT_WORD
- static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
- #endif
- int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
- BN_MONT_CTX *mont, BN_CTX *ctx)
- {
- BIGNUM *tmp;
- int ret=0;
- #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
- int num = mont->N.top;
- if (num>1 && a->top==num && b->top==num)
- {
- if (bn_wexpand(r,num) == NULL) return(0);
- if (bn_mul_mont(r->d,a->d,b->d,mont->N.d,mont->n0,num))
- {
- r->neg = a->neg^b->neg;
- r->top = num;
- bn_correct_top(r);
- return(1);
- }
- }
- #endif
- BN_CTX_start(ctx);
- tmp = BN_CTX_get(ctx);
- if (tmp == NULL) goto err;
- bn_check_top(tmp);
- if (a == b)
- {
- if (!BN_sqr(tmp,a,ctx)) goto err;
- }
- else
- {
- if (!BN_mul(tmp,a,b,ctx)) goto err;
- }
- /* reduce from aRR to aR */
- #ifdef MONT_WORD
- if (!BN_from_montgomery_word(r,tmp,mont)) goto err;
- #else
- if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
- #endif
- bn_check_top(r);
- ret=1;
- err:
- BN_CTX_end(ctx);
- return(ret);
- }
- #ifdef MONT_WORD
- static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
- {
- BIGNUM *n;
- BN_ULONG *ap,*np,*rp,n0,v,*nrp;
- int al,nl,max,i,x,ri;
- n= &(mont->N);
- /* 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)) { ret->top=0; return(1); }
- max=(nl+al+1); /* allow for overflow (no?) XXX */
- if (bn_wexpand(r,max) == NULL) return(0);
- r->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[0];
- #ifdef BN_COUNT
- fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
- #endif
- for (i=0; i<nl; i++)
- {
- #ifdef __TANDEM
- {
- long long t1;
- long long t2;
- long long t3;
- t1 = rp[0] * (n0 & 0177777);
- t2 = 037777600000l;
- t2 = n0 & t2;
- t3 = rp[0] & 0177777;
- t2 = (t3 * t2) & BN_MASK2;
- t1 = t1 + t2;
- v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
- }
- #else
- v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
- #endif
- 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_correct_top(r);
-
- /* mont->ri will be a multiple of the word size */
- #if 0
- BN_rshift(ret,r,mont->ri);
- #else
- if (r->top < ri)
- {
- ret->top=0;
- return(1);
- }
- al=r->top-ri;
- if (bn_wexpand(ret,al) == NULL) return(0);
- ret->neg=r->neg;
- ret->top=al;
- rp=ret->d;
- ap=&(r->d[ri]);
- 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
- if (BN_ucmp(ret, &(mont->N)) >= 0)
- {
- if (!BN_usub(ret,ret,&(mont->N))) return(0);
- }
- bn_check_top(ret);
- return(1);
- }
- #endif /* MONT_WORD */
- int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
- BN_CTX *ctx)
- {
- int retn=0;
- #ifdef MONT_WORD
- BIGNUM *t;
- BN_CTX_start(ctx);
- if ((t = BN_CTX_get(ctx)) && BN_copy(t,a))
- retn = BN_from_montgomery_word(ret,t,mont);
- BN_CTX_end(ctx);
- #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;
- if (!BN_rshift(ret,t2,mont->ri)) goto err;
- if (BN_ucmp(ret, &(mont->N)) >= 0)
- {
- if (!BN_usub(ret,ret,&(mont->N))) goto err;
- }
- retn=1;
- bn_check_top(ret);
- err:
- BN_CTX_end(ctx);
- #endif /* MONT_WORD */
- return(retn);
- }
- 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);
- }
- 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;
- }
- void BN_MONT_CTX_free(BN_MONT_CTX *mont)
- {
- 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)
- {
- int ret = 0;
- BIGNUM *Ri,*R;
- BN_CTX_start(ctx);
- if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
- R= &(mont->RR); /* grab RR as a temp */
- if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
- mont->N.neg = 0;
- #ifdef MONT_WORD
- {
- BIGNUM tmod;
- BN_ULONG buf[2];
- tmod.d=buf;
- tmod.dmax=2;
- tmod.neg=0;
- mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
- #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
- BN_zero(R);
- if (!(BN_set_bit(R,2*BN_BITS2))) goto err;
- tmod.top=0;
- if ((buf[0] = mod->d[0])) tmod.top=1;
- if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2;
- if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
- goto err;
- if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */
- if (!BN_is_zero(Ri))
- {
- if (!BN_sub_word(Ri,1)) goto err;
- }
- else /* if N mod word size == 1 */
- {
- if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL)
- goto err;
- /* Ri-- (mod double word size) */
- Ri->neg=0;
- Ri->d[0]=BN_MASK2;
- Ri->d[1]=BN_MASK2;
- Ri->top=2;
- }
- if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
- /* Ni = (R*Ri-1)/N,
- * keep only couple of least significant words: */
- mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
- mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
- #else
- BN_zero(R);
- if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
- buf[0]=mod->d[0]; /* tmod = N mod word size */
- buf[1]=0;
- tmod.top = buf[0] != 0 ? 1 : 0;
- /* Ri = R^-1 mod N*/
- if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
- goto err;
- if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
- if (!BN_is_zero(Ri))
- {
- if (!BN_sub_word(Ri,1)) goto err;
- }
- else /* if N mod word size == 1 */
- {
- if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
- }
- if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
- /* Ni = (R*Ri-1)/N,
- * keep only least significant word: */
- mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
- mont->n0[1] = 0;
- #endif
- }
- #else /* !MONT_WORD */
- { /* bignum version */
- mont->ri=BN_num_bits(&mont->N);
- BN_zero(R);
- if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
- /* Ri = R^-1 mod N*/
- if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
- goto err;
- if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
- if (!BN_sub_word(Ri,1)) goto err;
- /* Ni = (R*Ri-1) / N */
- if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
- }
- #endif
- /* setup RR for conversions */
- BN_zero(&(mont->RR));
- if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
- if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
- ret = 1;
- err:
- BN_CTX_end(ctx);
- return ret;
- }
- BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
- {
- if (to == from) return(to);
- if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
- if (!BN_copy(&(to->N),&(from->N))) return NULL;
- if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
- to->ri=from->ri;
- to->n0[0]=from->n0[0];
- to->n0[1]=from->n0[1];
- return(to);
- }
- BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
- const BIGNUM *mod, BN_CTX *ctx)
- {
- if (*pmont)
- return *pmont;
- CRYPTO_w_lock(lock);
- if (!*pmont)
- {
- BN_MONT_CTX *mtmp;
- mtmp = BN_MONT_CTX_new();
- if (mtmp && !BN_MONT_CTX_set(mtmp, mod, ctx))
- BN_MONT_CTX_free(mtmp);
- else
- *pmont = mtmp;
- }
- CRYPTO_w_unlock(lock);
- return *pmont;
- }
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