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 } 561