1 /* $OpenBSD: bn_prime.c,v 1.18 2017/01/29 17:49:22 beck 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/err.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; 170 171 if (bits < 2 || (bits == 2 && safe)) { 172 /* 173 * There are no prime numbers smaller than 2, and the smallest 174 * safe prime (7) spans three bits. 175 */ 176 BNerror(BN_R_BITS_TOO_SMALL); 177 return 0; 178 } 179 180 ctx = BN_CTX_new(); 181 if (ctx == NULL) 182 goto err; 183 BN_CTX_start(ctx); 184 if ((t = BN_CTX_get(ctx)) == NULL) 185 goto err; 186 187 checks = BN_prime_checks_for_size(bits); 188 189 loop: 190 /* make a random number and set the top and bottom bits */ 191 if (add == NULL) { 192 if (!probable_prime(ret, bits)) 193 goto err; 194 } else { 195 if (safe) { 196 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) 197 goto err; 198 } else { 199 if (!probable_prime_dh(ret, bits, add, rem, ctx)) 200 goto err; 201 } 202 } 203 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ 204 if (!BN_GENCB_call(cb, 0, c1++)) 205 /* aborted */ 206 goto err; 207 208 if (!safe) { 209 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); 210 if (i == -1) 211 goto err; 212 if (i == 0) 213 goto loop; 214 } else { 215 /* for "safe prime" generation, 216 * check that (p-1)/2 is prime. 217 * Since a prime is odd, We just 218 * need to divide by 2 */ 219 if (!BN_rshift1(t, ret)) 220 goto err; 221 222 for (i = 0; i < checks; i++) { 223 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); 224 if (j == -1) 225 goto err; 226 if (j == 0) 227 goto loop; 228 229 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); 230 if (j == -1) 231 goto err; 232 if (j == 0) 233 goto loop; 234 235 if (!BN_GENCB_call(cb, 2, c1 - 1)) 236 goto err; 237 /* We have a safe prime test pass */ 238 } 239 } 240 /* we have a prime :-) */ 241 found = 1; 242 243 err: 244 if (ctx != NULL) { 245 BN_CTX_end(ctx); 246 BN_CTX_free(ctx); 247 } 248 bn_check_top(ret); 249 return found; 250 } 251 252 int 253 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) 254 { 255 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 256 } 257 258 int 259 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 260 int do_trial_division, BN_GENCB *cb) 261 { 262 int i, j, ret = -1; 263 int k; 264 BN_CTX *ctx = NULL; 265 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ 266 BN_MONT_CTX *mont = NULL; 267 const BIGNUM *A = NULL; 268 269 if (BN_cmp(a, BN_value_one()) <= 0) 270 return 0; 271 272 if (checks == BN_prime_checks) 273 checks = BN_prime_checks_for_size(BN_num_bits(a)); 274 275 /* first look for small factors */ 276 if (!BN_is_odd(a)) 277 /* a is even => a is prime if and only if a == 2 */ 278 return BN_is_word(a, 2); 279 if (do_trial_division) { 280 for (i = 1; i < NUMPRIMES; i++) { 281 BN_ULONG mod = BN_mod_word(a, primes[i]); 282 if (mod == (BN_ULONG)-1) 283 goto err; 284 if (mod == 0) 285 return 0; 286 } 287 if (!BN_GENCB_call(cb, 1, -1)) 288 goto err; 289 } 290 291 if (ctx_passed != NULL) 292 ctx = ctx_passed; 293 else if ((ctx = BN_CTX_new()) == NULL) 294 goto err; 295 BN_CTX_start(ctx); 296 297 /* A := abs(a) */ 298 if (a->neg) { 299 BIGNUM *t; 300 if ((t = BN_CTX_get(ctx)) == NULL) 301 goto err; 302 BN_copy(t, a); 303 t->neg = 0; 304 A = t; 305 } else 306 A = a; 307 if ((A1 = BN_CTX_get(ctx)) == NULL) 308 goto err; 309 if ((A1_odd = BN_CTX_get(ctx)) == NULL) 310 goto err; 311 if ((check = BN_CTX_get(ctx)) == NULL) 312 goto err; 313 314 /* compute A1 := A - 1 */ 315 if (!BN_copy(A1, A)) 316 goto err; 317 if (!BN_sub_word(A1, 1)) 318 goto err; 319 if (BN_is_zero(A1)) { 320 ret = 0; 321 goto err; 322 } 323 324 /* write A1 as A1_odd * 2^k */ 325 k = 1; 326 while (!BN_is_bit_set(A1, k)) 327 k++; 328 if (!BN_rshift(A1_odd, A1, k)) 329 goto err; 330 331 /* Montgomery setup for computations mod A */ 332 mont = BN_MONT_CTX_new(); 333 if (mont == NULL) 334 goto err; 335 if (!BN_MONT_CTX_set(mont, A, ctx)) 336 goto err; 337 338 for (i = 0; i < checks; i++) { 339 if (!BN_pseudo_rand_range(check, A1)) 340 goto err; 341 if (!BN_add_word(check, 1)) 342 goto err; 343 /* now 1 <= check < A */ 344 345 j = witness(check, A, A1, A1_odd, k, ctx, mont); 346 if (j == -1) 347 goto err; 348 if (j) { 349 ret = 0; 350 goto err; 351 } 352 if (!BN_GENCB_call(cb, 1, i)) 353 goto err; 354 } 355 ret = 1; 356 357 err: 358 if (ctx != NULL) { 359 BN_CTX_end(ctx); 360 if (ctx_passed == NULL) 361 BN_CTX_free(ctx); 362 } 363 BN_MONT_CTX_free(mont); 364 365 return (ret); 366 } 367 368 static int 369 witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, 370 int k, BN_CTX *ctx, BN_MONT_CTX *mont) 371 { 372 if (!BN_mod_exp_mont_ct(w, w, a1_odd, a, ctx, mont)) 373 /* w := w^a1_odd mod a */ 374 return -1; 375 if (BN_is_one(w)) 376 return 0; /* probably prime */ 377 if (BN_cmp(w, a1) == 0) 378 return 0; /* w == -1 (mod a), 'a' is probably prime */ 379 while (--k) { 380 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ 381 return -1; 382 if (BN_is_one(w)) 383 return 1; /* 'a' is composite, otherwise a previous 'w' would 384 * have been == -1 (mod 'a') */ 385 if (BN_cmp(w, a1) == 0) 386 return 0; /* w == -1 (mod a), 'a' is probably prime */ 387 } 388 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', 389 * and it is neither -1 nor +1 -- so 'a' cannot be prime */ 390 bn_check_top(w); 391 return 1; 392 } 393 394 static int 395 probable_prime(BIGNUM *rnd, int bits) 396 { 397 int i; 398 prime_t mods[NUMPRIMES]; 399 BN_ULONG delta, maxdelta; 400 401 again: 402 if (!BN_rand(rnd, bits, 1, 1)) 403 return (0); 404 /* we now have a random number 'rand' to test. */ 405 for (i = 1; i < NUMPRIMES; i++) { 406 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); 407 if (mod == (BN_ULONG)-1) 408 return (0); 409 mods[i] = (prime_t)mod; 410 } 411 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 412 delta = 0; 413 loop: 414 for (i = 1; i < NUMPRIMES; i++) { 415 /* check that rnd is not a prime and also 416 * that gcd(rnd-1,primes) == 1 (except for 2) */ 417 if (((mods[i] + delta) % primes[i]) <= 1) { 418 delta += 2; 419 if (delta > maxdelta) 420 goto again; 421 goto loop; 422 } 423 } 424 if (!BN_add_word(rnd, delta)) 425 return (0); 426 bn_check_top(rnd); 427 return (1); 428 } 429 430 static int 431 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, 432 BN_CTX *ctx) 433 { 434 int i, ret = 0; 435 BIGNUM *t1; 436 437 BN_CTX_start(ctx); 438 if ((t1 = BN_CTX_get(ctx)) == NULL) 439 goto err; 440 441 if (!BN_rand(rnd, bits, 0, 1)) 442 goto err; 443 444 /* we need ((rnd-rem) % add) == 0 */ 445 446 if (!BN_mod_ct(t1, rnd, add, ctx)) 447 goto err; 448 if (!BN_sub(rnd, rnd, t1)) 449 goto err; 450 if (rem == NULL) { 451 if (!BN_add_word(rnd, 1)) 452 goto err; 453 } else { 454 if (!BN_add(rnd, rnd, rem)) 455 goto err; 456 } 457 458 /* we now have a random number 'rand' to test. */ 459 460 loop: 461 for (i = 1; i < NUMPRIMES; i++) { 462 /* check that rnd is a prime */ 463 BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); 464 if (mod == (BN_ULONG)-1) 465 goto err; 466 if (mod <= 1) { 467 if (!BN_add(rnd, rnd, add)) 468 goto err; 469 goto loop; 470 } 471 } 472 ret = 1; 473 474 err: 475 BN_CTX_end(ctx); 476 bn_check_top(rnd); 477 return (ret); 478 } 479 480 static int 481 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 482 const BIGNUM *rem, BN_CTX *ctx) 483 { 484 int i, ret = 0; 485 BIGNUM *t1, *qadd, *q; 486 487 bits--; 488 BN_CTX_start(ctx); 489 if ((t1 = BN_CTX_get(ctx)) == NULL) 490 goto err; 491 if ((q = BN_CTX_get(ctx)) == NULL) 492 goto err; 493 if ((qadd = BN_CTX_get(ctx)) == NULL) 494 goto err; 495 496 if (!BN_rshift1(qadd, padd)) 497 goto err; 498 499 if (!BN_rand(q, bits, 0, 1)) 500 goto err; 501 502 /* we need ((rnd-rem) % add) == 0 */ 503 if (!BN_mod_ct(t1, q,qadd, ctx)) 504 goto err; 505 if (!BN_sub(q, q, t1)) 506 goto err; 507 if (rem == NULL) { 508 if (!BN_add_word(q, 1)) 509 goto err; 510 } else { 511 if (!BN_rshift1(t1, rem)) 512 goto err; 513 if (!BN_add(q, q, t1)) 514 goto err; 515 } 516 517 /* we now have a random number 'rand' to test. */ 518 if (!BN_lshift1(p, q)) 519 goto err; 520 if (!BN_add_word(p, 1)) 521 goto err; 522 523 loop: 524 for (i = 1; i < NUMPRIMES; i++) { 525 /* check that p and q are prime */ 526 /* check that for p and q 527 * gcd(p-1,primes) == 1 (except for 2) */ 528 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]); 529 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]); 530 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) 531 goto err; 532 if (pmod == 0 || qmod == 0) { 533 if (!BN_add(p, p, padd)) 534 goto err; 535 if (!BN_add(q, q, qadd)) 536 goto err; 537 goto loop; 538 } 539 } 540 ret = 1; 541 542 err: 543 BN_CTX_end(ctx); 544 bn_check_top(p); 545 return (ret); 546 } 547