crypto/libressl/crypto/bn/bn_prime.c

   1 /* $OpenBSD: bn_prime.c,v 1.22 2022/07/19 16:19:19 tb 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 #define LIBRESSL_HAS_BPSW
 120
 121 /* NB: these functions have been "upgraded", the deprecated versions (which are
 122  * compatibility wrappers using these functions) are in bn_depr.c.
 123  * - Geoff
 124  */
 125
 126 /* The quick sieve algorithm approach to weeding out primes is
 127  * Philip Zimmermann's, as implemented in PGP.  I have had a read of
 128  * his comments and implemented my own version.
 129  */
 130 #include "bn_prime.h"
 131
 132 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 133     const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
 134 static int probable_prime(BIGNUM *rnd, int bits);
 135 static int probable_prime_dh(BIGNUM *rnd, int bits,
 136     const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 137 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
 138     const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 139
 140 int
 141 BN_GENCB_call(BN_GENCB *cb, int a, int b)
 142 {
 143         /* No callback means continue */
 144         if (!cb)
 145                 return 1;
 146         switch (cb->ver) {
 147         case 1:
 148                 /* Deprecated-style callbacks */
 149                 if (!cb->cb.cb_1)
 150                         return 1;
 151                 cb->cb.cb_1(a, b, cb->arg);
 152                 return 1;
 153         case 2:
 154                 /* New-style callbacks */
 155                 return cb->cb.cb_2(a, b, cb);
 156         default:
 157                 break;
 158         }
 159         /* Unrecognised callback type */
 160         return 0;
 161 }
 162
 163 int
 164 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
 165     const BIGNUM *rem, BN_GENCB *cb)
 166 {
 167         BIGNUM *t;
 168         int found = 0;
 169         int i, j, c1 = 0;
 170         BN_CTX *ctx;
 171         int checks = 1;
 172
 173         if (bits < 2 || (bits == 2 && safe)) {
 174                 /*
 175                  * There are no prime numbers smaller than 2, and the smallest
 176                  * safe prime (7) spans three bits.
 177                  */
 178                 BNerror(BN_R_BITS_TOO_SMALL);
 179                 return 0;
 180         }
 181
 182         ctx = BN_CTX_new();
 183         if (ctx == NULL)
 184                 goto err;
 185         BN_CTX_start(ctx);
 186         if ((t = BN_CTX_get(ctx)) == NULL)
 187                 goto err;
 188
 189 #ifndef LIBRESSL_HAS_BPSW
 190         checks = BN_prime_checks_for_size(bits);
 191 #endif
 192
 193 loop:
 194         /* make a random number and set the top and bottom bits */
 195         if (add == NULL) {
 196                 if (!probable_prime(ret, bits))
 197                         goto err;
 198         } else {
 199                 if (safe) {
 200                         if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
 201                                 goto err;
 202                 } else {
 203                         if (!probable_prime_dh(ret, bits, add, rem, ctx))
 204                                 goto err;
 205                 }
 206         }
 207         /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
 208         if (!BN_GENCB_call(cb, 0, c1++))
 209                 /* aborted */
 210                 goto err;
 211
 212         if (!safe) {
 213                 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
 214                 if (i == -1)
 215                         goto err;
 216                 if (i == 0)
 217                         goto loop;
 218         } else {
 219                 /* for "safe prime" generation,
 220                  * check that (p-1)/2 is prime.
 221                  * Since a prime is odd, We just
 222                  * need to divide by 2 */
 223                 if (!BN_rshift1(t, ret))
 224                         goto err;
 225
 226                 for (i = 0; i < checks; i++) {
 227                         j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
 228                         if (j == -1)
 229                                 goto err;
 230                         if (j == 0)
 231                                 goto loop;
 232
 233                         j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
 234                         if (j == -1)
 235                                 goto err;
 236                         if (j == 0)
 237                                 goto loop;
 238
 239                         if (!BN_GENCB_call(cb, 2, c1 - 1))
 240                                 goto err;
 241                         /* We have a safe prime test pass */
 242                 }
 243         }
 244         /* we have a prime :-) */
 245         found = 1;
 246
 247 err:
 248         if (ctx != NULL) {
 249                 BN_CTX_end(ctx);
 250                 BN_CTX_free(ctx);
 251         }
 252         bn_check_top(ret);
 253         return found;
 254 }
 255
 256 int
 257 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
 258 {
 259         return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
 260 }
 261
 262 int
 263 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 264     int do_trial_division, BN_GENCB *cb)
 265 {
 266         BN_CTX *ctx = NULL;
 267         BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 268         BN_MONT_CTX *mont = NULL;
 269         const BIGNUM *A = NULL;
 270         int i, j, k;
 271         int ret = -1;
 272
 273 #ifdef LIBRESSL_HAS_BPSW
 274         int is_prime;
 275
 276         /* XXX - tickle BN_GENCB in bn_is_prime_bpsw(). */
 277         if (!bn_is_prime_bpsw(&is_prime, a, ctx_passed))
 278                 return -1;
 279
 280         return is_prime;
 281 #endif
 282
 283         if (BN_cmp(a, BN_value_one()) <= 0)
 284                 return 0;
 285
 286         if (checks == BN_prime_checks)
 287                 checks = BN_prime_checks_for_size(BN_num_bits(a));
 288
 289         /* first look for small factors */
 290         if (!BN_is_odd(a))
 291                 /* a is even => a is prime if and only if a == 2 */
 292                 return BN_is_word(a, 2);
 293         if (do_trial_division) {
 294                 for (i = 1; i < NUMPRIMES; i++) {
 295                         BN_ULONG mod = BN_mod_word(a, primes[i]);
 296                         if (mod == (BN_ULONG)-1)
 297                                 goto err;
 298                         if (mod == 0)
 299                                 return BN_is_word(a, primes[i]);
 300                 }
 301                 if (!BN_GENCB_call(cb, 1, -1))
 302                         goto err;
 303         }
 304
 305         if (ctx_passed != NULL)
 306                 ctx = ctx_passed;
 307         else if ((ctx = BN_CTX_new()) == NULL)
 308                 goto err;
 309         BN_CTX_start(ctx);
 310
 311         /* A := abs(a) */
 312         if (a->neg) {
 313                 BIGNUM *t;
 314                 if ((t = BN_CTX_get(ctx)) == NULL)
 315                         goto err;
 316                 BN_copy(t, a);
 317                 t->neg = 0;
 318                 A = t;
 319         } else
 320                 A = a;
 321         if ((A1 = BN_CTX_get(ctx)) == NULL)
 322                 goto err;
 323         if ((A1_odd = BN_CTX_get(ctx)) == NULL)
 324                 goto err;
 325         if ((check = BN_CTX_get(ctx)) == NULL)
 326                 goto err;
 327
 328         /* compute A1 := A - 1 */
 329         if (!BN_copy(A1, A))
 330                 goto err;
 331         if (!BN_sub_word(A1, 1))
 332                 goto err;
 333         if (BN_is_zero(A1)) {
 334                 ret = 0;
 335                 goto err;
 336         }
 337
 338         /* write  A1  as  A1_odd * 2^k */
 339         k = 1;
 340         while (!BN_is_bit_set(A1, k))
 341                 k++;
 342         if (!BN_rshift(A1_odd, A1, k))
 343                 goto err;
 344
 345         /* Montgomery setup for computations mod A */
 346         mont = BN_MONT_CTX_new();
 347         if (mont == NULL)
 348                 goto err;
 349         if (!BN_MONT_CTX_set(mont, A, ctx))
 350                 goto err;
 351
 352         for (i = 0; i < checks; i++) {
 353                 if (!BN_pseudo_rand_range(check, A1))
 354                         goto err;
 355                 if (!BN_add_word(check, 1))
 356                         goto err;
 357                 /* now 1 <= check < A */
 358
 359                 j = witness(check, A, A1, A1_odd, k, ctx, mont);
 360                 if (j == -1)
 361                         goto err;
 362                 if (j) {
 363                         ret = 0;
 364                         goto err;
 365                 }
 366                 if (!BN_GENCB_call(cb, 1, i))
 367                         goto err;
 368         }
 369         ret = 1;
 370
 371 err:
 372         if (ctx != NULL) {
 373                 BN_CTX_end(ctx);
 374                 if (ctx_passed == NULL)
 375                         BN_CTX_free(ctx);
 376         }
 377         BN_MONT_CTX_free(mont);
 378
 379         return (ret);
 380 }
 381
 382 static int
 383 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
 384     int k, BN_CTX *ctx, BN_MONT_CTX *mont)
 385 {
 386         if (!BN_mod_exp_mont_ct(w, w, a1_odd, a, ctx, mont))
 387                 /* w := w^a1_odd mod a */
 388                 return -1;
 389         if (BN_is_one(w))
 390                 return 0; /* probably prime */
 391         if (BN_cmp(w, a1) == 0)
 392                 return 0; /* w == -1 (mod a),  'a' is probably prime */
 393         while (--k) {
 394                 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 395                         return -1;
 396                 if (BN_is_one(w))
 397                         return 1; /* 'a' is composite, otherwise a previous 'w' would
 398                                    * have been == -1 (mod 'a') */
 399                 if (BN_cmp(w, a1) == 0)
 400                         return 0; /* w == -1 (mod a), 'a' is probably prime */
 401         }
 402         /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
 403          * and it is neither -1 nor +1 -- so 'a' cannot be prime */
 404         bn_check_top(w);
 405         return 1;
 406 }
 407
 408 static int
 409 probable_prime(BIGNUM *rnd, int bits)
 410 {
 411         int i;
 412         prime_t mods[NUMPRIMES];
 413         BN_ULONG delta, maxdelta;
 414
 415 again:
 416         if (!BN_rand(rnd, bits, 1, 1))
 417                 return (0);
 418         /* we now have a random number 'rand' to test. */
 419         for (i = 1; i < NUMPRIMES; i++) {
 420                 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 421                 if (mod == (BN_ULONG)-1)
 422                         return (0);
 423                 mods[i] = (prime_t)mod;
 424         }
 425         maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
 426         delta = 0;
 427 loop:
 428         for (i = 1; i < NUMPRIMES; i++) {
 429                 /* check that rnd is not a prime and also
 430                  * that gcd(rnd-1,primes) == 1 (except for 2) */
 431                 if (((mods[i] + delta) % primes[i]) <= 1) {
 432                         delta += 2;
 433                         if (delta > maxdelta)
 434                                 goto again;
 435                         goto loop;
 436                 }
 437         }
 438         if (!BN_add_word(rnd, delta))
 439                 return (0);
 440         bn_check_top(rnd);
 441         return (1);
 442 }
 443
 444 static int
 445 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
 446     BN_CTX *ctx)
 447 {
 448         int i, ret = 0;
 449         BIGNUM *t1;
 450
 451         BN_CTX_start(ctx);
 452         if ((t1 = BN_CTX_get(ctx)) == NULL)
 453                 goto err;
 454
 455         if (!BN_rand(rnd, bits, 0, 1))
 456                 goto err;
 457
 458         /* we need ((rnd-rem) % add) == 0 */
 459
 460         if (!BN_mod_ct(t1, rnd, add, ctx))
 461                 goto err;
 462         if (!BN_sub(rnd, rnd, t1))
 463                 goto err;
 464         if (rem == NULL) {
 465                 if (!BN_add_word(rnd, 1))
 466                         goto err;
 467         } else {
 468                 if (!BN_add(rnd, rnd, rem))
 469                         goto err;
 470         }
 471
 472         /* we now have a random number 'rand' to test. */
 473
 474 loop:
 475         for (i = 1; i < NUMPRIMES; i++) {
 476                 /* check that rnd is a prime */
 477                 BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 478                 if (mod == (BN_ULONG)-1)
 479                         goto err;
 480                 if (mod <= 1) {
 481                         if (!BN_add(rnd, rnd, add))
 482                                 goto err;
 483                         goto loop;
 484                 }
 485         }
 486         ret = 1;
 487
 488 err:
 489         BN_CTX_end(ctx);
 490         bn_check_top(rnd);
 491         return (ret);
 492 }
 493
 494 static int
 495 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
 496     const BIGNUM *rem, BN_CTX *ctx)
 497 {
 498         int i, ret = 0;
 499         BIGNUM *t1, *qadd, *q;
 500
 501         bits--;
 502         BN_CTX_start(ctx);
 503         if ((t1 = BN_CTX_get(ctx)) == NULL)
 504                 goto err;
 505         if ((q = BN_CTX_get(ctx)) == NULL)
 506                 goto err;
 507         if ((qadd = BN_CTX_get(ctx)) == NULL)
 508                 goto err;
 509
 510         if (!BN_rshift1(qadd, padd))
 511                 goto err;
 512
 513         if (!BN_rand(q, bits, 0, 1))
 514                 goto err;
 515
 516         /* we need ((rnd-rem) % add) == 0 */
 517         if (!BN_mod_ct(t1, q,qadd, ctx))
 518                 goto err;
 519         if (!BN_sub(q, q, t1))
 520                 goto err;
 521         if (rem == NULL) {
 522                 if (!BN_add_word(q, 1))
 523                         goto err;
 524         } else {
 525                 if (!BN_rshift1(t1, rem))
 526                         goto err;
 527                 if (!BN_add(q, q, t1))
 528                         goto err;
 529         }
 530
 531         /* we now have a random number 'rand' to test. */
 532         if (!BN_lshift1(p, q))
 533                 goto err;
 534         if (!BN_add_word(p, 1))
 535                 goto err;
 536
 537 loop:
 538         for (i = 1; i < NUMPRIMES; i++) {
 539                 /* check that p and q are prime */
 540                 /* check that for p and q
 541                  * gcd(p-1,primes) == 1 (except for 2) */
 542                 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
 543                 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
 544                 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
 545                         goto err;
 546                 if (pmod == 0 || qmod == 0) {
 547                         if (!BN_add(p, p, padd))
 548                                 goto err;
 549                         if (!BN_add(q, q, qadd))
 550                                 goto err;
 551                         goto loop;
 552                 }
 553         }
 554         ret = 1;
 555
 556 err:
 557         BN_CTX_end(ctx);
 558         bn_check_top(p);
 559         return (ret);
 560 }