1 /* $OpenBSD: bn_prime.c,v 1.32 2023/05/10 12:21:55 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 } 153 154 int 155 BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 156 const BIGNUM *rem, BN_GENCB *cb) 157 { 158 BN_CTX *ctx; 159 BIGNUM *p; 160 int is_prime; 161 int loops = 0; 162 int found = 0; 163 164 if (bits < 2 || (bits == 2 && safe)) { 165 /* 166 * There are no prime numbers smaller than 2, and the smallest 167 * safe prime (7) spans three bits. 168 */ 169 BNerror(BN_R_BITS_TOO_SMALL); 170 return 0; 171 } 172 173 if ((ctx = BN_CTX_new()) == NULL) 174 goto err; 175 BN_CTX_start(ctx); 176 if ((p = BN_CTX_get(ctx)) == NULL) 177 goto err; 178 179 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 } 193 194 if (!BN_GENCB_call(cb, 0, loops++)) 195 goto err; 196 197 if (!safe) { 198 if (!bn_is_prime_bpsw(&is_prime, ret, ctx, 1)) 199 goto err; 200 if (!is_prime) 201 goto loop; 202 } else { 203 if (!bn_is_prime_bpsw(&is_prime, ret, ctx, 1)) 204 goto err; 205 if (!is_prime) 206 goto loop; 207 208 /* 209 * For safe prime generation, check that p = (ret-1)/2 is prime. 210 * Since this prime has >= 3 bits, it is odd, and we can simply 211 * divide by 2. 212 */ 213 if (!BN_rshift1(p, ret)) 214 goto err; 215 216 if (!bn_is_prime_bpsw(&is_prime, p, ctx, 1)) 217 goto err; 218 if (!is_prime) 219 goto loop; 220 221 if (!BN_GENCB_call(cb, 2, loops - 1)) 222 goto err; 223 } 224 225 found = 1; 226 227 err: 228 BN_CTX_end(ctx); 229 BN_CTX_free(ctx); 230 231 return found; 232 } 233 234 int 235 BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) 236 { 237 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); 238 } 239 240 int 241 BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, 242 int do_trial_division, BN_GENCB *cb) 243 { 244 int is_prime; 245 246 if (checks < 0) 247 return -1; 248 249 if (checks == BN_prime_checks) 250 checks = BN_prime_checks_for_size(BN_num_bits(a)); 251 252 /* XXX - tickle BN_GENCB in bn_is_prime_bpsw(). */ 253 if (!bn_is_prime_bpsw(&is_prime, a, ctx_passed, checks)) 254 return -1; 255 256 return is_prime; 257 } 258 259 static int 260 probable_prime(BIGNUM *rnd, int bits) 261 { 262 int i; 263 BN_ULONG mods[NUMPRIMES]; 264 BN_ULONG delta, maxdelta; 265 266 again: 267 if (!BN_rand(rnd, bits, 1, 1)) 268 return (0); 269 /* we now have a random number 'rand' to test. */ 270 for (i = 1; i < NUMPRIMES; i++) { 271 BN_ULONG mod = BN_mod_word(rnd, primes[i]); 272 if (mod == (BN_ULONG)-1) 273 return (0); 274 mods[i] = mod; 275 } 276 maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; 277 delta = 0; 278 loop: 279 for (i = 1; i < NUMPRIMES; i++) { 280 /* check that rnd is not a prime and also 281 * that gcd(rnd-1,primes) == 1 (except for 2) */ 282 if (((mods[i] + delta) % primes[i]) <= 1) { 283 delta += 2; 284 if (delta > maxdelta) 285 goto again; 286 goto loop; 287 } 288 } 289 if (!BN_add_word(rnd, delta)) 290 return (0); 291 return (1); 292 } 293 294 static int 295 probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, 296 BN_CTX *ctx) 297 { 298 int i, ret = 0; 299 BIGNUM *t1; 300 301 BN_CTX_start(ctx); 302 if ((t1 = BN_CTX_get(ctx)) == NULL) 303 goto err; 304 305 if (!BN_rand(rnd, bits, 0, 1)) 306 goto err; 307 308 /* we need ((rnd-rem) % add) == 0 */ 309 310 if (!BN_mod_ct(t1, rnd, add, ctx)) 311 goto err; 312 if (!BN_sub(rnd, rnd, t1)) 313 goto err; 314 if (rem == NULL) { 315 if (!BN_add_word(rnd, 1)) 316 goto err; 317 } else { 318 if (!BN_add(rnd, rnd, rem)) 319 goto err; 320 } 321 322 /* we now have a random number 'rand' to test. */ 323 324 loop: 325 for (i = 1; i < NUMPRIMES; i++) { 326 /* check that rnd is a prime */ 327 BN_LONG mod = BN_mod_word(rnd, primes[i]); 328 if (mod == (BN_ULONG)-1) 329 goto err; 330 if (mod <= 1) { 331 if (!BN_add(rnd, rnd, add)) 332 goto err; 333 goto loop; 334 } 335 } 336 ret = 1; 337 338 err: 339 BN_CTX_end(ctx); 340 return (ret); 341 } 342 343 static int 344 probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, 345 const BIGNUM *rem, BN_CTX *ctx) 346 { 347 int i, ret = 0; 348 BIGNUM *t1, *qadd, *q; 349 350 bits--; 351 BN_CTX_start(ctx); 352 if ((t1 = BN_CTX_get(ctx)) == NULL) 353 goto err; 354 if ((q = BN_CTX_get(ctx)) == NULL) 355 goto err; 356 if ((qadd = BN_CTX_get(ctx)) == NULL) 357 goto err; 358 359 if (!BN_rshift1(qadd, padd)) 360 goto err; 361 362 if (!BN_rand(q, bits, 0, 1)) 363 goto err; 364 365 /* we need ((rnd-rem) % add) == 0 */ 366 if (!BN_mod_ct(t1, q,qadd, ctx)) 367 goto err; 368 if (!BN_sub(q, q, t1)) 369 goto err; 370 if (rem == NULL) { 371 if (!BN_add_word(q, 1)) 372 goto err; 373 } else { 374 if (!BN_rshift1(t1, rem)) 375 goto err; 376 if (!BN_add(q, q, t1)) 377 goto err; 378 } 379 380 /* we now have a random number 'rand' to test. */ 381 if (!BN_lshift1(p, q)) 382 goto err; 383 if (!BN_add_word(p, 1)) 384 goto err; 385 386 loop: 387 for (i = 1; i < NUMPRIMES; i++) { 388 /* check that p and q are prime */ 389 /* check that for p and q 390 * gcd(p-1,primes) == 1 (except for 2) */ 391 BN_ULONG pmod = BN_mod_word(p, primes[i]); 392 BN_ULONG qmod = BN_mod_word(q, primes[i]); 393 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) 394 goto err; 395 if (pmod == 0 || qmod == 0) { 396 if (!BN_add(p, p, padd)) 397 goto err; 398 if (!BN_add(q, q, qadd)) 399 goto err; 400 goto loop; 401 } 402 } 403 ret = 1; 404 405 err: 406 BN_CTX_end(ctx); 407 return (ret); 408 } 409