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, BIGNUM *a, BIGNUM *b,
  73                           BN_MONT_CTX *mont, BN_CTX *ctx)
  74         {
  75         BIGNUM *tmp,*tmp2;
  76         int ret=0;
  77
  78         BN_CTX_start(ctx);
  79         tmp = BN_CTX_get(ctx);
  80         tmp2 = BN_CTX_get(ctx);
  81         if (tmp == NULL || tmp2 == NULL) goto err;
  82
  83         bn_check_top(tmp);
  84         bn_check_top(tmp2);
  85
  86         if (a == b)
  87                 {
  88 #if 1
  89                 bn_wexpand(tmp,a->top*2);
  90                 bn_wexpand(tmp2,a->top*4);
  91                 bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
  92                 tmp->top=a->top*2;
  93                 if (tmp->top > 0 && tmp->d[tmp->top-1] == 0)
  94                         tmp->top--;
  95 #else
  96                 if (!BN_sqr(tmp,a,ctx)) goto err;
  97 #endif
  98                 }
  99         else
 100                 {
 101                 if (!BN_mul(tmp,a,b,ctx)) goto err;
 102                 }
 103         /* reduce from aRR to aR */
 104         if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
 105         ret=1;
 106 err:
 107         BN_CTX_end(ctx);
 108         return(ret);
 109         }
 110
 111 int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
 112              BN_CTX *ctx)
 113         {
 114         int retn=0;
 115
 116 #ifdef MONT_WORD
 117         BIGNUM *n,*r;
 118         BN_ULONG *ap,*np,*rp,n0,v,*nrp;
 119         int al,nl,max,i,x,ri;
 120
 121         BN_CTX_start(ctx);
 122         if ((r = BN_CTX_get(ctx)) == NULL) goto err;
 123
 124         if (!BN_copy(r,a)) goto err;
 125         n= &(mont->N);
 126
 127         ap=a->d;
 128         /* mont->ri is the size of mont->N in bits (rounded up
 129            to the word size) */
 130         al=ri=mont->ri/BN_BITS2;
 131
 132         nl=n->top;
 133         if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
 134
 135         max=(nl+al+1); /* allow for overflow (no?) XXX */
 136         if (bn_wexpand(r,max) == NULL) goto err;
 137         if (bn_wexpand(ret,max) == NULL) goto err;
 138
 139         r->neg=a->neg^n->neg;
 140         np=n->d;
 141         rp=r->d;
 142         nrp= &(r->d[nl]);
 143
 144         /* clear the top words of T */
 145 #if 1
 146         for (i=r->top; i<max; i++) /* memset? XXX */
 147                 r->d[i]=0;
 148 #else
 149         memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
 150 #endif
 151
 152         r->top=max;
 153         n0=mont->n0;
 154
 155 #ifdef BN_COUNT
 156         printf("word BN_from_montgomery %d * %d\n",nl,nl);
 157 #endif
 158         for (i=0; i<nl; i++)
 159                 {
 160 #ifdef __TANDEM
 161                 {
 162                    long long t1;
 163                    long long t2;
 164                    long long t3;
 165                    t1 = rp[0] * (n0 & 0177777);
 166                    t2 = 037777600000l;
 167                    t2 = n0 & t2;
 168                    t3 = rp[0] & 0177777;
 169                    t2 = (t3 * t2) & BN_MASK2;
 170                    t1 = t1 + t2;
 171                    v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
 172                 }
 173 #else
 174                 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 175 #endif
 176                 nrp++;
 177                 rp++;
 178                 if (((nrp[-1]+=v)&BN_MASK2) >= v)
 179                         continue;
 180                 else
 181                         {
 182                         if (((++nrp[0])&BN_MASK2) != 0) continue;
 183                         if (((++nrp[1])&BN_MASK2) != 0) continue;
 184                         for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
 185                         }
 186                 }
 187         bn_fix_top(r);
 188
 189         /* mont->ri will be a multiple of the word size */
 190 #if 0
 191         BN_rshift(ret,r,mont->ri);
 192 #else
 193         x=ri;
 194         rp=ret->d;
 195         ap= &(r->d[x]);
 196         if (r->top < x)
 197                 al=0;
 198         else
 199                 al=r->top-x;
 200         ret->top=al;
 201         al-=4;
 202         for (i=0; i<al; i+=4)
 203                 {
 204                 BN_ULONG t1,t2,t3,t4;
 205
 206                 t1=ap[i+0];
 207                 t2=ap[i+1];
 208                 t3=ap[i+2];
 209                 t4=ap[i+3];
 210                 rp[i+0]=t1;
 211                 rp[i+1]=t2;
 212                 rp[i+2]=t3;
 213                 rp[i+3]=t4;
 214                 }
 215         al+=4;
 216         for (; i<al; i++)
 217                 rp[i]=ap[i];
 218 #endif
 219 #else /* !MONT_WORD */
 220         BIGNUM *t1,*t2;
 221
 222         BN_CTX_start(ctx);
 223         t1 = BN_CTX_get(ctx);
 224         t2 = BN_CTX_get(ctx);
 225         if (t1 == NULL || t2 == NULL) goto err;
 226
 227         if (!BN_copy(t1,a)) goto err;
 228         BN_mask_bits(t1,mont->ri);
 229
 230         if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
 231         BN_mask_bits(t2,mont->ri);
 232
 233         if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
 234         if (!BN_add(t2,a,t1)) goto err;
 235         BN_rshift(ret,t2,mont->ri);
 236 #endif /* MONT_WORD */
 237
 238         if (BN_ucmp(ret, &(mont->N)) >= 0)
 239                 {
 240                 BN_usub(ret,ret,&(mont->N));
 241                 }
 242         retn=1;
 243  err:
 244         BN_CTX_end(ctx);
 245         return(retn);
 246         }
 247
 248 BN_MONT_CTX *BN_MONT_CTX_new(void)
 249         {
 250         BN_MONT_CTX *ret;
 251
 252         if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
 253                 return(NULL);
 254
 255         BN_MONT_CTX_init(ret);
 256         ret->flags=BN_FLG_MALLOCED;
 257         return(ret);
 258         }
 259
 260 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 261         {
 262         ctx->ri=0;
 263         BN_init(&(ctx->RR));
 264         BN_init(&(ctx->N));
 265         BN_init(&(ctx->Ni));
 266         ctx->flags=0;
 267         }
 268
 269 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 270         {
 271         if(mont == NULL)
 272             return;
 273
 274         BN_free(&(mont->RR));
 275         BN_free(&(mont->N));
 276         BN_free(&(mont->Ni));
 277         if (mont->flags & BN_FLG_MALLOCED)
 278                 OPENSSL_free(mont);
 279         }
 280
 281 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 282         {
 283         BIGNUM Ri,*R;
 284
 285         BN_init(&Ri);
 286         R= &(mont->RR);                                 /* grab RR as a temp */
 287         BN_copy(&(mont->N),mod);                        /* Set N */
 288
 289 #ifdef MONT_WORD
 290                 {
 291                 BIGNUM tmod;
 292                 BN_ULONG buf[2];
 293
 294                 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
 295                 BN_zero(R);
 296                 BN_set_bit(R,BN_BITS2);                 /* R */
 297
 298                 buf[0]=mod->d[0]; /* tmod = N mod word size */
 299                 buf[1]=0;
 300                 tmod.d=buf;
 301                 tmod.top=1;
 302                 tmod.dmax=2;
 303                 tmod.neg=mod->neg;
 304                                                         /* Ri = R^-1 mod N*/
 305                 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
 306                         goto err;
 307                 BN_lshift(&Ri,&Ri,BN_BITS2);            /* R*Ri */
 308                 if (!BN_is_zero(&Ri))
 309                         BN_sub_word(&Ri,1);
 310                 else /* if N mod word size == 1 */
 311                         BN_set_word(&Ri,BN_MASK2);  /* Ri-- (mod word size) */
 312                 BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N,
 313                                                  * keep only least significant word: */
 314                 mont->n0=Ri.d[0];
 315                 BN_free(&Ri);
 316                 }
 317 #else /* !MONT_WORD */
 318                 { /* bignum version */
 319                 mont->ri=BN_num_bits(mod);
 320                 BN_zero(R);
 321                 BN_set_bit(R,mont->ri);                 /* R = 2^ri */
 322                                                         /* Ri = R^-1 mod N*/
 323                 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
 324                         goto err;
 325                 BN_lshift(&Ri,&Ri,mont->ri);            /* R*Ri */
 326                 BN_sub_word(&Ri,1);
 327                                                         /* Ni = (R*Ri-1) / N */
 328                 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
 329                 BN_free(&Ri);
 330                 }
 331 #endif
 332
 333         /* setup RR for conversions */
 334         BN_zero(&(mont->RR));
 335         BN_set_bit(&(mont->RR),mont->ri*2);
 336         BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
 337
 338         return(1);
 339 err:
 340         return(0);
 341         }
 342
 343 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 344         {
 345         if (to == from) return(to);
 346
 347         BN_copy(&(to->RR),&(from->RR));
 348         BN_copy(&(to->N),&(from->N));
 349         BN_copy(&(to->Ni),&(from->Ni));
 350         to->ri=from->ri;
 351         to->n0=from->n0;
 352         return(to);
 353         }
 354