Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 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 | } |