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  * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
  60  *
  61  * Redistribution and use in source and binary forms, with or without
  62  * modification, are permitted provided that the following conditions
  63  * are met:
  64  *
  65  * 1. Redistributions of source code must retain the above copyright
  66  *    notice, this list of conditions and the following disclaimer.
  67  *
  68  * 2. Redistributions in binary form must reproduce the above copyright
  69  *    notice, this list of conditions and the following disclaimer in
  70  *    the documentation and/or other materials provided with the
  71  *    distribution.
  72  *
  73  * 3. All advertising materials mentioning features or use of this
  74  *    software must display the following acknowledgment:
  75  *    "This product includes software developed by the OpenSSL Project
  76  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  77  *
  78  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  79  *    endorse or promote products derived from this software without
  80  *    prior written permission. For written permission, please contact
  81  *    openssl-core@openssl.org.
  82  *
  83  * 5. Products derived from this software may not be called "OpenSSL"
  84  *    nor may "OpenSSL" appear in their names without prior written
  85  *    permission of the OpenSSL Project.
  86  *
  87  * 6. Redistributions of any form whatsoever must retain the following
  88  *    acknowledgment:
  89  *    "This product includes software developed by the OpenSSL Project
  90  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  91  *
  92  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  93  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  94  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  95  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  96  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  97  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  98  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  99  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 100  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 101  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 102  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 103  * OF THE POSSIBILITY OF SUCH DAMAGE.
 104  * ====================================================================
 105  *
 106  * This product includes cryptographic software written by Eric Young
 107  * (eay@cryptsoft.com).  This product includes software written by Tim
 108  * Hudson (tjh@cryptsoft.com).
 109  *
 110  */
 111 
 112 /*
 113  * Details about Montgomery multiplication algorithms can be found at
 114  * http://security.ece.orst.edu/publications.html, e.g.
 115  * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
 116  * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
 117  */
 118 
 119 #include <stdio.h>
 120 #include "cryptlib.h"
 121 #include "bn_lcl.h"
 122 
 123 #define MONT_WORD /* use the faster word-based algorithm */
 124 
 125 #ifdef MONT_WORD
 126 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
 127 #endif
 128 
 129 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 130                           BN_MONT_CTX *mont, BN_CTX *ctx)
 131         {
 132         BIGNUM *tmp;
 133         int ret=0;
 134 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
 135         int num = mont->N.top;
 136 
 137         if (num>1 && a->top==num && b->top==num)
 138                 {
 139                 if (bn_wexpand(r,num) == NULL) return(0);
 140                 if (bn_mul_mont(r->d,a->d,b->d,mont->N.d,mont->n0,num))
 141                         {
 142                         r->neg = a->neg^b->neg;
 143                         r->top = num;
 144                         bn_correct_top(r);
 145                         return(1);
 146                         }
 147                 }
 148 #endif
 149 
 150         BN_CTX_start(ctx);
 151         tmp = BN_CTX_get(ctx);
 152         if (tmp == NULL) goto err;
 153 
 154         bn_check_top(tmp);
 155         if (a == b)
 156                 {
 157                 if (!BN_sqr(tmp,a,ctx)) goto err;
 158                 }
 159         else
 160                 {
 161                 if (!BN_mul(tmp,a,b,ctx)) goto err;
 162                 }
 163         /* reduce from aRR to aR */
 164 #ifdef MONT_WORD
 165         if (!BN_from_montgomery_word(r,tmp,mont)) goto err;
 166 #else
 167         if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
 168 #endif
 169         bn_check_top(r);
 170         ret=1;
 171 err:
 172         BN_CTX_end(ctx);
 173         return(ret);
 174         }
 175 
 176 #ifdef MONT_WORD
 177 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
 178         {
 179         BIGNUM *n;
 180         BN_ULONG *ap,*np,*rp,n0,v,carry;
 181         int nl,max,i;
 182 
 183         n= &(mont->N);
 184         nl=n->top;
 185         if (nl == 0) { ret->top=0; return(1); }
 186 
 187         max=(2*nl); /* carry is stored separately */
 188         if (bn_wexpand(r,max) == NULL) return(0);
 189 
 190         r->neg^=n->neg;
 191         np=n->d;
 192         rp=r->d;
 193 
 194         /* clear the top words of T */
 195 #if 1
 196         for (i=r->top; i<max; i++) /* memset? XXX */
 197                 rp[i]=0;
 198 #else
 199         memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
 200 #endif
 201 
 202         r->top=max;
 203         n0=mont->n0[0];
 204 
 205 #ifdef BN_COUNT
 206         fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
 207 #endif
 208         for (carry=0, i=0; i<nl; i++, rp++)
 209                 {
 210 #ifdef __TANDEM
 211                 {
 212                    long long t1;
 213                    long long t2;
 214                    long long t3;
 215                    t1 = rp[0] * (n0 & 0177777);
 216                    t2 = 037777600000l;
 217                    t2 = n0 & t2;
 218                    t3 = rp[0] & 0177777;
 219                    t2 = (t3 * t2) & BN_MASK2;
 220                    t1 = t1 + t2;
 221                    v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
 222                 }
 223 #else
 224                 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
 225 #endif
 226                 v = (v+carry+rp[nl])&BN_MASK2;
 227                 carry |= (v != rp[nl]);
 228                 carry &= (v <= rp[nl]);
 229                 rp[nl]=v;
 230                 }
 231 
 232         if (bn_wexpand(ret,nl) == NULL) return(0);
 233         ret->top=nl;
 234         ret->neg=r->neg;
 235 
 236         rp=ret->d;
 237         ap=&(r->d[nl]);
 238 
 239 #define BRANCH_FREE 1
 240 #if BRANCH_FREE
 241         {
 242         BN_ULONG *nrp;
 243         size_t m;
 244 
 245         v=bn_sub_words(rp,ap,np,nl)-carry;
 246         /* if subtraction result is real, then
 247          * trick unconditional memcpy below to perform in-place
 248          * "refresh" instead of actual copy. */
 249         m=(0-(size_t)v);
 250         nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m));
 251 
 252         for (i=0,nl-=4; i<nl; i+=4)
 253                 {
 254                 BN_ULONG t1,t2,t3,t4;
 255 
 256                 t1=nrp[i+0];
 257                 t2=nrp[i+1];
 258                 t3=nrp[i+2];    ap[i+0]=0;
 259                 t4=nrp[i+3];    ap[i+1]=0;
 260                 rp[i+0]=t1;     ap[i+2]=0;
 261                 rp[i+1]=t2;     ap[i+3]=0;
 262                 rp[i+2]=t3;
 263                 rp[i+3]=t4;
 264                 }
 265         for (nl+=4; i<nl; i++)
 266                 rp[i]=nrp[i], ap[i]=0;
 267         }
 268 #else
 269         if (bn_sub_words (rp,ap,np,nl)-carry)
 270                 memcpy(rp,ap,nl*sizeof(BN_ULONG));
 271 #endif
 272         bn_correct_top(r);
 273         bn_correct_top(ret);
 274         bn_check_top(ret);
 275 
 276         return(1);
 277         }
 278 #endif  /* MONT_WORD */
 279 
 280 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 281              BN_CTX *ctx)
 282         {
 283         int retn=0;
 284 #ifdef MONT_WORD
 285         BIGNUM *t;
 286 
 287         BN_CTX_start(ctx);
 288         if ((t = BN_CTX_get(ctx)) && BN_copy(t,a))
 289                 retn = BN_from_montgomery_word(ret,t,mont);
 290         BN_CTX_end(ctx);
 291 #else /* !MONT_WORD */
 292         BIGNUM *t1,*t2;
 293 
 294         BN_CTX_start(ctx);
 295         t1 = BN_CTX_get(ctx);
 296         t2 = BN_CTX_get(ctx);
 297         if (t1 == NULL || t2 == NULL) goto err;
 298 
 299         if (!BN_copy(t1,a)) goto err;
 300         BN_mask_bits(t1,mont->ri);
 301 
 302         if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
 303         BN_mask_bits(t2,mont->ri);
 304 
 305         if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
 306         if (!BN_add(t2,a,t1)) goto err;
 307         if (!BN_rshift(ret,t2,mont->ri)) goto err;
 308 
 309         if (BN_ucmp(ret, &(mont->N)) >= 0)
 310                 {
 311                 if (!BN_usub(ret,ret,&(mont->N))) goto err;
 312                 }
 313         retn=1;
 314         bn_check_top(ret);
 315  err:
 316         BN_CTX_end(ctx);
 317 #endif /* MONT_WORD */
 318         return(retn);
 319         }
 320 
 321 BN_MONT_CTX *BN_MONT_CTX_new(void)
 322         {
 323         BN_MONT_CTX *ret;
 324 
 325         if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
 326                 return(NULL);
 327 
 328         BN_MONT_CTX_init(ret);
 329         ret->flags=BN_FLG_MALLOCED;
 330         return(ret);
 331         }
 332 
 333 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 334         {
 335         ctx->ri=0;
 336         BN_init(&(ctx->RR));
 337         BN_init(&(ctx->N));
 338         BN_init(&(ctx->Ni));
 339         ctx->n0[0] = ctx->n0[1] = 0;
 340         ctx->flags=0;
 341         }
 342 
 343 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 344         {
 345         if(mont == NULL)
 346             return;
 347 
 348         BN_free(&(mont->RR));
 349         BN_free(&(mont->N));
 350         BN_free(&(mont->Ni));
 351         if (mont->flags & BN_FLG_MALLOCED)
 352                 OPENSSL_free(mont);
 353         }
 354 
 355 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 356         {
 357         int ret = 0;
 358         BIGNUM *Ri,*R;
 359 
 360         BN_CTX_start(ctx);
 361         if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
 362         R= &(mont->RR);                                  /* grab RR as a temp */
 363         if (!BN_copy(&(mont->N),mod)) goto err;          /* Set N */
 364         mont->N.neg = 0;
 365 
 366 #ifdef MONT_WORD
 367                 {
 368                 BIGNUM tmod;
 369                 BN_ULONG buf[2];
 370 
 371                 BN_init(&tmod);
 372                 tmod.d=buf;
 373                 tmod.dmax=2;
 374                 tmod.neg=0;
 375 
 376                 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
 377 
 378 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
 379                 /* Only certain BN_BITS2<=32 platforms actually make use of
 380                  * n0[1], and we could use the #else case (with a shorter R
 381                  * value) for the others.  However, currently only the assembler
 382                  * files do know which is which. */
 383 
 384                 BN_zero(R);
 385                 if (!(BN_set_bit(R,2*BN_BITS2))) goto err;
 386 
 387                                                                 tmod.top=0;
 388                 if ((buf[0] = mod->d[0]))                    tmod.top=1;
 389                 if ((buf[1] = mod->top>1 ? mod->d[1] : 0))     tmod.top=2;
 390 
 391                 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
 392                         goto err;
 393                 if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */
 394                 if (!BN_is_zero(Ri))
 395                         {
 396                         if (!BN_sub_word(Ri,1)) goto err;
 397                         }
 398                 else /* if N mod word size == 1 */
 399                         {
 400                         if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL)
 401                                 goto err;
 402                         /* Ri-- (mod double word size) */
 403                         Ri->neg=0;
 404                         Ri->d[0]=BN_MASK2;
 405                         Ri->d[1]=BN_MASK2;
 406                         Ri->top=2;
 407                         }
 408                 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
 409                 /* Ni = (R*Ri-1)/N,
 410                  * keep only couple of least significant words: */
 411                 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 412                 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
 413 #else
 414                 BN_zero(R);
 415                 if (!(BN_set_bit(R,BN_BITS2))) goto err;        /* R */
 416 
 417                 buf[0]=mod->d[0]; /* tmod = N mod word size */
 418                 buf[1]=0;
 419                 tmod.top = buf[0] != 0 ? 1 : 0;
 420                                                         /* Ri = R^-1 mod N*/
 421                 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
 422                         goto err;
 423                 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
 424                 if (!BN_is_zero(Ri))
 425                         {
 426                         if (!BN_sub_word(Ri,1)) goto err;
 427                         }
 428                 else /* if N mod word size == 1 */
 429                         {
 430                         if (!BN_set_word(Ri,BN_MASK2)) goto err;  /* Ri-- (mod word size) */
 431                         }
 432                 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
 433                 /* Ni = (R*Ri-1)/N,
 434                  * keep only least significant word: */
 435                 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 436                 mont->n0[1] = 0;
 437 #endif
 438                 }
 439 #else /* !MONT_WORD */
 440                 { /* bignum version */
 441                 mont->ri=BN_num_bits(&mont->N);
 442                 BN_zero(R);
 443                 if (!BN_set_bit(R,mont->ri)) goto err;  /* R = 2^ri */
 444                                                         /* Ri = R^-1 mod N*/
 445                 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
 446                         goto err;
 447                 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
 448                 if (!BN_sub_word(Ri,1)) goto err;
 449                                                         /* Ni = (R*Ri-1) / N */
 450                 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
 451                 }
 452 #endif
 453 
 454         /* setup RR for conversions */
 455         BN_zero(&(mont->RR));
 456         if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
 457         if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
 458 
 459         ret = 1;
 460 err:
 461         BN_CTX_end(ctx);
 462         return ret;
 463         }
 464 
 465 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 466         {
 467         if (to == from) return(to);
 468 
 469         if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
 470         if (!BN_copy(&(to->N),&(from->N))) return NULL;
 471         if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
 472         to->ri=from->ri;
 473         to->n0[0]=from->n0[0];
 474         to->n0[1]=from->n0[1];
 475         return(to);
 476         }
 477 
 478 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
 479                                         const BIGNUM *mod, BN_CTX *ctx)
 480         {
 481         BN_MONT_CTX *ret;
 482 
 483         CRYPTO_r_lock(lock);
 484         ret = *pmont;
 485         CRYPTO_r_unlock(lock);
 486         if (ret)
 487                 return ret;
 488 
 489         /* We don't want to serialise globally while doing our lazy-init math in
 490          * BN_MONT_CTX_set. That punishes threads that are doing independent
 491          * things. Instead, punish the case where more than one thread tries to
 492          * lazy-init the same 'pmont', by having each do the lazy-init math work
 493          * independently and only use the one from the thread that wins the race
 494          * (the losers throw away the work they've done). */
 495         ret = BN_MONT_CTX_new();
 496         if (!ret)
 497                 return NULL;
 498         if (!BN_MONT_CTX_set(ret, mod, ctx))
 499                 {
 500                 BN_MONT_CTX_free(ret);
 501                 return NULL;
 502                 }
 503 
 504         /* The locked compare-and-set, after the local work is done. */
 505         CRYPTO_w_lock(lock);
 506         if (*pmont)
 507                 {
 508                 BN_MONT_CTX_free(ret);
 509                 ret = *pmont;
 510                 }
 511         else
 512                 *pmont = ret;
 513         CRYPTO_w_unlock(lock);
 514         return ret;
 515         }