bn_prime.c revision 312826
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 const BIGNUM *A = NULL; 256 257 if (BN_cmp(a, BN_value_one()) <= 0) 258 return 0; 259 260 if (checks == BN_prime_checks) 261 checks = BN_prime_checks_for_size(BN_num_bits(a)); 262 263 /* first look for small factors */ 264 if (!BN_is_odd(a)) 265 /* a is even => a is prime if and only if a == 2 */ 266 return BN_is_word(a, 2); 267 if (do_trial_division) { 268 for (i = 1; i < NUMPRIMES; i++) 269 if (BN_mod_word(a, primes[i]) == 0) 270 return 0; 271 if (!BN_GENCB_call(cb, 1, -1)) 272 goto err; 273 } 274 275 if (ctx_passed != NULL) 276 ctx = ctx_passed; 277 else if ((ctx = BN_CTX_new()) == NULL) 278 goto err; 279 BN_CTX_start(ctx); 280 281 /* A := abs(a) */ 282 if (a->neg) { 283 BIGNUM *t; 284 if ((t = BN_CTX_get(ctx)) == NULL) 285 goto err; 286 if (BN_copy(t, a) == NULL) 287 goto err; 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 err: 341 if (ctx != NULL) { 342 BN_CTX_end(ctx); 343 if (ctx_passed == NULL) 344 BN_CTX_free(ctx); 345 } 346 if (mont != NULL) 347 BN_MONT_CTX_free(mont); 348 349 return (ret); 350} 351 352static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 353 const BIGNUM *a1_odd, int k, BN_CTX *ctx, 354 BN_MONT_CTX *mont) 355{ 356 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ 357 return -1; 358 if (BN_is_one(w)) 359 return 0; /* probably prime */ 360 if (BN_cmp(w, a1) == 0) 361 return 0; /* w == -1 (mod a), 'a' is probably prime */ 362 while (--k) { 363 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 364 return -1; 365 if (BN_is_one(w)) 366 return 1; /* 'a' is composite, otherwise a previous 'w' 367 * would have been == -1 (mod 'a') */ 368 if (BN_cmp(w, a1) == 0) 369 return 0; /* w == -1 (mod a), 'a' is probably prime */ 370 } 371 /* 372 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and 373 * it is neither -1 nor +1 -- so 'a' cannot be prime 374 */ 375 bn_check_top(w); 376 return 1; 377} 378 379static int 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:for (i = 1; i < NUMPRIMES; i++) { 394 /* 395 * check that rnd is not a prime and also that gcd(rnd-1,primes) == 1 396 * (except for 2) 397 */ 398 if (((mods[i] + delta) % primes[i]) <= 1) { 399 delta += 2; 400 if (delta > maxdelta) 401 goto again; 402 goto loop; 403 } 404 } 405 if (!BN_add_word(rnd, delta)) 406 return (0); 407 bn_check_top(rnd); 408 return (1); 409} 410 411static int probable_prime_dh(BIGNUM *rnd, int bits, 412 const BIGNUM *add, const BIGNUM *rem, 413 BN_CTX *ctx) 414{ 415 int i, ret = 0; 416 BIGNUM *t1; 417 418 BN_CTX_start(ctx); 419 if ((t1 = BN_CTX_get(ctx)) == NULL) 420 goto err; 421 422 if (!BN_rand(rnd, bits, 0, 1)) 423 goto err; 424 425 /* we need ((rnd-rem) % add) == 0 */ 426 427 if (!BN_mod(t1, rnd, add, ctx)) 428 goto err; 429 if (!BN_sub(rnd, rnd, t1)) 430 goto err; 431 if (rem == NULL) { 432 if (!BN_add_word(rnd, 1)) 433 goto err; 434 } else { 435 if (!BN_add(rnd, rnd, rem)) 436 goto err; 437 } 438 439 /* we now have a random number 'rand' to test. */ 440 441 loop: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 err: 451 BN_CTX_end(ctx); 452 bn_check_top(rnd); 453 return (ret); 454} 455 456static int 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:for (i = 1; i < NUMPRIMES; i++) { 498 /* check that p and q are prime */ 499 /* 500 * check that for p and q gcd(p-1,primes) == 1 (except for 2) 501 */ 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 err: 513 BN_CTX_end(ctx); 514 bn_check_top(p); 515 return (ret); 516} 517