lib/libcrypto/bn/bn_prime.c

   1 /* $OpenBSD: bn_prime.c,v 1.18 2017/01/29 17:49:22 beck Exp $ */
   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) 1998-2001 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 #include <stdio.h>
 113 #include <time.h>
 114
 115 #include <openssl/err.h>
 116
 117 #include "bn_lcl.h"
 118
 119 /* NB: these functions have been "upgraded", the deprecated versions (which are
 120  * compatibility wrappers using these functions) are in bn_depr.c.
 121  * - Geoff
 122  */
 123
 124 /* The quick sieve algorithm approach to weeding out primes is
 125  * Philip Zimmermann's, as implemented in PGP.  I have had a read of
 126  * his comments and implemented my own version.
 127  */
 128 #include "bn_prime.h"
 129
 130 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 131     const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
 132 static int probable_prime(BIGNUM *rnd, int bits);
 133 static int probable_prime_dh(BIGNUM *rnd, int bits,
 134     const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 135 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
 136     const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 137
 138 int
 139 BN_GENCB_call(BN_GENCB *cb, int a, int b)
 140 {
 141         /* No callback means continue */
 142         if (!cb)
 143                 return 1;
 144         switch (cb->ver) {
 145         case 1:
 146                 /* Deprecated-style callbacks */
 147                 if (!cb->cb.cb_1)
 148                         return 1;
 149                 cb->cb.cb_1(a, b, cb->arg);
 150                 return 1;
 151         case 2:
 152                 /* New-style callbacks */
 153                 return cb->cb.cb_2(a, b, cb);
 154         default:
 155                 break;
 156         }
 157         /* Unrecognised callback type */
 158         return 0;
 159 }
 160
 161 int
 162 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
 163     const BIGNUM *rem, BN_GENCB *cb)
 164 {
 165         BIGNUM *t;
 166         int found = 0;
 167         int i, j, c1 = 0;
 168         BN_CTX *ctx;
 169         int checks;
 170
 171         if (bits < 2 || (bits == 2 && safe)) {
 172                 /*
 173                  * There are no prime numbers smaller than 2, and the smallest
 174                  * safe prime (7) spans three bits.
 175                  */
 176                 BNerror(BN_R_BITS_TOO_SMALL);
 177                 return 0;
 178         }
 179
 180         ctx = BN_CTX_new();
 181         if (ctx == NULL)
 182                 goto err;
 183         BN_CTX_start(ctx);
 184         if ((t = BN_CTX_get(ctx)) == NULL)
 185                 goto err;
 186
 187         checks = BN_prime_checks_for_size(bits);
 188
 189 loop:
 190         /* make a random number and set the top and bottom bits */
 191         if (add == NULL) {
 192                 if (!probable_prime(ret, bits))
 193                         goto err;
 194         } else {
 195                 if (safe) {
 196                         if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
 197                                 goto err;
 198                 } else {
 199                         if (!probable_prime_dh(ret, bits, add, rem, ctx))
 200                                 goto err;
 201                 }
 202         }
 203         /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
 204         if (!BN_GENCB_call(cb, 0, c1++))
 205                 /* aborted */
 206                 goto err;
 207
 208         if (!safe) {
 209                 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
 210                 if (i == -1)
 211                         goto err;
 212                 if (i == 0)
 213                         goto loop;
 214         } else {
 215                 /* for "safe prime" generation,
 216                  * check that (p-1)/2 is prime.
 217                  * Since a prime is odd, We just
 218                  * need to divide by 2 */
 219                 if (!BN_rshift1(t, ret))
 220                         goto err;
 221
 222                 for (i = 0; i < checks; i++) {
 223                         j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
 224                         if (j == -1)
 225                                 goto err;
 226                         if (j == 0)
 227                                 goto loop;
 228
 229                         j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
 230                         if (j == -1)
 231                                 goto err;
 232                         if (j == 0)
 233                                 goto loop;
 234
 235                         if (!BN_GENCB_call(cb, 2, c1 - 1))
 236                                 goto err;
 237                         /* We have a safe prime test pass */
 238                 }
 239         }
 240         /* we have a prime :-) */
 241         found = 1;
 242
 243 err:
 244         if (ctx != NULL) {
 245                 BN_CTX_end(ctx);
 246                 BN_CTX_free(ctx);
 247         }
 248         bn_check_top(ret);
 249         return found;
 250 }
 251
 252 int
 253 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
 254 {
 255         return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
 256 }
 257
 258 int
 259 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 260     int do_trial_division, BN_GENCB *cb)
 261 {
 262         int i, j, ret = -1;
 263         int k;
 264         BN_CTX *ctx = NULL;
 265         BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 266         BN_MONT_CTX *mont = NULL;
 267         const BIGNUM *A = NULL;
 268
 269         if (BN_cmp(a, BN_value_one()) <= 0)
 270                 return 0;
 271
 272         if (checks == BN_prime_checks)
 273                 checks = BN_prime_checks_for_size(BN_num_bits(a));
 274
 275         /* first look for small factors */
 276         if (!BN_is_odd(a))
 277                 /* a is even => a is prime if and only if a == 2 */
 278                 return BN_is_word(a, 2);
 279         if (do_trial_division) {
 280                 for (i = 1; i < NUMPRIMES; i++) {
 281                         BN_ULONG mod = BN_mod_word(a, primes[i]);
 282                         if (mod == (BN_ULONG)-1)
 283                                 goto err;
 284                         if (mod == 0)
 285                                 return 0;
 286                 }
 287                 if (!BN_GENCB_call(cb, 1, -1))
 288                         goto err;
 289         }
 290
 291         if (ctx_passed != NULL)
 292                 ctx = ctx_passed;
 293         else if ((ctx = BN_CTX_new()) == NULL)
 294                 goto err;
 295         BN_CTX_start(ctx);
 296
 297         /* A := abs(a) */
 298         if (a->neg) {
 299                 BIGNUM *t;
 300                 if ((t = BN_CTX_get(ctx)) == NULL)
 301                         goto err;
 302                 BN_copy(t, a);
 303                 t->neg = 0;
 304                 A = t;
 305         } else
 306                 A = a;
 307         if ((A1 = BN_CTX_get(ctx)) == NULL)
 308                 goto err;
 309         if ((A1_odd = BN_CTX_get(ctx)) == NULL)
 310                 goto err;
 311         if ((check = BN_CTX_get(ctx)) == NULL)
 312                 goto err;
 313
 314         /* compute A1 := A - 1 */
 315         if (!BN_copy(A1, A))
 316                 goto err;
 317         if (!BN_sub_word(A1, 1))
 318                 goto err;
 319         if (BN_is_zero(A1)) {
 320                 ret = 0;
 321                 goto err;
 322         }
 323
 324         /* write  A1  as  A1_odd * 2^k */
 325         k = 1;
 326         while (!BN_is_bit_set(A1, k))
 327                 k++;
 328         if (!BN_rshift(A1_odd, A1, k))
 329                 goto err;
 330
 331         /* Montgomery setup for computations mod A */
 332         mont = BN_MONT_CTX_new();
 333         if (mont == NULL)
 334                 goto err;
 335         if (!BN_MONT_CTX_set(mont, A, ctx))
 336                 goto err;
 337
 338         for (i = 0; i < checks; i++) {
 339                 if (!BN_pseudo_rand_range(check, A1))
 340                         goto err;
 341                 if (!BN_add_word(check, 1))
 342                         goto err;
 343                 /* now 1 <= check < A */
 344
 345                 j = witness(check, A, A1, A1_odd, k, ctx, mont);
 346                 if (j == -1)
 347                         goto err;
 348                 if (j) {
 349                         ret = 0;
 350                         goto err;
 351                 }
 352                 if (!BN_GENCB_call(cb, 1, i))
 353                         goto err;
 354         }
 355         ret = 1;
 356
 357 err:
 358         if (ctx != NULL) {
 359                 BN_CTX_end(ctx);
 360                 if (ctx_passed == NULL)
 361                         BN_CTX_free(ctx);
 362         }
 363         BN_MONT_CTX_free(mont);
 364
 365         return (ret);
 366 }
 367
 368 static int
 369 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
 370     int k, BN_CTX *ctx, BN_MONT_CTX *mont)
 371 {
 372         if (!BN_mod_exp_mont_ct(w, w, a1_odd, a, ctx, mont))
 373                 /* w := w^a1_odd mod a */
 374                 return -1;
 375         if (BN_is_one(w))
 376                 return 0; /* probably prime */
 377         if (BN_cmp(w, a1) == 0)
 378                 return 0; /* w == -1 (mod a),  'a' is probably prime */
 379         while (--k) {
 380                 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 381                         return -1;
 382                 if (BN_is_one(w))
 383                         return 1; /* 'a' is composite, otherwise a previous 'w' would
 384                                    * have been == -1 (mod 'a') */
 385                 if (BN_cmp(w, a1) == 0)
 386                         return 0; /* w == -1 (mod a), 'a' is probably prime */
 387         }
 388         /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
 389          * and it is neither -1 nor +1 -- so 'a' cannot be prime */
 390         bn_check_top(w);
 391         return 1;
 392 }
 393
 394 static int
 395 probable_prime(BIGNUM *rnd, int bits)
 396 {
 397         int i;
 398         prime_t mods[NUMPRIMES];
 399         BN_ULONG delta, maxdelta;
 400
 401 again:
 402         if (!BN_rand(rnd, bits, 1, 1))
 403                 return (0);
 404         /* we now have a random number 'rand' to test. */
 405         for (i = 1; i < NUMPRIMES; i++) {
 406                 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 407                 if (mod == (BN_ULONG)-1)
 408                         return (0);
 409                 mods[i] = (prime_t)mod;
 410         }
 411         maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
 412         delta = 0;
 413 loop:
 414         for (i = 1; i < NUMPRIMES; i++) {
 415                 /* check that rnd is not a prime and also
 416                  * that gcd(rnd-1,primes) == 1 (except for 2) */
 417                 if (((mods[i] + delta) % primes[i]) <= 1) {
 418                         delta += 2;
 419                         if (delta > maxdelta)
 420                                 goto again;
 421                         goto loop;
 422                 }
 423         }
 424         if (!BN_add_word(rnd, delta))
 425                 return (0);
 426         bn_check_top(rnd);
 427         return (1);
 428 }
 429
 430 static int
 431 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
 432     BN_CTX *ctx)
 433 {
 434         int i, ret = 0;
 435         BIGNUM *t1;
 436
 437         BN_CTX_start(ctx);
 438         if ((t1 = BN_CTX_get(ctx)) == NULL)
 439                 goto err;
 440
 441         if (!BN_rand(rnd, bits, 0, 1))
 442                 goto err;
 443
 444         /* we need ((rnd-rem) % add) == 0 */
 445
 446         if (!BN_mod_ct(t1, rnd, add, ctx))
 447                 goto err;
 448         if (!BN_sub(rnd, rnd, t1))
 449                 goto err;
 450         if (rem == NULL) {
 451                 if (!BN_add_word(rnd, 1))
 452                         goto err;
 453         } else {
 454                 if (!BN_add(rnd, rnd, rem))
 455                         goto err;
 456         }
 457
 458         /* we now have a random number 'rand' to test. */
 459
 460 loop:
 461         for (i = 1; i < NUMPRIMES; i++) {
 462                 /* check that rnd is a prime */
 463                 BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 464                 if (mod == (BN_ULONG)-1)
 465                         goto err;
 466                 if (mod <= 1) {
 467                         if (!BN_add(rnd, rnd, add))
 468                                 goto err;
 469                         goto loop;
 470                 }
 471         }
 472         ret = 1;
 473
 474 err:
 475         BN_CTX_end(ctx);
 476         bn_check_top(rnd);
 477         return (ret);
 478 }
 479
 480 static int
 481 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
 482     const BIGNUM *rem, BN_CTX *ctx)
 483 {
 484         int i, ret = 0;
 485         BIGNUM *t1, *qadd, *q;
 486
 487         bits--;
 488         BN_CTX_start(ctx);
 489         if ((t1 = BN_CTX_get(ctx)) == NULL)
 490                 goto err;
 491         if ((q = BN_CTX_get(ctx)) == NULL)
 492                 goto err;
 493         if ((qadd = BN_CTX_get(ctx)) == NULL)
 494                 goto err;
 495
 496         if (!BN_rshift1(qadd, padd))
 497                 goto err;
 498
 499         if (!BN_rand(q, bits, 0, 1))
 500                 goto err;
 501
 502         /* we need ((rnd-rem) % add) == 0 */
 503         if (!BN_mod_ct(t1, q,qadd, ctx))
 504                 goto err;
 505         if (!BN_sub(q, q, t1))
 506                 goto err;
 507         if (rem == NULL) {
 508                 if (!BN_add_word(q, 1))
 509                         goto err;
 510         } else {
 511                 if (!BN_rshift1(t1, rem))
 512                         goto err;
 513                 if (!BN_add(q, q, t1))
 514                         goto err;
 515         }
 516
 517         /* we now have a random number 'rand' to test. */
 518         if (!BN_lshift1(p, q))
 519                 goto err;
 520         if (!BN_add_word(p, 1))
 521                 goto err;
 522
 523 loop:
 524         for (i = 1; i < NUMPRIMES; i++) {
 525                 /* check that p and q are prime */
 526                 /* check that for p and q
 527                  * gcd(p-1,primes) == 1 (except for 2) */
 528                 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
 529                 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
 530                 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
 531                         goto err;
 532                 if (pmod == 0 || qmod == 0) {
 533                         if (!BN_add(p, p, padd))
 534                                 goto err;
 535                         if (!BN_add(q, q, qadd))
 536                                 goto err;
 537                         goto loop;
 538                 }
 539         }
 540         ret = 1;
 541
 542 err:
 543         BN_CTX_end(ctx);
 544         bn_check_top(p);
 545         return (ret);
 546 }