1 /* $OpenBSD: bn_prime.c,v 1.11 2014/07/12 16:03:36 miod 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/rand.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 = BN_prime_checks_for_size(bits); 170 171 ctx = BN_CTX_new(); 172 if (ctx == NULL) 173 goto err; 174 BN_CTX_start(ctx); 175 t = BN_CTX_get(ctx); 176 if (!t) 177 goto err; 178 loop: 179 /* make a random number and set the top and bottom bits */ 180 if (add == NULL) { 181 if (!probable_prime(ret, bits)) 182 goto err; 183 } else { 184 if (safe) { 185 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) 186 goto err; 187 } else { 188 if (!probable_prime_dh(ret, bits, add, rem, ctx)) 189 goto err; 190 } 191 } 192 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ 193 if (!BN_GENCB_call(cb, 0, c1++)) 194 /* aborted */ 195 goto err; 196 197 if (!safe) { 198 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); 199 if (i == -1) 200 goto err; 201 if (i == 0) 202 goto loop; 203 } else { 204 /* for "safe prime" generation, 205 * check that (p-1)/2 is prime. 206 * Since a prime is odd, We just 207 * need to divide by 2 */ 208 if (!BN_rshift1(t, ret)) 209 goto err; 210 211 for (i = 0; i < checks; i++) { 212 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); 213 if (j == -1) 214 goto err; 215 if (j == 0) 216 goto loop; 217 218 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); 219 if (j == -1) 220 goto err; 221 if (j == 0) 222 goto loop; 223 224 if (!BN_GENCB_call(cb, 2, c1 - 1)) 225 goto err; 226 /* We have a safe prime test pass */ 227 } 228 } 229 /* we have a prime :-) */ 230 found = 1; 231 232 err: 233 if (ctx != NULL) { 234 BN_CTX_end(ctx); 235 BN_CTX_free(ctx); 236 } 237 bn_check_top(ret); 238 return found; 239 } 240 241 int 242 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) 243 { 244 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 245 } 246 247 int 248 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 249 int do_trial_division, BN_GENCB *cb) 250 { 251 int i, j, ret = -1; 252 int k; 253 BN_CTX *ctx = NULL; 254 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ 255 BN_MONT_CTX *mont = NULL; 256 const BIGNUM *A = NULL; 257 258 if (BN_cmp(a, BN_value_one()) <= 0) 259 return 0; 260 261 if (checks == BN_prime_checks) 262 checks = BN_prime_checks_for_size(BN_num_bits(a)); 263 264 /* first look for small factors */ 265 if (!BN_is_odd(a)) 266 /* a is even => a is prime if and only if a == 2 */ 267 return BN_is_word(a, 2); 268 if (do_trial_division) { 269 for (i = 1; i < NUMPRIMES; i++) 270 if (BN_mod_word(a, primes[i]) == 0) 271 return 0; 272 if (!BN_GENCB_call(cb, 1, -1)) 273 goto err; 274 } 275 276 if (ctx_passed != NULL) 277 ctx = ctx_passed; 278 else if ((ctx = BN_CTX_new()) == NULL) 279 goto err; 280 BN_CTX_start(ctx); 281 282 /* A := abs(a) */ 283 if (a->neg) { 284 BIGNUM *t; 285 if ((t = BN_CTX_get(ctx)) == NULL) 286 goto err; 287 BN_copy(t, a); 288 t->neg = 0; 289 A = t; 290 } else 291 A = a; 292 A1 = BN_CTX_get(ctx); 293 A1_odd = BN_CTX_get(ctx); 294 check = BN_CTX_get(ctx); 295 if (check == NULL) 296 goto err; 297 298 /* compute A1 := A - 1 */ 299 if (!BN_copy(A1, A)) 300 goto err; 301 if (!BN_sub_word(A1, 1)) 302 goto err; 303 if (BN_is_zero(A1)) { 304 ret = 0; 305 goto err; 306 } 307 308 /* write A1 as A1_odd * 2^k */ 309 k = 1; 310 while (!BN_is_bit_set(A1, k)) 311 k++; 312 if (!BN_rshift(A1_odd, A1, k)) 313 goto err; 314 315 /* Montgomery setup for computations mod A */ 316 mont = BN_MONT_CTX_new(); 317 if (mont == NULL) 318 goto err; 319 if (!BN_MONT_CTX_set(mont, A, ctx)) 320 goto err; 321 322 for (i = 0; i < checks; i++) { 323 if (!BN_pseudo_rand_range(check, A1)) 324 goto err; 325 if (!BN_add_word(check, 1)) 326 goto err; 327 /* now 1 <= check < A */ 328 329 j = witness(check, A, A1, A1_odd, k, ctx, mont); 330 if (j == -1) 331 goto err; 332 if (j) { 333 ret = 0; 334 goto err; 335 } 336 if (!BN_GENCB_call(cb, 1, i)) 337 goto err; 338 } 339 ret = 1; 340 341 err: 342 if (ctx != NULL) { 343 BN_CTX_end(ctx); 344 if (ctx_passed == NULL) 345 BN_CTX_free(ctx); 346 } 347 BN_MONT_CTX_free(mont); 348 349 return (ret); 350 } 351 352 static int 353 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, 354 int k, BN_CTX *ctx, BN_MONT_CTX *mont) 355 { 356 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) 357 /* w := w^a1_odd mod a */ 358 return -1; 359 if (BN_is_one(w)) 360 return 0; /* probably prime */ 361 if (BN_cmp(w, a1) == 0) 362 return 0; /* w == -1 (mod a), 'a' is probably prime */ 363 while (--k) { 364 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 365 return -1; 366 if (BN_is_one(w)) 367 return 1; /* 'a' is composite, otherwise a previous 'w' would 368 * have been == -1 (mod 'a') */ 369 if (BN_cmp(w, a1) == 0) 370 return 0; /* w == -1 (mod a), 'a' is probably prime */ 371 } 372 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', 373 * and it is neither -1 nor +1 -- so 'a' cannot be prime */ 374 bn_check_top(w); 375 return 1; 376 } 377 378 static int 379 probable_prime(BIGNUM *rnd, int bits) 380 { 381 int i; 382 prime_t mods[NUMPRIMES]; 383 BN_ULONG delta, maxdelta; 384 385 again: 386 if (!BN_rand(rnd, bits, 1, 1)) 387 return (0); 388 /* we now have a random number 'rand' to test. */ 389 for (i = 1; i < NUMPRIMES; i++) 390 mods[i] = (prime_t)BN_mod_word(rnd, (BN_ULONG)primes[i]); 391 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 392 delta = 0; 393 loop: 394 for (i = 1; i < NUMPRIMES; i++) { 395 /* check that rnd is not a prime and also 396 * that gcd(rnd-1,primes) == 1 (except for 2) */ 397 if (((mods[i] + delta) % primes[i]) <= 1) { 398 delta += 2; 399 if (delta > maxdelta) 400 goto again; 401 goto loop; 402 } 403 } 404 if (!BN_add_word(rnd, delta)) 405 return (0); 406 bn_check_top(rnd); 407 return (1); 408 } 409 410 static int 411 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, 412 BN_CTX *ctx) 413 { 414 int i, ret = 0; 415 BIGNUM *t1; 416 417 BN_CTX_start(ctx); 418 if ((t1 = BN_CTX_get(ctx)) == NULL) 419 goto err; 420 421 if (!BN_rand(rnd, bits, 0, 1)) 422 goto err; 423 424 /* we need ((rnd-rem) % add) == 0 */ 425 426 if (!BN_mod(t1, rnd, add, ctx)) 427 goto err; 428 if (!BN_sub(rnd, rnd, t1)) 429 goto err; 430 if (rem == NULL) { 431 if (!BN_add_word(rnd, 1)) 432 goto err; 433 } else { 434 if (!BN_add(rnd, rnd, rem)) 435 goto err; 436 } 437 438 /* we now have a random number 'rand' to test. */ 439 440 loop: 441 for (i = 1; i < NUMPRIMES; i++) { 442 /* check that rnd is a prime */ 443 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { 444 if (!BN_add(rnd, rnd, add)) 445 goto err; 446 goto loop; 447 } 448 } 449 ret = 1; 450 451 err: 452 BN_CTX_end(ctx); 453 bn_check_top(rnd); 454 return (ret); 455 } 456 457 static int 458 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 459 const BIGNUM *rem, BN_CTX *ctx) 460 { 461 int i, ret = 0; 462 BIGNUM *t1, *qadd, *q; 463 464 bits--; 465 BN_CTX_start(ctx); 466 t1 = BN_CTX_get(ctx); 467 q = BN_CTX_get(ctx); 468 qadd = BN_CTX_get(ctx); 469 if (qadd == NULL) 470 goto err; 471 472 if (!BN_rshift1(qadd, padd)) 473 goto err; 474 475 if (!BN_rand(q, bits, 0, 1)) 476 goto err; 477 478 /* we need ((rnd-rem) % add) == 0 */ 479 if (!BN_mod(t1, q,qadd, ctx)) 480 goto err; 481 if (!BN_sub(q, q, t1)) 482 goto err; 483 if (rem == NULL) { 484 if (!BN_add_word(q, 1)) 485 goto err; 486 } else { 487 if (!BN_rshift1(t1, rem)) 488 goto err; 489 if (!BN_add(q, q, t1)) 490 goto err; 491 } 492 493 /* we now have a random number 'rand' to test. */ 494 if (!BN_lshift1(p, q)) 495 goto err; 496 if (!BN_add_word(p, 1)) 497 goto err; 498 499 loop: 500 for (i = 1; i < NUMPRIMES; i++) { 501 /* check that p and q are prime */ 502 /* check that for p and q 503 * gcd(p-1,primes) == 1 (except for 2) */ 504 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || 505 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { 506 if (!BN_add(p, p, padd)) 507 goto err; 508 if (!BN_add(q, q, qadd)) 509 goto err; 510 goto loop; 511 } 512 } 513 ret = 1; 514 515 err: 516 BN_CTX_end(ctx); 517 bn_check_top(p); 518 return (ret); 519 } 520