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         }