bn_prime.c revision 325335
1/* crypto/bn/bn_prime.c */ 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#include "cryptlib.h" 115#include "bn_lcl.h" 116#include <openssl/rand.h> 117 118/* 119 * NB: these functions have been "upgraded", the deprecated versions (which 120 * are compatibility wrappers using these functions) are in bn_depr.c. - 121 * Geoff 122 */ 123 124/* 125 * The quick sieve algorithm approach to weeding out primes is Philip 126 * Zimmermann's, as implemented in PGP. I have had a read of his comments 127 * and implemented my own version. 128 */ 129#include "bn_prime.h" 130 131static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 132 const BIGNUM *a1_odd, int k, BN_CTX *ctx, 133 BN_MONT_CTX *mont); 134static int probable_prime(BIGNUM *rnd, int bits); 135static int probable_prime_dh(BIGNUM *rnd, int bits, 136 const BIGNUM *add, const BIGNUM *rem, 137 BN_CTX *ctx); 138static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, 139 const BIGNUM *rem, BN_CTX *ctx); 140 141int 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 163int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, 164 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) 165{ 166 BIGNUM *t; 167 int found = 0; 168 int i, j, c1 = 0; 169 BN_CTX *ctx; 170 int checks = BN_prime_checks_for_size(bits); 171 172 ctx = BN_CTX_new(); 173 if (ctx == NULL) 174 goto err; 175 BN_CTX_start(ctx); 176 t = BN_CTX_get(ctx); 177 if (!t) 178 goto err; 179 loop: 180 /* make a random number and set the top and bottom bits */ 181 if (add == NULL) { 182 if (!probable_prime(ret, bits)) 183 goto err; 184 } else { 185 if (safe) { 186 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) 187 goto err; 188 } else { 189 if (!probable_prime_dh(ret, bits, add, rem, ctx)) 190 goto err; 191 } 192 } 193 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ 194 if (!BN_GENCB_call(cb, 0, c1++)) 195 /* aborted */ 196 goto err; 197 198 if (!safe) { 199 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); 200 if (i == -1) 201 goto err; 202 if (i == 0) 203 goto loop; 204 } else { 205 /* 206 * for "safe prime" generation, check that (p-1)/2 is prime. Since a 207 * prime is odd, We just need to divide by 2 208 */ 209 if (!BN_rshift1(t, ret)) 210 goto err; 211 212 for (i = 0; i < checks; i++) { 213 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); 214 if (j == -1) 215 goto err; 216 if (j == 0) 217 goto loop; 218 219 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); 220 if (j == -1) 221 goto err; 222 if (j == 0) 223 goto loop; 224 225 if (!BN_GENCB_call(cb, 2, c1 - 1)) 226 goto err; 227 /* We have a safe prime test pass */ 228 } 229 } 230 /* we have a prime :-) */ 231 found = 1; 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 241int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 242 BN_GENCB *cb) 243{ 244 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 245} 246 247int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 248 int do_trial_division, BN_GENCB *cb) 249{ 250 int i, j, ret = -1; 251 int k; 252 BN_CTX *ctx = NULL; 253 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ 254 BN_MONT_CTX *mont = 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 A1 = BN_CTX_get(ctx); 281 A1_odd = BN_CTX_get(ctx); 282 check = BN_CTX_get(ctx); 283 if (check == NULL) 284 goto err; 285 286 /* compute A1 := a - 1 */ 287 if (!BN_copy(A1, a)) 288 goto err; 289 if (!BN_sub_word(A1, 1)) 290 goto err; 291 if (BN_is_zero(A1)) { 292 ret = 0; 293 goto err; 294 } 295 296 /* write A1 as A1_odd * 2^k */ 297 k = 1; 298 while (!BN_is_bit_set(A1, k)) 299 k++; 300 if (!BN_rshift(A1_odd, A1, k)) 301 goto err; 302 303 /* Montgomery setup for computations mod a */ 304 mont = BN_MONT_CTX_new(); 305 if (mont == NULL) 306 goto err; 307 if (!BN_MONT_CTX_set(mont, a, ctx)) 308 goto err; 309 310 for (i = 0; i < checks; i++) { 311 if (!BN_pseudo_rand_range(check, A1)) 312 goto err; 313 if (!BN_add_word(check, 1)) 314 goto err; 315 /* now 1 <= check < a */ 316 317 j = witness(check, a, A1, A1_odd, k, ctx, mont); 318 if (j == -1) 319 goto err; 320 if (j) { 321 ret = 0; 322 goto err; 323 } 324 if (!BN_GENCB_call(cb, 1, i)) 325 goto err; 326 } 327 ret = 1; 328 err: 329 if (ctx != NULL) { 330 BN_CTX_end(ctx); 331 if (ctx_passed == NULL) 332 BN_CTX_free(ctx); 333 } 334 if (mont != NULL) 335 BN_MONT_CTX_free(mont); 336 337 return (ret); 338} 339 340static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 341 const BIGNUM *a1_odd, int k, BN_CTX *ctx, 342 BN_MONT_CTX *mont) 343{ 344 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ 345 return -1; 346 if (BN_is_one(w)) 347 return 0; /* probably prime */ 348 if (BN_cmp(w, a1) == 0) 349 return 0; /* w == -1 (mod a), 'a' is probably prime */ 350 while (--k) { 351 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 352 return -1; 353 if (BN_is_one(w)) 354 return 1; /* 'a' is composite, otherwise a previous 'w' 355 * would have been == -1 (mod 'a') */ 356 if (BN_cmp(w, a1) == 0) 357 return 0; /* w == -1 (mod a), 'a' is probably prime */ 358 } 359 /* 360 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and 361 * it is neither -1 nor +1 -- so 'a' cannot be prime 362 */ 363 bn_check_top(w); 364 return 1; 365} 366 367static int probable_prime(BIGNUM *rnd, int bits) 368{ 369 int i; 370 prime_t mods[NUMPRIMES]; 371 BN_ULONG delta, maxdelta; 372 373 again: 374 if (!BN_rand(rnd, bits, 1, 1)) 375 return (0); 376 /* we now have a random number 'rand' to test. */ 377 for (i = 1; i < NUMPRIMES; i++) 378 mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); 379 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 380 delta = 0; 381 loop:for (i = 1; i < NUMPRIMES; i++) { 382 /* 383 * check that rnd is not a prime and also that gcd(rnd-1,primes) == 1 384 * (except for 2) 385 */ 386 if (((mods[i] + delta) % primes[i]) <= 1) { 387 delta += 2; 388 if (delta > maxdelta) 389 goto again; 390 goto loop; 391 } 392 } 393 if (!BN_add_word(rnd, delta)) 394 return (0); 395 bn_check_top(rnd); 396 return (1); 397} 398 399static int probable_prime_dh(BIGNUM *rnd, int bits, 400 const BIGNUM *add, const BIGNUM *rem, 401 BN_CTX *ctx) 402{ 403 int i, ret = 0; 404 BIGNUM *t1; 405 406 BN_CTX_start(ctx); 407 if ((t1 = BN_CTX_get(ctx)) == NULL) 408 goto err; 409 410 if (!BN_rand(rnd, bits, 0, 1)) 411 goto err; 412 413 /* we need ((rnd-rem) % add) == 0 */ 414 415 if (!BN_mod(t1, rnd, add, ctx)) 416 goto err; 417 if (!BN_sub(rnd, rnd, t1)) 418 goto err; 419 if (rem == NULL) { 420 if (!BN_add_word(rnd, 1)) 421 goto err; 422 } else { 423 if (!BN_add(rnd, rnd, rem)) 424 goto err; 425 } 426 427 /* we now have a random number 'rand' to test. */ 428 429 loop:for (i = 1; i < NUMPRIMES; i++) { 430 /* check that rnd is a prime */ 431 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { 432 if (!BN_add(rnd, rnd, add)) 433 goto err; 434 goto loop; 435 } 436 } 437 ret = 1; 438 err: 439 BN_CTX_end(ctx); 440 bn_check_top(rnd); 441 return (ret); 442} 443 444static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 445 const BIGNUM *rem, BN_CTX *ctx) 446{ 447 int i, ret = 0; 448 BIGNUM *t1, *qadd, *q; 449 450 bits--; 451 BN_CTX_start(ctx); 452 t1 = BN_CTX_get(ctx); 453 q = BN_CTX_get(ctx); 454 qadd = BN_CTX_get(ctx); 455 if (qadd == NULL) 456 goto err; 457 458 if (!BN_rshift1(qadd, padd)) 459 goto err; 460 461 if (!BN_rand(q, bits, 0, 1)) 462 goto err; 463 464 /* we need ((rnd-rem) % add) == 0 */ 465 if (!BN_mod(t1, q, qadd, ctx)) 466 goto err; 467 if (!BN_sub(q, q, t1)) 468 goto err; 469 if (rem == NULL) { 470 if (!BN_add_word(q, 1)) 471 goto err; 472 } else { 473 if (!BN_rshift1(t1, rem)) 474 goto err; 475 if (!BN_add(q, q, t1)) 476 goto err; 477 } 478 479 /* we now have a random number 'rand' to test. */ 480 if (!BN_lshift1(p, q)) 481 goto err; 482 if (!BN_add_word(p, 1)) 483 goto err; 484 485 loop:for (i = 1; i < NUMPRIMES; i++) { 486 /* check that p and q are prime */ 487 /* 488 * check that for p and q gcd(p-1,primes) == 1 (except for 2) 489 */ 490 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || 491 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { 492 if (!BN_add(p, p, padd)) 493 goto err; 494 if (!BN_add(q, q, qadd)) 495 goto err; 496 goto loop; 497 } 498 } 499 ret = 1; 500 err: 501 BN_CTX_end(ctx); 502 bn_check_top(p); 503 return (ret); 504} 505