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bn_mont.c

/* 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, const BIGNUM *a, const BIGNUM *b,
                    BN_MONT_CTX *mont, BN_CTX *ctx)
      {
      BIGNUM *tmp;
      int ret=0;

      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 */
      if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
      ret=1;
err:
      BN_CTX_end(ctx);
      return(ret);
      }

int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
           BN_CTX *ctx)
      {
      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
      fprintf(stderr,"word BN_from_montgomery %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_fix_top(r);
      
      /* mont->ri will be a multiple of the word size */
#if 0
      BN_rshift(ret,r,mont->ri);
#else
      ret->neg = r->neg;
      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;
      if (!BN_rshift(ret,t2,mont->ri)) goto err;
#endif /* MONT_WORD */

      if (BN_ucmp(ret, &(mont->N)) >= 0)
            {
            if (!BN_usub(ret,ret,&(mont->N))) goto err;
            }
      retn=1;
 err:
      BN_CTX_end(ctx);
      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)
      {
      BIGNUM Ri,*R;

      BN_init(&Ri);
      R= &(mont->RR);                           /* grab RR as a temp */
      BN_copy(&(mont->N),mod);                  /* Set N */
      mont->N.neg = 0;

#ifdef MONT_WORD
            {
            BIGNUM tmod;
            BN_ULONG buf[2];

            mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
            if (!(BN_zero(R))) goto err;
            if (!(BN_set_bit(R,BN_BITS2))) goto err;  /* R */

            buf[0]=mod->d[0]; /* tmod = N mod word size */
            buf[1]=0;
            tmod.d=buf;
            tmod.top=1;
            tmod.dmax=2;
            tmod.neg=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 = (Ri.top > 0) ? Ri.d[0] : 0;
            BN_free(&Ri);
            }
#else /* !MONT_WORD */
            { /* bignum version */
            mont->ri=BN_num_bits(&mont->N);
            if (!BN_zero(R)) goto err;
            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;
            BN_free(&Ri);
            }
#endif

      /* setup RR for conversions */
      if (!BN_zero(&(mont->RR))) goto err;
      if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
      if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;

      return(1);
err:
      return(0);
      }

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=from->n0;
      return(to);
      }


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