crypto/bn/bn_mont.c

   1 /* crypto/bn/bn_mont.c */
   2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
   3  * All rights reserved.
   4  *
   5  * This package is an SSL implementation written
   6  * by Eric Young (eay@cryptsoft.com).
   7  * The implementation was written so as to conform with Netscapes SSL.
   8  *
   9  * This library is free for commercial and non-commercial use as long as
  10  * the following conditions are aheared to.  The following conditions
  11  * apply to all code found in this distribution, be it the RC4, RSA,
  12  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
  13  * included with this distribution is covered by the same copyright terms
  14  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
  15  *
  16  * Copyright remains Eric Young's, and as such any Copyright notices in
  17  * the code are not to be removed.
  18  * If this package is used in a product, Eric Young should be given attribution
  19  * as the author of the parts of the library used.
  20  * This can be in the form of a textual message at program startup or
  21  * in documentation (online or textual) provided with the package.
  22  *
  23  * Redistribution and use in source and binary forms, with or without
  24  * modification, are permitted provided that the following conditions
  25  * are met:
  26  * 1. Redistributions of source code must retain the copyright
  27  *    notice, this list of conditions and the following disclaimer.
  28  * 2. Redistributions in binary form must reproduce the above copyright
  29  *    notice, this list of conditions and the following disclaimer in the
  30  *    documentation and/or other materials provided with the distribution.
  31  * 3. All advertising materials mentioning features or use of this software
  32  *    must display the following acknowledgement:
  33  *    "This product includes cryptographic software written by
  34  *     Eric Young (eay@cryptsoft.com)"
  35  *    The word 'cryptographic' can be left out if the rouines from the library
  36  *    being used are not cryptographic related :-).
  37  * 4. If you include any Windows specific code (or a derivative thereof) from
  38  *    the apps directory (application code) you must include an acknowledgement:
  39  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
  40  *
  41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
  42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  44  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  51  * SUCH DAMAGE.
  52  *
  53  * The licence and distribution terms for any publically available version or
  54  * derivative of this code cannot be changed.  i.e. this code cannot simply be
  55  * copied and put under another distribution licence
  56  * [including the GNU Public Licence.]
  57  */
  58
  59 /*
  60  * Details about Montgomery multiplication algorithms can be found at
  61  * http://security.ece.orst.edu/publications.html, e.g.
  62  * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
  63  * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
  64  */
  65
  66 #include <stdio.h>
  67 #include "cryptlib.h"
  68 #include "bn_lcl.h"
  69
  70 #define MONT_WORD /* use the faster word-based algorithm */
  71
  72 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  73                           BN_MONT_CTX *mont, BN_CTX *ctx)
  74         {
  75         BIGNUM *tmp;
  76         int ret=0;
  77
  78         BN_CTX_start(ctx);
  79         tmp = BN_CTX_get(ctx);
  80         if (tmp == NULL) goto err;
  81
  82         bn_check_top(tmp);
  83         if (a == b)
  84                 {
  85                 if (!BN_sqr(tmp,a,ctx)) goto err;
  86                 }
  87         else
  88                 {
  89                 if (!BN_mul(tmp,a,b,ctx)) goto err;
  90                 }
  91         /* reduce from aRR to aR */
  92         if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
  93         bn_check_top(r);
  94         ret=1;
  95 err:
  96         BN_CTX_end(ctx);
  97         return(ret);
  98         }
  99
 100 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 101              BN_CTX *ctx)
 102         {
 103         int retn=0;
 104
 105 #ifdef MONT_WORD
 106         BIGNUM *n,*r;
 107         BN_ULONG *ap,*np,*rp,n0,v,*nrp;
 108         int al,nl,max,i,x,ri;
 109
 110         BN_CTX_start(ctx);
 111         if ((r = BN_CTX_get(ctx)) == NULL) goto err;
 112
 113         if (!BN_copy(r,a)) goto err;
 114         n= &(mont->N);
 115
 116         ap=a->d;
 117         /* mont->ri is the size of mont->N in bits (rounded up
 118            to the word size) */
 119         al=ri=mont->ri/BN_BITS2;
 120
 121         nl=n->top;
 122         if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
 123
 124         max=(nl+al+1); /* allow for overflow (no?) XXX */
 125         if (bn_wexpand(r,max) == NULL) goto err;
 126         if (bn_wexpand(ret,max) == NULL) goto err;
 127
 128         r->neg=a->neg^n->neg;
 129         np=n->d;
 130         rp=r->d;
 131         nrp= &(r->d[nl]);
 132
 133         /* clear the top words of T */
 134 #if 1
 135         for (i=r->top; i<max; i++) /* memset? XXX */
 136                 r->d[i]=0;
 137 #else
 138         memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
 139 #endif
 140
 141         r->top=max;
 142         n0=mont->n0;
 143
 144 #ifdef BN_COUNT
 145         fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl);
 146 #endif
 147         for (i=0; i<nl; i++)
 148                 {
 149 #ifdef __TANDEM
 150                 {
 151                    long long t1;
 152                    long long t2;
 153                    long long t3;
 154                    t1 = rp[0] * (n0 & 0177777);
 155                    t2 = 037777600000l;
 156                    t2 = n0 & t2;
 157                    t3 = rp[0] & 0177777;
 158                    t2 = (t3 * t2) & BN_MASK2;
 159                    t1 = t1 + t2;
 160                    v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
 161                 }
 162 #else
 163                 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 164 #endif
 165                 nrp++;
 166                 rp++;
 167                 if (((nrp[-1]+=v)&BN_MASK2) >= v)
 168                         continue;
 169                 else
 170                         {
 171                         if (((++nrp[0])&BN_MASK2) != 0) continue;
 172                         if (((++nrp[1])&BN_MASK2) != 0) continue;
 173                         for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
 174                         }
 175                 }
 176         bn_correct_top(r);
 177
 178         /* mont->ri will be a multiple of the word size */
 179 #if 0
 180         BN_rshift(ret,r,mont->ri);
 181 #else
 182         ret->neg = r->neg;
 183         x=ri;
 184         rp=ret->d;
 185         ap= &(r->d[x]);
 186         if (r->top < x)
 187                 al=0;
 188         else
 189                 al=r->top-x;
 190         ret->top=al;
 191         al-=4;
 192         for (i=0; i<al; i+=4)
 193                 {
 194                 BN_ULONG t1,t2,t3,t4;
 195
 196                 t1=ap[i+0];
 197                 t2=ap[i+1];
 198                 t3=ap[i+2];
 199                 t4=ap[i+3];
 200                 rp[i+0]=t1;
 201                 rp[i+1]=t2;
 202                 rp[i+2]=t3;
 203                 rp[i+3]=t4;
 204                 }
 205         al+=4;
 206         for (; i<al; i++)
 207                 rp[i]=ap[i];
 208 #endif
 209 #else /* !MONT_WORD */
 210         BIGNUM *t1,*t2;
 211
 212         BN_CTX_start(ctx);
 213         t1 = BN_CTX_get(ctx);
 214         t2 = BN_CTX_get(ctx);
 215         if (t1 == NULL || t2 == NULL) goto err;
 216
 217         if (!BN_copy(t1,a)) goto err;
 218         BN_mask_bits(t1,mont->ri);
 219
 220         if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
 221         BN_mask_bits(t2,mont->ri);
 222
 223         if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
 224         if (!BN_add(t2,a,t1)) goto err;
 225         if (!BN_rshift(ret,t2,mont->ri)) goto err;
 226 #endif /* MONT_WORD */
 227
 228         if (BN_ucmp(ret, &(mont->N)) >= 0)
 229                 {
 230                 if (!BN_usub(ret,ret,&(mont->N))) goto err;
 231                 }
 232         retn=1;
 233         bn_check_top(ret);
 234  err:
 235         BN_CTX_end(ctx);
 236         return(retn);
 237         }
 238
 239 BN_MONT_CTX *BN_MONT_CTX_new(void)
 240         {
 241         BN_MONT_CTX *ret;
 242
 243         if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
 244                 return(NULL);
 245
 246         BN_MONT_CTX_init(ret);
 247         ret->flags=BN_FLG_MALLOCED;
 248         return(ret);
 249         }
 250
 251 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 252         {
 253         ctx->ri=0;
 254         BN_init(&(ctx->RR));
 255         BN_init(&(ctx->N));
 256         BN_init(&(ctx->Ni));
 257         ctx->flags=0;
 258         }
 259
 260 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 261         {
 262         if(mont == NULL)
 263             return;
 264
 265         BN_free(&(mont->RR));
 266         BN_free(&(mont->N));
 267         BN_free(&(mont->Ni));
 268         if (mont->flags & BN_FLG_MALLOCED)
 269                 OPENSSL_free(mont);
 270         }
 271
 272 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 273         {
 274         int ret = 0;
 275         BIGNUM *Ri,*R;
 276
 277         BN_CTX_start(ctx);
 278         if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
 279         R= &(mont->RR);                                 /* grab RR as a temp */
 280         if (!BN_copy(&(mont->N),mod)) goto err;         /* Set N */
 281         mont->N.neg = 0;
 282
 283 #ifdef MONT_WORD
 284                 {
 285                 BIGNUM tmod;
 286                 BN_ULONG buf[2];
 287
 288                 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
 289                 BN_zero(R);
 290                 if (!(BN_set_bit(R,BN_BITS2))) goto err;        /* R */
 291
 292                 buf[0]=mod->d[0]; /* tmod = N mod word size */
 293                 buf[1]=0;
 294                 tmod.d=buf;
 295                 tmod.top=1;
 296                 tmod.dmax=2;
 297                 tmod.neg=0;
 298                                                         /* Ri = R^-1 mod N*/
 299                 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
 300                         goto err;
 301                 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
 302                 if (!BN_is_zero(Ri))
 303                         {
 304                         if (!BN_sub_word(Ri,1)) goto err;
 305                         }
 306                 else /* if N mod word size == 1 */
 307                         {
 308                         if (!BN_set_word(Ri,BN_MASK2)) goto err;  /* Ri-- (mod word size) */
 309                         }
 310                 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
 311                 /* Ni = (R*Ri-1)/N,
 312                  * keep only least significant word: */
 313                 mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;
 314                 }
 315 #else /* !MONT_WORD */
 316                 { /* bignum version */
 317                 mont->ri=BN_num_bits(&mont->N);
 318                 BN_zero(R);
 319                 if (!BN_set_bit(R,mont->ri)) goto err;  /* R = 2^ri */
 320                                                         /* Ri = R^-1 mod N*/
 321                 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
 322                         goto err;
 323                 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
 324                 if (!BN_sub_word(Ri,1)) goto err;
 325                                                         /* Ni = (R*Ri-1) / N */
 326                 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
 327                 }
 328 #endif
 329
 330         /* setup RR for conversions */
 331         BN_zero(&(mont->RR));
 332         if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
 333         if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
 334
 335         ret = 1;
 336 err:
 337         BN_CTX_end(ctx);
 338         return ret;
 339         }
 340
 341 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 342         {
 343         if (to == from) return(to);
 344
 345         if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
 346         if (!BN_copy(&(to->N),&(from->N))) return NULL;
 347         if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
 348         to->ri=from->ri;
 349         to->n0=from->n0;
 350         return(to);
 351         }
 352