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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.]
 */
/* ====================================================================
 * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
 *
 * 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 above 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 acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

/*
 * 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 and below code
       * is kind of BN_rshift(ret,r,mont->ri) equivalent */
      if (r->top <= ri)
            {
            ret->top=0;
            return(1);
            }
      al=r->top-ri;

#define BRANCH_FREE 1
#if BRANCH_FREE
      if (bn_wexpand(ret,ri) == NULL) return(0);
      x=0-(((al-ri)>>(sizeof(al)*8-1))&1);
      ret->top=x=(ri&~x)|(al&x);    /* min(ri,al) */
      ret->neg=r->neg;

      rp=ret->d;
      ap=&(r->d[ri]);

      {
      size_t m1,m2;

      v=bn_sub_words(rp,ap,np,ri);
      /* this ----------------^^ works even in al<ri case
       * thanks to zealous zeroing of top of the vector in the
       * beginning. */

      /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
      /* in other words if subtraction result is real, then
       * trick unconditional memcpy below to perform in-place
       * "refresh" instead of actual copy. */
      m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1);   /* al<ri */
      m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1);   /* al>ri */
      m1|=m2;                 /* (al!=ri) */
      m1|=(0-(size_t)v);      /* (al!=ri || v) */
      m1&=~m2;          /* (al!=ri || v) && !al>ri */
      nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m1)|((PTR_SIZE_INT)ap&m1));
      }

      /* 'i<ri' is chosen to eliminate dependency on input data, even
       * though it results in redundant copy in al<ri case. */
      for (i=0,ri-=4; i<ri; i+=4)
            {
            BN_ULONG t1,t2,t3,t4;
            
            t1=nrp[i+0];
            t2=nrp[i+1];
            t3=nrp[i+2];      ap[i+0]=0;
            t4=nrp[i+3];      ap[i+1]=0;
            rp[i+0]=t1; ap[i+2]=0;
            rp[i+1]=t2; ap[i+3]=0;
            rp[i+2]=t3;
            rp[i+3]=t4;
            }
      for (ri+=4; i<ri; i++)
            rp[i]=nrp[i], ap[i]=0;
      bn_correct_top(r);
      bn_correct_top(ret);
#else
      if (bn_wexpand(ret,al) == NULL) return(0);
      ret->top=al;
      ret->neg=r->neg;

      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];

      if (BN_ucmp(ret, &(mont->N)) >= 0)
            {
            if (!BN_usub(ret,ret,&(mont->N))) return(0);
            }
#endif
      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->n0[0] = ctx->n0[1] = 0;
      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];

            BN_init(&tmod);
            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)
            /* Only certain BN_BITS2<=32 platforms actually make use of
             * n0[1], and we could use the #else case (with a shorter R
             * value) for the others.  However, currently only the assembler
             * files do know which is which. */

            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)
      {
      int got_write_lock = 0;
      BN_MONT_CTX *ret;

      CRYPTO_r_lock(lock);
      if (!*pmont)
            {
            CRYPTO_r_unlock(lock);
            CRYPTO_w_lock(lock);
            got_write_lock = 1;

            if (!*pmont)
                  {
                  ret = BN_MONT_CTX_new();
                  if (ret && !BN_MONT_CTX_set(ret, mod, ctx))
                        BN_MONT_CTX_free(ret);
                  else
                        *pmont = ret;
                  }
            }
      
      ret = *pmont;
      
      if (got_write_lock)
            CRYPTO_w_unlock(lock);
      else
            CRYPTO_r_unlock(lock);
            
      return ret;
      }

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