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 129static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, 130 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); 131static int probable_prime(BIGNUM *rnd, int bits); 132static int probable_prime_dh(BIGNUM *rnd, int bits, 133 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 134static int probable_prime_dh_safe(BIGNUM *rnd, int bits, 135 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); 136 137int 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 159int 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; 173loop: 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; 228err: 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 238int 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 243int 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; 339err: 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 352static 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 377static int probable_prime(BIGNUM *rnd, int bits) 378 { 379 int i; 380 prime_t mods[NUMPRIMES]; 381 BN_ULONG delta,maxdelta; 382 383again: 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 406static 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; 438err: 439 BN_CTX_end(ctx); 440 bn_check_top(rnd); 441 return(ret); 442 } 443 444static 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; 490err: 491 BN_CTX_end(ctx); 492 bn_check_top(p); 493 return(ret); 494 } 495