1 /* $OpenBSD: bn_prime.c,v 1.12 2014/10/18 17:20:40 jsing 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 "bn_lcl.h" 116 117 /* NB: these functions have been "upgraded", the deprecated versions (which are 118 * compatibility wrappers using these functions) are in bn_depr.c. 119 * - Geoff 120 */ 121 122 /* The quick sieve algorithm approach to weeding out primes is 123 * Philip Zimmermann's, as implemented in PGP. I have had a read of 124 * his comments and implemented my own version. 125 */ 126 #include "bn_prime.h" 127 128 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 129 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); 130 static int probable_prime(BIGNUM *rnd, int bits); 131 static int probable_prime_dh(BIGNUM *rnd, int bits, 132 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 133 static int probable_prime_dh_safe(BIGNUM *rnd, int bits, 134 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 135 136 int 137 BN_GENCB_call(BN_GENCB *cb, int a, int b) 138 { 139 /* No callback means continue */ 140 if (!cb) 141 return 1; 142 switch (cb->ver) { 143 case 1: 144 /* Deprecated-style callbacks */ 145 if (!cb->cb.cb_1) 146 return 1; 147 cb->cb.cb_1(a, b, cb->arg); 148 return 1; 149 case 2: 150 /* New-style callbacks */ 151 return cb->cb.cb_2(a, b, cb); 152 default: 153 break; 154 } 155 /* Unrecognised callback type */ 156 return 0; 157 } 158 159 int 160 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 161 const BIGNUM *rem, BN_GENCB *cb) 162 { 163 BIGNUM *t; 164 int found = 0; 165 int i, j, c1 = 0; 166 BN_CTX *ctx; 167 int checks = BN_prime_checks_for_size(bits); 168 169 ctx = BN_CTX_new(); 170 if (ctx == NULL) 171 goto err; 172 BN_CTX_start(ctx); 173 t = BN_CTX_get(ctx); 174 if (!t) 175 goto err; 176 loop: 177 /* make a random number and set the top and bottom bits */ 178 if (add == NULL) { 179 if (!probable_prime(ret, bits)) 180 goto err; 181 } else { 182 if (safe) { 183 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) 184 goto err; 185 } else { 186 if (!probable_prime_dh(ret, bits, add, rem, ctx)) 187 goto err; 188 } 189 } 190 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ 191 if (!BN_GENCB_call(cb, 0, c1++)) 192 /* aborted */ 193 goto err; 194 195 if (!safe) { 196 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); 197 if (i == -1) 198 goto err; 199 if (i == 0) 200 goto loop; 201 } else { 202 /* for "safe prime" generation, 203 * check that (p-1)/2 is prime. 204 * Since a prime is odd, We just 205 * need to divide by 2 */ 206 if (!BN_rshift1(t, ret)) 207 goto err; 208 209 for (i = 0; i < checks; i++) { 210 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); 211 if (j == -1) 212 goto err; 213 if (j == 0) 214 goto loop; 215 216 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); 217 if (j == -1) 218 goto err; 219 if (j == 0) 220 goto loop; 221 222 if (!BN_GENCB_call(cb, 2, c1 - 1)) 223 goto err; 224 /* We have a safe prime test pass */ 225 } 226 } 227 /* we have a prime :-) */ 228 found = 1; 229 230 err: 231 if (ctx != NULL) { 232 BN_CTX_end(ctx); 233 BN_CTX_free(ctx); 234 } 235 bn_check_top(ret); 236 return found; 237 } 238 239 int 240 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) 241 { 242 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 243 } 244 245 int 246 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 247 int do_trial_division, BN_GENCB *cb) 248 { 249 int i, j, ret = -1; 250 int k; 251 BN_CTX *ctx = NULL; 252 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ 253 BN_MONT_CTX *mont = NULL; 254 const BIGNUM *A = NULL; 255 256 if (BN_cmp(a, BN_value_one()) <= 0) 257 return 0; 258 259 if (checks == BN_prime_checks) 260 checks = BN_prime_checks_for_size(BN_num_bits(a)); 261 262 /* first look for small factors */ 263 if (!BN_is_odd(a)) 264 /* a is even => a is prime if and only if a == 2 */ 265 return BN_is_word(a, 2); 266 if (do_trial_division) { 267 for (i = 1; i < NUMPRIMES; i++) 268 if (BN_mod_word(a, primes[i]) == 0) 269 return 0; 270 if (!BN_GENCB_call(cb, 1, -1)) 271 goto err; 272 } 273 274 if (ctx_passed != NULL) 275 ctx = ctx_passed; 276 else if ((ctx = BN_CTX_new()) == NULL) 277 goto err; 278 BN_CTX_start(ctx); 279 280 /* A := abs(a) */ 281 if (a->neg) { 282 BIGNUM *t; 283 if ((t = BN_CTX_get(ctx)) == NULL) 284 goto err; 285 BN_copy(t, a); 286 t->neg = 0; 287 A = t; 288 } else 289 A = a; 290 A1 = BN_CTX_get(ctx); 291 A1_odd = BN_CTX_get(ctx); 292 check = BN_CTX_get(ctx); 293 if (check == NULL) 294 goto err; 295 296 /* compute A1 := A - 1 */ 297 if (!BN_copy(A1, A)) 298 goto err; 299 if (!BN_sub_word(A1, 1)) 300 goto err; 301 if (BN_is_zero(A1)) { 302 ret = 0; 303 goto err; 304 } 305 306 /* write A1 as A1_odd * 2^k */ 307 k = 1; 308 while (!BN_is_bit_set(A1, k)) 309 k++; 310 if (!BN_rshift(A1_odd, A1, k)) 311 goto err; 312 313 /* Montgomery setup for computations mod A */ 314 mont = BN_MONT_CTX_new(); 315 if (mont == NULL) 316 goto err; 317 if (!BN_MONT_CTX_set(mont, A, ctx)) 318 goto err; 319 320 for (i = 0; i < checks; i++) { 321 if (!BN_pseudo_rand_range(check, A1)) 322 goto err; 323 if (!BN_add_word(check, 1)) 324 goto err; 325 /* now 1 <= check < A */ 326 327 j = witness(check, A, A1, A1_odd, k, ctx, mont); 328 if (j == -1) 329 goto err; 330 if (j) { 331 ret = 0; 332 goto err; 333 } 334 if (!BN_GENCB_call(cb, 1, i)) 335 goto err; 336 } 337 ret = 1; 338 339 err: 340 if (ctx != NULL) { 341 BN_CTX_end(ctx); 342 if (ctx_passed == NULL) 343 BN_CTX_free(ctx); 344 } 345 BN_MONT_CTX_free(mont); 346 347 return (ret); 348 } 349 350 static int 351 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, 352 int k, BN_CTX *ctx, BN_MONT_CTX *mont) 353 { 354 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) 355 /* w := w^a1_odd mod a */ 356 return -1; 357 if (BN_is_one(w)) 358 return 0; /* probably prime */ 359 if (BN_cmp(w, a1) == 0) 360 return 0; /* w == -1 (mod a), 'a' is probably prime */ 361 while (--k) { 362 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 363 return -1; 364 if (BN_is_one(w)) 365 return 1; /* 'a' is composite, otherwise a previous 'w' would 366 * have been == -1 (mod 'a') */ 367 if (BN_cmp(w, a1) == 0) 368 return 0; /* w == -1 (mod a), 'a' is probably prime */ 369 } 370 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', 371 * and it is neither -1 nor +1 -- so 'a' cannot be prime */ 372 bn_check_top(w); 373 return 1; 374 } 375 376 static int 377 probable_prime(BIGNUM *rnd, int bits) 378 { 379 int i; 380 prime_t mods[NUMPRIMES]; 381 BN_ULONG delta, maxdelta; 382 383 again: 384 if (!BN_rand(rnd, bits, 1, 1)) 385 return (0); 386 /* we now have a random number 'rand' to test. */ 387 for (i = 1; i < NUMPRIMES; i++) 388 mods[i] = (prime_t)BN_mod_word(rnd, (BN_ULONG)primes[i]); 389 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 390 delta = 0; 391 loop: 392 for (i = 1; i < NUMPRIMES; i++) { 393 /* check that rnd is not a prime and also 394 * that gcd(rnd-1,primes) == 1 (except for 2) */ 395 if (((mods[i] + delta) % primes[i]) <= 1) { 396 delta += 2; 397 if (delta > maxdelta) 398 goto again; 399 goto loop; 400 } 401 } 402 if (!BN_add_word(rnd, delta)) 403 return (0); 404 bn_check_top(rnd); 405 return (1); 406 } 407 408 static int 409 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, 410 BN_CTX *ctx) 411 { 412 int i, ret = 0; 413 BIGNUM *t1; 414 415 BN_CTX_start(ctx); 416 if ((t1 = BN_CTX_get(ctx)) == NULL) 417 goto err; 418 419 if (!BN_rand(rnd, bits, 0, 1)) 420 goto err; 421 422 /* we need ((rnd-rem) % add) == 0 */ 423 424 if (!BN_mod(t1, rnd, add, ctx)) 425 goto err; 426 if (!BN_sub(rnd, rnd, t1)) 427 goto err; 428 if (rem == NULL) { 429 if (!BN_add_word(rnd, 1)) 430 goto err; 431 } else { 432 if (!BN_add(rnd, rnd, rem)) 433 goto err; 434 } 435 436 /* we now have a random number 'rand' to test. */ 437 438 loop: 439 for (i = 1; i < NUMPRIMES; i++) { 440 /* check that rnd is a prime */ 441 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { 442 if (!BN_add(rnd, rnd, add)) 443 goto err; 444 goto loop; 445 } 446 } 447 ret = 1; 448 449 err: 450 BN_CTX_end(ctx); 451 bn_check_top(rnd); 452 return (ret); 453 } 454 455 static int 456 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 457 const BIGNUM *rem, BN_CTX *ctx) 458 { 459 int i, ret = 0; 460 BIGNUM *t1, *qadd, *q; 461 462 bits--; 463 BN_CTX_start(ctx); 464 t1 = BN_CTX_get(ctx); 465 q = BN_CTX_get(ctx); 466 qadd = BN_CTX_get(ctx); 467 if (qadd == NULL) 468 goto err; 469 470 if (!BN_rshift1(qadd, padd)) 471 goto err; 472 473 if (!BN_rand(q, bits, 0, 1)) 474 goto err; 475 476 /* we need ((rnd-rem) % add) == 0 */ 477 if (!BN_mod(t1, q,qadd, ctx)) 478 goto err; 479 if (!BN_sub(q, q, t1)) 480 goto err; 481 if (rem == NULL) { 482 if (!BN_add_word(q, 1)) 483 goto err; 484 } else { 485 if (!BN_rshift1(t1, rem)) 486 goto err; 487 if (!BN_add(q, q, t1)) 488 goto err; 489 } 490 491 /* we now have a random number 'rand' to test. */ 492 if (!BN_lshift1(p, q)) 493 goto err; 494 if (!BN_add_word(p, 1)) 495 goto err; 496 497 loop: 498 for (i = 1; i < NUMPRIMES; i++) { 499 /* check that p and q are prime */ 500 /* check that for p and q 501 * gcd(p-1,primes) == 1 (except for 2) */ 502 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || 503 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { 504 if (!BN_add(p, p, padd)) 505 goto err; 506 if (!BN_add(q, q, qadd)) 507 goto err; 508 goto loop; 509 } 510 } 511 ret = 1; 512 513 err: 514 BN_CTX_end(ctx); 515 bn_check_top(p); 516 return (ret); 517 } 518