1 /* $OpenBSD: bn_prime.c,v 1.34 2023/07/20 06:26:27 tb 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_local.h" 118 119 /* The quick sieve algorithm approach to weeding out primes is 120 * Philip Zimmermann's, as implemented in PGP. I have had a read of 121 * his comments and implemented my own version. 122 */ 123 #include "bn_prime.h" 124 125 static int probable_prime(BIGNUM *rnd, int bits); 126 static int probable_prime_dh(BIGNUM *rnd, int bits, 127 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 128 static int probable_prime_dh_safe(BIGNUM *rnd, int bits, 129 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 130 131 int 132 BN_GENCB_call(BN_GENCB *cb, int a, int b) 133 { 134 /* No callback means continue */ 135 if (!cb) 136 return 1; 137 switch (cb->ver) { 138 case 1: 139 /* Deprecated-style callbacks */ 140 if (!cb->cb.cb_1) 141 return 1; 142 cb->cb.cb_1(a, b, cb->arg); 143 return 1; 144 case 2: 145 /* New-style callbacks */ 146 return cb->cb.cb_2(a, b, cb); 147 default: 148 break; 149 } 150 /* Unrecognised callback type */ 151 return 0; 152 } 153 LCRYPTO_ALIAS(BN_GENCB_call); 154 155 int 156 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 157 const BIGNUM *rem, BN_GENCB *cb) 158 { 159 BN_CTX *ctx; 160 BIGNUM *p; 161 int is_prime; 162 int loops = 0; 163 int found = 0; 164 165 if (bits < 2 || (bits == 2 && safe)) { 166 /* 167 * There are no prime numbers smaller than 2, and the smallest 168 * safe prime (7) spans three bits. 169 */ 170 BNerror(BN_R_BITS_TOO_SMALL); 171 return 0; 172 } 173 174 if ((ctx = BN_CTX_new()) == NULL) 175 goto err; 176 BN_CTX_start(ctx); 177 if ((p = BN_CTX_get(ctx)) == NULL) 178 goto err; 179 180 loop: 181 /* Make a random number and set the top and bottom bits. */ 182 if (add == NULL) { 183 if (!probable_prime(ret, bits)) 184 goto err; 185 } else { 186 if (safe) { 187 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) 188 goto err; 189 } else { 190 if (!probable_prime_dh(ret, bits, add, rem, ctx)) 191 goto err; 192 } 193 } 194 195 if (!BN_GENCB_call(cb, 0, loops++)) 196 goto err; 197 198 if (!safe) { 199 if (!bn_is_prime_bpsw(&is_prime, ret, ctx, 1)) 200 goto err; 201 if (!is_prime) 202 goto loop; 203 } else { 204 if (!bn_is_prime_bpsw(&is_prime, ret, ctx, 1)) 205 goto err; 206 if (!is_prime) 207 goto loop; 208 209 /* 210 * For safe prime generation, check that p = (ret-1)/2 is prime. 211 * Since this prime has >= 3 bits, it is odd, and we can simply 212 * divide by 2. 213 */ 214 if (!BN_rshift1(p, ret)) 215 goto err; 216 217 if (!bn_is_prime_bpsw(&is_prime, p, ctx, 1)) 218 goto err; 219 if (!is_prime) 220 goto loop; 221 222 if (!BN_GENCB_call(cb, 2, loops - 1)) 223 goto err; 224 } 225 226 found = 1; 227 228 err: 229 BN_CTX_end(ctx); 230 BN_CTX_free(ctx); 231 232 return found; 233 } 234 LCRYPTO_ALIAS(BN_generate_prime_ex); 235 236 int 237 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) 238 { 239 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 240 } 241 LCRYPTO_ALIAS(BN_is_prime_ex); 242 243 #define BN_PRIME_MAXIMUM_BITS (32 * 1024) 244 245 int 246 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 247 int do_trial_division, BN_GENCB *cb) 248 { 249 int is_prime; 250 251 if (checks < 0) 252 return -1; 253 254 /* 255 * Prime numbers this large do not appear in everyday cryptography 256 * and checking such numbers for primality is very expensive. 257 */ 258 if (BN_num_bits(a) > BN_PRIME_MAXIMUM_BITS) { 259 BNerror(BN_R_BIGNUM_TOO_LONG); 260 return -1; 261 } 262 263 if (checks == BN_prime_checks) 264 checks = BN_prime_checks_for_size(BN_num_bits(a)); 265 266 /* XXX - tickle BN_GENCB in bn_is_prime_bpsw(). */ 267 if (!bn_is_prime_bpsw(&is_prime, a, ctx_passed, checks)) 268 return -1; 269 270 return is_prime; 271 } 272 LCRYPTO_ALIAS(BN_is_prime_fasttest_ex); 273 274 static int 275 probable_prime(BIGNUM *rnd, int bits) 276 { 277 int i; 278 BN_ULONG mods[NUMPRIMES]; 279 BN_ULONG delta, maxdelta; 280 281 again: 282 if (!BN_rand(rnd, bits, 1, 1)) 283 return (0); 284 /* we now have a random number 'rand' to test. */ 285 for (i = 1; i < NUMPRIMES; i++) { 286 BN_ULONG mod = BN_mod_word(rnd, primes[i]); 287 if (mod == (BN_ULONG)-1) 288 return (0); 289 mods[i] = mod; 290 } 291 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 292 delta = 0; 293 loop: 294 for (i = 1; i < NUMPRIMES; i++) { 295 /* check that rnd is not a prime and also 296 * that gcd(rnd-1,primes) == 1 (except for 2) */ 297 if (((mods[i] + delta) % primes[i]) <= 1) { 298 delta += 2; 299 if (delta > maxdelta) 300 goto again; 301 goto loop; 302 } 303 } 304 if (!BN_add_word(rnd, delta)) 305 return (0); 306 return (1); 307 } 308 309 static int 310 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, 311 BN_CTX *ctx) 312 { 313 int i, ret = 0; 314 BIGNUM *t1; 315 316 BN_CTX_start(ctx); 317 if ((t1 = BN_CTX_get(ctx)) == NULL) 318 goto err; 319 320 if (!BN_rand(rnd, bits, 0, 1)) 321 goto err; 322 323 /* we need ((rnd-rem) % add) == 0 */ 324 325 if (!BN_mod_ct(t1, rnd, add, ctx)) 326 goto err; 327 if (!BN_sub(rnd, rnd, t1)) 328 goto err; 329 if (rem == NULL) { 330 if (!BN_add_word(rnd, 1)) 331 goto err; 332 } else { 333 if (!BN_add(rnd, rnd, rem)) 334 goto err; 335 } 336 337 /* we now have a random number 'rand' to test. */ 338 339 loop: 340 for (i = 1; i < NUMPRIMES; i++) { 341 /* check that rnd is a prime */ 342 BN_LONG mod = BN_mod_word(rnd, primes[i]); 343 if (mod == (BN_ULONG)-1) 344 goto err; 345 if (mod <= 1) { 346 if (!BN_add(rnd, rnd, add)) 347 goto err; 348 goto loop; 349 } 350 } 351 ret = 1; 352 353 err: 354 BN_CTX_end(ctx); 355 return (ret); 356 } 357 358 static int 359 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 360 const BIGNUM *rem, BN_CTX *ctx) 361 { 362 int i, ret = 0; 363 BIGNUM *t1, *qadd, *q; 364 365 bits--; 366 BN_CTX_start(ctx); 367 if ((t1 = BN_CTX_get(ctx)) == NULL) 368 goto err; 369 if ((q = BN_CTX_get(ctx)) == NULL) 370 goto err; 371 if ((qadd = BN_CTX_get(ctx)) == NULL) 372 goto err; 373 374 if (!BN_rshift1(qadd, padd)) 375 goto err; 376 377 if (!BN_rand(q, bits, 0, 1)) 378 goto err; 379 380 /* we need ((rnd-rem) % add) == 0 */ 381 if (!BN_mod_ct(t1, q,qadd, ctx)) 382 goto err; 383 if (!BN_sub(q, q, t1)) 384 goto err; 385 if (rem == NULL) { 386 if (!BN_add_word(q, 1)) 387 goto err; 388 } else { 389 if (!BN_rshift1(t1, rem)) 390 goto err; 391 if (!BN_add(q, q, t1)) 392 goto err; 393 } 394 395 /* we now have a random number 'rand' to test. */ 396 if (!BN_lshift1(p, q)) 397 goto err; 398 if (!BN_add_word(p, 1)) 399 goto err; 400 401 loop: 402 for (i = 1; i < NUMPRIMES; i++) { 403 /* check that p and q are prime */ 404 /* check that for p and q 405 * gcd(p-1,primes) == 1 (except for 2) */ 406 BN_ULONG pmod = BN_mod_word(p, primes[i]); 407 BN_ULONG qmod = BN_mod_word(q, primes[i]); 408 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) 409 goto err; 410 if (pmod == 0 || qmod == 0) { 411 if (!BN_add(p, p, padd)) 412 goto err; 413 if (!BN_add(q, q, qadd)) 414 goto err; 415 goto loop; 416 } 417 } 418 ret = 1; 419 420 err: 421 BN_CTX_end(ctx); 422 return (ret); 423 } 424