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, especially
  62  * http://security.ece.orst.edu/koc/papers/j37acmon.pdf
  63  */
  64
  65 #include <stdio.h>
  66 #include "cryptlib.h"
  67 #include "bn_lcl.h"
  68
  69 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
  70                           BN_MONT_CTX *mont, BN_CTX *ctx)
  71         {
  72         BIGNUM *tmp,*tmp2;
  73
  74         tmp= &(ctx->bn[ctx->tos]);
  75         tmp2= &(ctx->bn[ctx->tos]);
  76         ctx->tos+=2;
  77
  78         bn_check_top(tmp);
  79         bn_check_top(tmp2);
  80
  81         if (a == b)
  82                 {
  83 #if 0
  84                 bn_wexpand(tmp,a->top*2);
  85                 bn_wexpand(tmp2,a->top*4);
  86                 bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
  87                 tmp->top=a->top*2;
  88                 if (tmp->d[tmp->top-1] == 0)
  89                         tmp->top--;
  90 #else
  91                 if (!BN_sqr(tmp,a,ctx)) goto err;
  92 #endif
  93                 }
  94         else
  95                 {
  96                 if (!BN_mul(tmp,a,b,ctx)) goto err;
  97                 }
  98         /* reduce from aRR to aR */
  99         if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
 100         ctx->tos-=2;
 101         return(1);
 102 err:
 103         return(0);
 104         }
 105
 106 int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
 107              BN_CTX *ctx)
 108         {
 109         int retn=0;
 110 #ifdef BN_RECURSION_MONT
 111         if (mont->use_word)
 112 #endif
 113                 {
 114                 BIGNUM *n,*r;
 115                 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
 116                 int al,nl,max,i,x,ri;
 117
 118                 r= &(ctx->bn[ctx->tos]);
 119
 120                 if (!BN_copy(r,a)) goto err;
 121                 n= &(mont->N);
 122
 123                 ap=a->d;
 124                 /* mont->ri is the size of mont->N in bits (rounded up
 125                    to the word size) */
 126                 al=ri=mont->ri/BN_BITS2;
 127
 128                 nl=n->top;
 129                 if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
 130
 131                 max=(nl+al+1); /* allow for overflow (no?) XXX */
 132                 if (bn_wexpand(r,max) == NULL) goto err;
 133                 if (bn_wexpand(ret,max) == NULL) goto err;
 134
 135                 r->neg=a->neg^n->neg;
 136                 np=n->d;
 137                 rp=r->d;
 138                 nrp= &(r->d[nl]);
 139
 140                 /* clear the top words of T */
 141 #if 1
 142                 for (i=r->top; i<max; i++) /* memset? XXX */
 143                         r->d[i]=0;
 144 #else
 145                 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
 146 #endif
 147
 148                 r->top=max;
 149                 n0=mont->n0;
 150
 151 #ifdef BN_COUNT
 152 printf("word BN_from_montgomery %d * %d\n",nl,nl);
 153 #endif
 154                 for (i=0; i<nl; i++)
 155                         {
 156                         v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 157                         nrp++;
 158                         rp++;
 159                         if (((nrp[-1]+=v)&BN_MASK2) >= v)
 160                                 continue;
 161                         else
 162                                 {
 163                                 if (((++nrp[0])&BN_MASK2) != 0) continue;
 164                                 if (((++nrp[1])&BN_MASK2) != 0) continue;
 165                                 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
 166                                 }
 167                         }
 168                 bn_fix_top(r);
 169
 170                 /* mont->ri will be a multiple of the word size */
 171 #if 0
 172                 BN_rshift(ret,r,mont->ri);
 173 #else
 174                 x=ri;
 175                 rp=ret->d;
 176                 ap= &(r->d[x]);
 177                 if (r->top < x)
 178                         al=0;
 179                 else
 180                         al=r->top-x;
 181                 ret->top=al;
 182                 al-=4;
 183                 for (i=0; i<al; i+=4)
 184                         {
 185                         BN_ULONG t1,t2,t3,t4;
 186
 187                         t1=ap[i+0];
 188                         t2=ap[i+1];
 189                         t3=ap[i+2];
 190                         t4=ap[i+3];
 191                         rp[i+0]=t1;
 192                         rp[i+1]=t2;
 193                         rp[i+2]=t3;
 194                         rp[i+3]=t4;
 195                         }
 196                 al+=4;
 197                 for (; i<al; i++)
 198                         rp[i]=ap[i];
 199 #endif
 200
 201                 if (BN_ucmp(ret, &(mont->N)) >= 0)
 202                         {
 203                         BN_usub(ret,ret,&(mont->N)); /* XXX */
 204                         }
 205                 retn=1;
 206                 }
 207 #ifdef BN_RECURSION_MONT
 208         else /* bignum version */
 209                 {
 210                 BIGNUM *t1,*t2;
 211
 212                 t1=&(ctx->bn[ctx->tos]);
 213                 t2=&(ctx->bn[ctx->tos+1]);
 214                 ctx->tos+=2;
 215
 216                 if (!BN_copy(t1,a)) goto err;
 217                 BN_mask_bits(t1,mont->ri);
 218
 219                 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
 220                 BN_mask_bits(t2,mont->ri);
 221
 222                 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
 223                 if (!BN_add(t2,a,t1)) goto err;
 224                 BN_rshift(ret,t2,mont->ri);
 225
 226                 if (BN_ucmp(ret,&mont->N) >= 0)
 227                         BN_usub(ret,ret,&mont->N);
 228                 ctx->tos-=2;
 229                 retn=1;
 230                 }
 231 #endif
 232  err:
 233         return(retn);
 234         }
 235
 236 BN_MONT_CTX *BN_MONT_CTX_new(void)
 237         {
 238         BN_MONT_CTX *ret;
 239
 240         if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
 241                 return(NULL);
 242
 243         BN_MONT_CTX_init(ret);
 244         ret->flags=BN_FLG_MALLOCED;
 245         return(ret);
 246         }
 247
 248 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 249         {
 250         ctx->use_word=0;
 251         ctx->ri=0;
 252         BN_init(&(ctx->RR));
 253         BN_init(&(ctx->N));
 254         BN_init(&(ctx->Ni));
 255         ctx->flags=0;
 256         }
 257
 258 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 259         {
 260         if(mont == NULL)
 261             return;
 262
 263         BN_free(&(mont->RR));
 264         BN_free(&(mont->N));
 265         BN_free(&(mont->Ni));
 266         if (mont->flags & BN_FLG_MALLOCED)
 267                 Free(mont);
 268         }
 269
 270 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 271         {
 272         BIGNUM Ri,*R;
 273
 274         BN_init(&Ri);
 275         R= &(mont->RR);                                 /* grab RR as a temp */
 276         BN_copy(&(mont->N),mod);                        /* Set N */
 277
 278 #ifdef BN_RECURSION_MONT
 279         /* the word-based algorithm is faster */
 280         if (mont->N.top > BN_MONT_CTX_SET_SIZE_WORD)
 281 #endif
 282                 {
 283                 BIGNUM tmod;
 284                 BN_ULONG buf[2];
 285
 286                 mont->use_word=1;
 287
 288                 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
 289                 BN_zero(R);
 290                 BN_set_bit(R,BN_BITS2);                 /* R = 2^ri */
 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.max=2;
 297                 tmod.neg=mod->neg;
 298                                                         /* Ri = R^-1 mod N*/
 299                 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
 300                         goto err;
 301                 BN_lshift(&Ri,&Ri,BN_BITS2);            /* R*Ri */
 302                 if (!BN_is_zero(&Ri))
 303                         BN_sub_word(&Ri,1);
 304                 else /* if N mod word size == 1 */
 305                         BN_set_word(&Ri,BN_MASK2);  /* Ri-- (mod word size) */
 306                 BN_div(&Ri,NULL,&Ri,&tmod,ctx);          /* Ni = (R*Ri-1)/N */
 307                 mont->n0=Ri.d[0];
 308                 BN_free(&Ri);
 309                 }
 310 #ifdef BN_RECURSION_MONT
 311         else
 312                 { /* bignum version */
 313                 mont->use_word=0;
 314                 mont->ri=BN_num_bits(mod);
 315                 BN_zero(R);
 316                 BN_set_bit(R,mont->ri);                 /* R = 2^ri */
 317                                                         /* Ri = R^-1 mod N*/
 318                 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
 319                         goto err;
 320                 BN_lshift(&Ri,&Ri,mont->ri);            /* R*Ri */
 321                 BN_sub_word(&Ri,1);
 322                                                         /* Ni = (R*Ri-1) / N */
 323                 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
 324                 BN_free(&Ri);
 325                 }
 326 #endif
 327
 328         /* setup RR for conversions */
 329         BN_zero(&(mont->RR));
 330         BN_set_bit(&(mont->RR),mont->ri*2);
 331         BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
 332
 333         return(1);
 334 err:
 335         return(0);
 336         }
 337
 338 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 339         {
 340         if (to == from) return(to);
 341
 342         BN_copy(&(to->RR),&(from->RR));
 343         BN_copy(&(to->N),&(from->N));
 344         BN_copy(&(to->Ni),&(from->Ni));
 345         to->use_word=from->use_word;
 346         to->ri=from->ri;
 347         to->n0=from->n0;
 348         return(to);
 349         }
 350