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  * 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 "internal/cryptlib.h"
 120 #include "bn_lcl.h"
 121
 122 #define MONT_WORD               /* use the faster word-based algorithm */
 123
 124 #ifdef MONT_WORD
 125 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
 126 #endif
 127
 128 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 129                           BN_MONT_CTX *mont, BN_CTX *ctx)
 130 {
 131     BIGNUM *tmp;
 132     int ret = 0;
 133 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
 134     int num = mont->N.top;
 135
 136     if (num > 1 && a->top == num && b->top == num) {
 137         if (bn_wexpand(r, num) == NULL)
 138             return (0);
 139         if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
 140             r->neg = a->neg ^ b->neg;
 141             r->top = num;
 142             bn_correct_top(r);
 143             return (1);
 144         }
 145     }
 146 #endif
 147
 148     BN_CTX_start(ctx);
 149     tmp = BN_CTX_get(ctx);
 150     if (tmp == NULL)
 151         goto err;
 152
 153     bn_check_top(tmp);
 154     if (a == b) {
 155         if (!BN_sqr(tmp, a, ctx))
 156             goto err;
 157     } else {
 158         if (!BN_mul(tmp, a, b, ctx))
 159             goto err;
 160     }
 161     /* reduce from aRR to aR */
 162 #ifdef MONT_WORD
 163     if (!BN_from_montgomery_word(r, tmp, mont))
 164         goto err;
 165 #else
 166     if (!BN_from_montgomery(r, tmp, mont, ctx))
 167         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) {
 186         ret->top = 0;
 187         return (1);
 188     }
 189
 190     max = (2 * nl);             /* carry is stored separately */
 191     if (bn_wexpand(r, max) == NULL)
 192         return (0);
 193
 194     r->neg ^= n->neg;
 195     np = n->d;
 196     rp = r->d;
 197
 198     /* clear the top words of T */
 199     i = max - r->top;
 200     if (i)
 201         memset(&rp[r->top], 0, sizeof(*rp) * i);
 202
 203     r->top = max;
 204     n0 = mont->n0[0];
 205
 206     for (carry = 0, i = 0; i < nl; i++, rp++) {
 207         v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
 208         v = (v + carry + rp[nl]) & BN_MASK2;
 209         carry |= (v != rp[nl]);
 210         carry &= (v <= rp[nl]);
 211         rp[nl] = v;
 212     }
 213
 214     if (bn_wexpand(ret, nl) == NULL)
 215         return (0);
 216     ret->top = nl;
 217     ret->neg = r->neg;
 218
 219     rp = ret->d;
 220     ap = &(r->d[nl]);
 221
 222 # define BRANCH_FREE 1
 223 # if BRANCH_FREE
 224     {
 225         BN_ULONG *nrp;
 226         size_t m;
 227
 228         v = bn_sub_words(rp, ap, np, nl) - carry;
 229         /*
 230          * if subtraction result is real, then trick unconditional memcpy
 231          * below to perform in-place "refresh" instead of actual copy.
 232          */
 233         m = (0 - (size_t)v);
 234         nrp =
 235             (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
 236
 237         for (i = 0, nl -= 4; i < nl; i += 4) {
 238             BN_ULONG t1, t2, t3, t4;
 239
 240             t1 = nrp[i + 0];
 241             t2 = nrp[i + 1];
 242             t3 = nrp[i + 2];
 243             ap[i + 0] = 0;
 244             t4 = nrp[i + 3];
 245             ap[i + 1] = 0;
 246             rp[i + 0] = t1;
 247             ap[i + 2] = 0;
 248             rp[i + 1] = t2;
 249             ap[i + 3] = 0;
 250             rp[i + 2] = t3;
 251             rp[i + 3] = t4;
 252         }
 253         for (nl += 4; i < nl; i++)
 254             rp[i] = nrp[i], ap[i] = 0;
 255     }
 256 # else
 257     if (bn_sub_words(rp, ap, np, nl) - carry)
 258         memcpy(rp, ap, nl * sizeof(BN_ULONG));
 259 # endif
 260     bn_correct_top(r);
 261     bn_correct_top(ret);
 262     bn_check_top(ret);
 263
 264     return (1);
 265 }
 266 #endif                          /* MONT_WORD */
 267
 268 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 269                        BN_CTX *ctx)
 270 {
 271     int retn = 0;
 272 #ifdef MONT_WORD
 273     BIGNUM *t;
 274
 275     BN_CTX_start(ctx);
 276     if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
 277         retn = BN_from_montgomery_word(ret, t, mont);
 278     BN_CTX_end(ctx);
 279 #else                           /* !MONT_WORD */
 280     BIGNUM *t1, *t2;
 281
 282     BN_CTX_start(ctx);
 283     t1 = BN_CTX_get(ctx);
 284     t2 = BN_CTX_get(ctx);
 285     if (t1 == NULL || t2 == NULL)
 286         goto err;
 287
 288     if (!BN_copy(t1, a))
 289         goto err;
 290     BN_mask_bits(t1, mont->ri);
 291
 292     if (!BN_mul(t2, t1, &mont->Ni, ctx))
 293         goto err;
 294     BN_mask_bits(t2, mont->ri);
 295
 296     if (!BN_mul(t1, t2, &mont->N, ctx))
 297         goto err;
 298     if (!BN_add(t2, a, t1))
 299         goto err;
 300     if (!BN_rshift(ret, t2, mont->ri))
 301         goto err;
 302
 303     if (BN_ucmp(ret, &(mont->N)) >= 0) {
 304         if (!BN_usub(ret, ret, &(mont->N)))
 305             goto err;
 306     }
 307     retn = 1;
 308     bn_check_top(ret);
 309  err:
 310     BN_CTX_end(ctx);
 311 #endif                          /* MONT_WORD */
 312     return (retn);
 313 }
 314
 315 BN_MONT_CTX *BN_MONT_CTX_new(void)
 316 {
 317     BN_MONT_CTX *ret;
 318
 319     if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
 320         return (NULL);
 321
 322     BN_MONT_CTX_init(ret);
 323     ret->flags = BN_FLG_MALLOCED;
 324     return (ret);
 325 }
 326
 327 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 328 {
 329     ctx->ri = 0;
 330     BN_init(&(ctx->RR));
 331     BN_init(&(ctx->N));
 332     BN_init(&(ctx->Ni));
 333     ctx->n0[0] = ctx->n0[1] = 0;
 334     ctx->flags = 0;
 335 }
 336
 337 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 338 {
 339     if (mont == NULL)
 340         return;
 341
 342     BN_clear_free(&(mont->RR));
 343     BN_clear_free(&(mont->N));
 344     BN_clear_free(&(mont->Ni));
 345     if (mont->flags & BN_FLG_MALLOCED)
 346         OPENSSL_free(mont);
 347 }
 348
 349 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 350 {
 351     int ret = 0;
 352     BIGNUM *Ri, *R;
 353
 354     if (BN_is_zero(mod))
 355         return 0;
 356
 357     BN_CTX_start(ctx);
 358     if ((Ri = BN_CTX_get(ctx)) == NULL)
 359         goto err;
 360     R = &(mont->RR);            /* grab RR as a temp */
 361     if (!BN_copy(&(mont->N), mod))
 362         goto err;               /* Set N */
 363     mont->N.neg = 0;
 364
 365 #ifdef MONT_WORD
 366     {
 367         BIGNUM tmod;
 368         BN_ULONG buf[2];
 369
 370         BN_init(&tmod);
 371         tmod.d = buf;
 372         tmod.dmax = 2;
 373         tmod.neg = 0;
 374
 375         mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
 376
 377 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
 378         /*
 379          * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
 380          * and we could use the #else case (with a shorter R value) for the
 381          * others.  However, currently only the assembler files do know which
 382          * is which.
 383          */
 384
 385         BN_zero(R);
 386         if (!(BN_set_bit(R, 2 * BN_BITS2)))
 387             goto err;
 388
 389         tmod.top = 0;
 390         if ((buf[0] = mod->d[0]))
 391             tmod.top = 1;
 392         if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
 393             tmod.top = 2;
 394
 395         if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 396             goto err;
 397         if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
 398             goto err;           /* R*Ri */
 399         if (!BN_is_zero(Ri)) {
 400             if (!BN_sub_word(Ri, 1))
 401                 goto err;
 402         } else {                /* if N mod word size == 1 */
 403
 404             if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
 405                 goto err;
 406             /* Ri-- (mod double word size) */
 407             Ri->neg = 0;
 408             Ri->d[0] = BN_MASK2;
 409             Ri->d[1] = BN_MASK2;
 410             Ri->top = 2;
 411         }
 412         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 413             goto err;
 414         /*
 415          * Ni = (R*Ri-1)/N, keep only couple of least significant words:
 416          */
 417         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 418         mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
 419 # else
 420         BN_zero(R);
 421         if (!(BN_set_bit(R, BN_BITS2)))
 422             goto err;           /* R */
 423
 424         buf[0] = mod->d[0];     /* tmod = N mod word size */
 425         buf[1] = 0;
 426         tmod.top = buf[0] != 0 ? 1 : 0;
 427         /* Ri = R^-1 mod N */
 428         if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 429             goto err;
 430         if (!BN_lshift(Ri, Ri, BN_BITS2))
 431             goto err;           /* R*Ri */
 432         if (!BN_is_zero(Ri)) {
 433             if (!BN_sub_word(Ri, 1))
 434                 goto err;
 435         } else {                /* if N mod word size == 1 */
 436
 437             if (!BN_set_word(Ri, BN_MASK2))
 438                 goto err;       /* Ri-- (mod word size) */
 439         }
 440         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 441             goto err;
 442         /*
 443          * Ni = (R*Ri-1)/N, keep only least significant word:
 444          */
 445         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 446         mont->n0[1] = 0;
 447 # endif
 448     }
 449 #else                           /* !MONT_WORD */
 450     {                           /* bignum version */
 451         mont->ri = BN_num_bits(&mont->N);
 452         BN_zero(R);
 453         if (!BN_set_bit(R, mont->ri))
 454             goto err;           /* R = 2^ri */
 455         /* Ri = R^-1 mod N */
 456         if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
 457             goto err;
 458         if (!BN_lshift(Ri, Ri, mont->ri))
 459             goto err;           /* R*Ri */
 460         if (!BN_sub_word(Ri, 1))
 461             goto err;
 462         /*
 463          * Ni = (R*Ri-1) / N
 464          */
 465         if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
 466             goto err;
 467     }
 468 #endif
 469
 470     /* setup RR for conversions */
 471     BN_zero(&(mont->RR));
 472     if (!BN_set_bit(&(mont->RR), mont->ri * 2))
 473         goto err;
 474     if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
 475         goto err;
 476
 477     ret = 1;
 478  err:
 479     BN_CTX_end(ctx);
 480     return ret;
 481 }
 482
 483 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 484 {
 485     if (to == from)
 486         return (to);
 487
 488     if (!BN_copy(&(to->RR), &(from->RR)))
 489         return NULL;
 490     if (!BN_copy(&(to->N), &(from->N)))
 491         return NULL;
 492     if (!BN_copy(&(to->Ni), &(from->Ni)))
 493         return NULL;
 494     to->ri = from->ri;
 495     to->n0[0] = from->n0[0];
 496     to->n0[1] = from->n0[1];
 497     return (to);
 498 }
 499
 500 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
 501                                     const BIGNUM *mod, BN_CTX *ctx)
 502 {
 503     BN_MONT_CTX *ret;
 504
 505     CRYPTO_r_lock(lock);
 506     ret = *pmont;
 507     CRYPTO_r_unlock(lock);
 508     if (ret)
 509         return ret;
 510
 511     /*
 512      * We don't want to serialise globally while doing our lazy-init math in
 513      * BN_MONT_CTX_set. That punishes threads that are doing independent
 514      * things. Instead, punish the case where more than one thread tries to
 515      * lazy-init the same 'pmont', by having each do the lazy-init math work
 516      * independently and only use the one from the thread that wins the race
 517      * (the losers throw away the work they've done).
 518      */
 519     ret = BN_MONT_CTX_new();
 520     if (ret == NULL)
 521         return NULL;
 522     if (!BN_MONT_CTX_set(ret, mod, ctx)) {
 523         BN_MONT_CTX_free(ret);
 524         return NULL;
 525     }
 526
 527     /* The locked compare-and-set, after the local work is done. */
 528     CRYPTO_w_lock(lock);
 529     if (*pmont) {
 530         BN_MONT_CTX_free(ret);
 531         ret = *pmont;
 532     } else
 533         *pmont = ret;
 534     CRYPTO_w_unlock(lock);
 535     return ret;
 536 }