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 BN_copy(t, a); 287 t->neg = 0; 288 A = t; 289 } else 290 A = a; 291 A1 = BN_CTX_get(ctx); 292 A1_odd = BN_CTX_get(ctx); 293 check = BN_CTX_get(ctx); 294 if (check == NULL) 295 goto err; 296 297 /* compute A1 := A - 1 */ 298 if (!BN_copy(A1, A)) 299 goto err; 300 if (!BN_sub_word(A1, 1)) 301 goto err; 302 if (BN_is_zero(A1)) { 303 ret = 0; 304 goto err; 305 } 306 307 /* write A1 as A1_odd * 2^k */ 308 k = 1; 309 while (!BN_is_bit_set(A1, k)) 310 k++; 311 if (!BN_rshift(A1_odd, A1, k)) 312 goto err; 313 314 /* Montgomery setup for computations mod A */ 315 mont = BN_MONT_CTX_new(); 316 if (mont == NULL) 317 goto err; 318 if (!BN_MONT_CTX_set(mont, A, ctx)) 319 goto err; 320 321 for (i = 0; i < checks; i++) { 322 if (!BN_pseudo_rand_range(check, A1)) 323 goto err; 324 if (!BN_add_word(check, 1)) 325 goto err; 326 /* now 1 <= check < A */ 327 328 j = witness(check, A, A1, A1_odd, k, ctx, mont); 329 if (j == -1) 330 goto err; 331 if (j) { 332 ret = 0; 333 goto err; 334 } 335 if (!BN_GENCB_call(cb, 1, i)) 336 goto err; 337 } 338 ret = 1; 339 err: 340 if (ctx != NULL) { 341 BN_CTX_end(ctx); 342 if (ctx_passed == NULL) 343 BN_CTX_free(ctx); 344 } 345 if (mont != NULL) 346 BN_MONT_CTX_free(mont); 347 348 return (ret); 349} 350 351static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 352 const BIGNUM *a1_odd, int k, BN_CTX *ctx, 353 BN_MONT_CTX *mont) 354{ 355 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* 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' 366 * would 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 /* 371 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and 372 * it is neither -1 nor +1 -- so 'a' cannot be prime 373 */ 374 bn_check_top(w); 375 return 1; 376} 377 378static int probable_prime(BIGNUM *rnd, int bits) 379{ 380 int i; 381 prime_t mods[NUMPRIMES]; 382 BN_ULONG delta, maxdelta; 383 384 again: 385 if (!BN_rand(rnd, bits, 1, 1)) 386 return (0); 387 /* we now have a random number 'rand' to test. */ 388 for (i = 1; i < NUMPRIMES; i++) 389 mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); 390 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 391 delta = 0; 392 loop:for (i = 1; i < NUMPRIMES; i++) { 393 /* 394 * check that rnd is not a prime and also that gcd(rnd-1,primes) == 1 395 * (except for 2) 396 */ 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 410static int probable_prime_dh(BIGNUM *rnd, int bits, 411 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:for (i = 1; i < NUMPRIMES; i++) { 441 /* check that rnd is a prime */ 442 if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { 443 if (!BN_add(rnd, rnd, add)) 444 goto err; 445 goto loop; 446 } 447 } 448 ret = 1; 449 err: 450 BN_CTX_end(ctx); 451 bn_check_top(rnd); 452 return (ret); 453} 454 455static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 456 const BIGNUM *rem, BN_CTX *ctx) 457{ 458 int i, ret = 0; 459 BIGNUM *t1, *qadd, *q; 460 461 bits--; 462 BN_CTX_start(ctx); 463 t1 = BN_CTX_get(ctx); 464 q = BN_CTX_get(ctx); 465 qadd = BN_CTX_get(ctx); 466 if (qadd == NULL) 467 goto err; 468 469 if (!BN_rshift1(qadd, padd)) 470 goto err; 471 472 if (!BN_rand(q, bits, 0, 1)) 473 goto err; 474 475 /* we need ((rnd-rem) % add) == 0 */ 476 if (!BN_mod(t1, q, qadd, ctx)) 477 goto err; 478 if (!BN_sub(q, q, t1)) 479 goto err; 480 if (rem == NULL) { 481 if (!BN_add_word(q, 1)) 482 goto err; 483 } else { 484 if (!BN_rshift1(t1, rem)) 485 goto err; 486 if (!BN_add(q, q, t1)) 487 goto err; 488 } 489 490 /* we now have a random number 'rand' to test. */ 491 if (!BN_lshift1(p, q)) 492 goto err; 493 if (!BN_add_word(p, 1)) 494 goto err; 495 496 loop:for (i = 1; i < NUMPRIMES; i++) { 497 /* check that p and q are prime */ 498 /* 499 * check that for p and q gcd(p-1,primes) == 1 (except for 2) 500 */ 501 if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || 502 (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { 503 if (!BN_add(p, p, padd)) 504 goto err; 505 if (!BN_add(q, q, qadd)) 506 goto err; 507 goto loop; 508 } 509 } 510 ret = 1; 511 err: 512 BN_CTX_end(ctx); 513 bn_check_top(p); 514 return (ret); 515} 516