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| 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 /* NB: these functions have been "upgraded", the deprecated versions (which are | |
| 119 * compatibility wrappers using these functions) are in bn_depr.c. | |
| 120 * - Geoff | |
| 121 */ | |
| 122 | |
| 123 /* The quick sieve algorithm approach to weeding out primes is | |
| 124 * Philip Zimmermann's, as implemented in PGP. I have had a read of | |
| 125 * his comments and implemented my own version. | |
| 126 */ | |
| 127 #include "bn_prime.h" | |
| 128 | |
| 129 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, | |
| 130 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); | |
| 131 static int probable_prime(BIGNUM *rnd, int bits); | |
| 132 static int probable_prime_dh(BIGNUM *rnd, int bits, | |
| 133 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); | |
| 134 static int probable_prime_dh_safe(BIGNUM *rnd, int bits, | |
| 135 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); | |
| 136 | |
| 137 int BN_GENCB_call(BN_GENCB *cb, int a, int b) | |
| 138 { | |
| 139 /* No callback means continue */ | |
| 140 if(!cb) return 1; | |
| 141 switch(cb->ver) | |
| 142 { | |
| 143 case 1: | |
| 144 /* Deprecated-style callbacks */ | |
| 145 if(!cb->cb.cb_1) | |
| 146 return 1; | |
| 147 cb->cb.cb_1(a, b, cb->arg); | |
| 148 return 1; | |
| 149 case 2: | |
| 150 /* New-style callbacks */ | |
| 151 return cb->cb.cb_2(a, b, cb); | |
| 152 default: | |
| 153 break; | |
| 154 } | |
| 155 /* Unrecognised callback type */ | |
| 156 return 0; | |
| 157 } | |
| 158 | |
| 159 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, | |
| 160 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) | |
| 161 { | |
| 162 BIGNUM *t; | |
| 163 int found=0; | |
| 164 int i,j,c1=0; | |
| 165 BN_CTX *ctx; | |
| 166 int checks = BN_prime_checks_for_size(bits); | |
| 167 | |
| 168 ctx=BN_CTX_new(); | |
| 169 if (ctx == NULL) goto err; | |
| 170 BN_CTX_start(ctx); | |
| 171 t = BN_CTX_get(ctx); | |
| 172 if(!t) goto err; | |
| 173 loop: | |
| 174 /* make a random number and set the top and bottom bits */ | |
| 175 if (add == NULL) | |
| 176 { | |
| 177 if (!probable_prime(ret,bits)) goto err; | |
| 178 } | |
| 179 else | |
| 180 { | |
| 181 if (safe) | |
| 182 { | |
| 183 if (!probable_prime_dh_safe(ret,bits,add,rem,ctx)) | |
| 184 goto err; | |
| 185 } | |
| 186 else | |
| 187 { | |
| 188 if (!probable_prime_dh(ret,bits,add,rem,ctx)) | |
| 189 goto err; | |
| 190 } | |
| 191 } | |
| 192 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ | |
| 193 if(!BN_GENCB_call(cb, 0, c1++)) | |
| 194 /* aborted */ | |
| 195 goto err; | |
| 196 | |
| 197 if (!safe) | |
| 198 { | |
| 199 i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb); | |
| 200 if (i == -1) goto err; | |
| 201 if (i == 0) goto loop; | |
| 202 } | |
| 203 else | |
| 204 { | |
| 205 /* for "safe prime" generation, | |
| 206 * check that (p-1)/2 is prime. | |
| 207 * Since a prime is odd, We just | |
| 208 * need to divide by 2 */ | |
| 209 if (!BN_rshift1(t,ret)) goto err; | |
| 210 | |
| 211 for (i=0; i<checks; i++) | |
| 212 { | |
| 213 j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb); | |
| 214 if (j == -1) goto err; | |
| 215 if (j == 0) goto loop; | |
| 216 | |
| 217 j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb); | |
| 218 if (j == -1) goto err; | |
| 219 if (j == 0) goto loop; | |
| 220 | |
| 221 if(!BN_GENCB_call(cb, 2, c1-1)) | |
| 222 goto err; | |
| 223 /* We have a safe prime test pass */ | |
| 224 } | |
| 225 } | |
| 226 /* we have a prime :-) */ | |
| 227 found = 1; | |
| 228 err: | |
| 229 if (ctx != NULL) | |
| 230 { | |
| 231 BN_CTX_end(ctx); | |
| 232 BN_CTX_free(ctx); | |
| 233 } | |
| 234 bn_check_top(ret); | |
| 235 return found; | |
| 236 } | |
| 237 | |
| 238 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb
) | |
| 239 { | |
| 240 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); | |
| 241 } | |
| 242 | |
| 243 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, | |
| 244 int do_trial_division, BN_GENCB *cb) | |
| 245 { | |
| 246 int i, j, ret = -1; | |
| 247 int k; | |
| 248 BN_CTX *ctx = NULL; | |
| 249 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ | |
| 250 BN_MONT_CTX *mont = NULL; | |
| 251 const BIGNUM *A = NULL; | |
| 252 | |
| 253 if (BN_cmp(a, BN_value_one()) <= 0) | |
| 254 return 0; | |
| 255 | |
| 256 if (checks == BN_prime_checks) | |
| 257 checks = BN_prime_checks_for_size(BN_num_bits(a)); | |
| 258 | |
| 259 /* first look for small factors */ | |
| 260 if (!BN_is_odd(a)) | |
| 261 /* a is even => a is prime if and only if a == 2 */ | |
| 262 return BN_is_word(a, 2); | |
| 263 if (do_trial_division) | |
| 264 { | |
| 265 for (i = 1; i < NUMPRIMES; i++) | |
| 266 if (BN_mod_word(a, primes[i]) == 0) | |
| 267 return 0; | |
| 268 if(!BN_GENCB_call(cb, 1, -1)) | |
| 269 goto err; | |
| 270 } | |
| 271 | |
| 272 if (ctx_passed != NULL) | |
| 273 ctx = ctx_passed; | |
| 274 else | |
| 275 if ((ctx=BN_CTX_new()) == NULL) | |
| 276 goto err; | |
| 277 BN_CTX_start(ctx); | |
| 278 | |
| 279 /* A := abs(a) */ | |
| 280 if (a->neg) | |
| 281 { | |
| 282 BIGNUM *t; | |
| 283 if ((t = BN_CTX_get(ctx)) == NULL) goto err; | |
| 284 BN_copy(t, a); | |
| 285 t->neg = 0; | |
| 286 A = t; | |
| 287 } | |
| 288 else | |
| 289 A = a; | |
| 290 A1 = BN_CTX_get(ctx); | |
| 291 A1_odd = BN_CTX_get(ctx); | |
| 292 check = BN_CTX_get(ctx); | |
| 293 if (check == NULL) goto err; | |
| 294 | |
| 295 /* compute A1 := A - 1 */ | |
| 296 if (!BN_copy(A1, A)) | |
| 297 goto err; | |
| 298 if (!BN_sub_word(A1, 1)) | |
| 299 goto err; | |
| 300 if (BN_is_zero(A1)) | |
| 301 { | |
| 302 ret = 0; | |
| 303 goto err; | |
| 304 } | |
| 305 | |
| 306 /* write A1 as A1_odd * 2^k */ | |
| 307 k = 1; | |
| 308 while (!BN_is_bit_set(A1, k)) | |
| 309 k++; | |
| 310 if (!BN_rshift(A1_odd, A1, k)) | |
| 311 goto err; | |
| 312 | |
| 313 /* Montgomery setup for computations mod A */ | |
| 314 mont = BN_MONT_CTX_new(); | |
| 315 if (mont == NULL) | |
| 316 goto err; | |
| 317 if (!BN_MONT_CTX_set(mont, A, ctx)) | |
| 318 goto err; | |
| 319 | |
| 320 for (i = 0; i < checks; i++) | |
| 321 { | |
| 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) goto err; | |
| 330 if (j) | |
| 331 { | |
| 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 { | |
| 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 | |
| 352 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, | |
| 353 const BIGNUM *a1_odd, int k, BN_CTX *ctx, 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 { | |
| 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'
would | |
| 367 * 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 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', | |
| 372 * and it is neither -1 nor +1 -- so 'a' cannot be prime */ | |
| 373 bn_check_top(w); | |
| 374 return 1; | |
| 375 } | |
| 376 | |
| 377 static int probable_prime(BIGNUM *rnd, int bits) | |
| 378 { | |
| 379 int i; | |
| 380 prime_t mods[NUMPRIMES]; | |
| 381 BN_ULONG delta,maxdelta; | |
| 382 | |
| 383 again: | |
| 384 if (!BN_rand(rnd,bits,1,1)) return(0); | |
| 385 /* we now have a random number 'rand' to test. */ | |
| 386 for (i=1; i<NUMPRIMES; i++) | |
| 387 mods[i]=(prime_t)BN_mod_word(rnd,(BN_ULONG)primes[i]); | |
| 388 maxdelta=BN_MASK2 - primes[NUMPRIMES-1]; | |
| 389 delta=0; | |
| 390 loop: for (i=1; i<NUMPRIMES; i++) | |
| 391 { | |
| 392 /* check that rnd is not a prime and also | |
| 393 * that gcd(rnd-1,primes) == 1 (except for 2) */ | |
| 394 if (((mods[i]+delta)%primes[i]) <= 1) | |
| 395 { | |
| 396 delta+=2; | |
| 397 if (delta > maxdelta) goto again; | |
| 398 goto loop; | |
| 399 } | |
| 400 } | |
| 401 if (!BN_add_word(rnd,delta)) return(0); | |
| 402 bn_check_top(rnd); | |
| 403 return(1); | |
| 404 } | |
| 405 | |
| 406 static int probable_prime_dh(BIGNUM *rnd, int bits, | |
| 407 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) | |
| 408 { | |
| 409 int i,ret=0; | |
| 410 BIGNUM *t1; | |
| 411 | |
| 412 BN_CTX_start(ctx); | |
| 413 if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; | |
| 414 | |
| 415 if (!BN_rand(rnd,bits,0,1)) goto err; | |
| 416 | |
| 417 /* we need ((rnd-rem) % add) == 0 */ | |
| 418 | |
| 419 if (!BN_mod(t1,rnd,add,ctx)) goto err; | |
| 420 if (!BN_sub(rnd,rnd,t1)) goto err; | |
| 421 if (rem == NULL) | |
| 422 { if (!BN_add_word(rnd,1)) goto err; } | |
| 423 else | |
| 424 { if (!BN_add(rnd,rnd,rem)) goto err; } | |
| 425 | |
| 426 /* we now have a random number 'rand' to test. */ | |
| 427 | |
| 428 loop: for (i=1; i<NUMPRIMES; i++) | |
| 429 { | |
| 430 /* check that rnd is a prime */ | |
| 431 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1) | |
| 432 { | |
| 433 if (!BN_add(rnd,rnd,add)) goto err; | |
| 434 goto loop; | |
| 435 } | |
| 436 } | |
| 437 ret=1; | |
| 438 err: | |
| 439 BN_CTX_end(ctx); | |
| 440 bn_check_top(rnd); | |
| 441 return(ret); | |
| 442 } | |
| 443 | |
| 444 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, | |
| 445 const BIGNUM *rem, BN_CTX *ctx) | |
| 446 { | |
| 447 int i,ret=0; | |
| 448 BIGNUM *t1,*qadd,*q; | |
| 449 | |
| 450 bits--; | |
| 451 BN_CTX_start(ctx); | |
| 452 t1 = BN_CTX_get(ctx); | |
| 453 q = BN_CTX_get(ctx); | |
| 454 qadd = BN_CTX_get(ctx); | |
| 455 if (qadd == NULL) goto err; | |
| 456 | |
| 457 if (!BN_rshift1(qadd,padd)) goto err; | |
| 458 | |
| 459 if (!BN_rand(q,bits,0,1)) goto err; | |
| 460 | |
| 461 /* we need ((rnd-rem) % add) == 0 */ | |
| 462 if (!BN_mod(t1,q,qadd,ctx)) goto err; | |
| 463 if (!BN_sub(q,q,t1)) goto err; | |
| 464 if (rem == NULL) | |
| 465 { if (!BN_add_word(q,1)) goto err; } | |
| 466 else | |
| 467 { | |
| 468 if (!BN_rshift1(t1,rem)) goto err; | |
| 469 if (!BN_add(q,q,t1)) goto err; | |
| 470 } | |
| 471 | |
| 472 /* we now have a random number 'rand' to test. */ | |
| 473 if (!BN_lshift1(p,q)) goto err; | |
| 474 if (!BN_add_word(p,1)) goto err; | |
| 475 | |
| 476 loop: for (i=1; i<NUMPRIMES; i++) | |
| 477 { | |
| 478 /* check that p and q are prime */ | |
| 479 /* check that for p and q | |
| 480 * gcd(p-1,primes) == 1 (except for 2) */ | |
| 481 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) || | |
| 482 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0)) | |
| 483 { | |
| 484 if (!BN_add(p,p,padd)) goto err; | |
| 485 if (!BN_add(q,q,qadd)) goto err; | |
| 486 goto loop; | |
| 487 } | |
| 488 } | |
| 489 ret=1; | |
| 490 err: | |
| 491 BN_CTX_end(ctx); | |
| 492 bn_check_top(p); | |
| 493 return(ret); | |
| 494 } | |
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Chromium Code Reviews
Issue 2072073002:
Delete bundled copy of OpenSSL and replace with README. (Closed)
Base URL: https://chromium.googlesource.com/chromium/deps/openssl@master