crypto/bn/bn_prime.c

   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) 1998-2000 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 /* The quick sieve algorithm approach to weeding out primes is
 119  * Philip Zimmermann's, as implemented in PGP.  I have had a read of
 120  * his comments and implemented my own version.
 121  */
 122 #include "bn_prime.h"
 123
 124 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 125         const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
 126 static int probable_prime(BIGNUM *rnd, int bits);
 127 static int probable_prime_dh(BIGNUM *rnd, int bits,
 128         const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 129 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
 130         const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
 131
 132 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
 133         const BIGNUM *add, const BIGNUM *rem,
 134         void (*callback)(int,int,void *), void *cb_arg)
 135         {
 136         BIGNUM *rnd=NULL;
 137         BIGNUM t;
 138         int found=0;
 139         int i,j,c1=0;
 140         BN_CTX *ctx;
 141         int checks = BN_prime_checks_for_size(bits);
 142
 143         ctx=BN_CTX_new();
 144         if (ctx == NULL) goto err;
 145         if (ret == NULL)
 146                 {
 147                 if ((rnd=BN_new()) == NULL) goto err;
 148                 }
 149         else
 150                 rnd=ret;
 151         BN_init(&t);
 152 loop:
 153         /* make a random number and set the top and bottom bits */
 154         if (add == NULL)
 155                 {
 156                 if (!probable_prime(rnd,bits)) goto err;
 157                 }
 158         else
 159                 {
 160                 if (safe)
 161                         {
 162                         if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
 163                                  goto err;
 164                         }
 165                 else
 166                         {
 167                         if (!probable_prime_dh(rnd,bits,add,rem,ctx))
 168                                 goto err;
 169                         }
 170                 }
 171         /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
 172         if (callback != NULL) callback(0,c1++,cb_arg);
 173
 174         if (!safe)
 175                 {
 176                 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
 177                 if (i == -1) goto err;
 178                 if (i == 0) goto loop;
 179                 }
 180         else
 181                 {
 182                 /* for "safe prime" generation,
 183                  * check that (p-1)/2 is prime.
 184                  * Since a prime is odd, We just
 185                  * need to divide by 2 */
 186                 if (!BN_rshift1(&t,rnd)) goto err;
 187
 188                 for (i=0; i<checks; i++)
 189                         {
 190                         j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
 191                         if (j == -1) goto err;
 192                         if (j == 0) goto loop;
 193
 194                         j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
 195                         if (j == -1) goto err;
 196                         if (j == 0) goto loop;
 197
 198                         if (callback != NULL) callback(2,c1-1,cb_arg);
 199                         /* We have a safe prime test pass */
 200                         }
 201                 }
 202         /* we have a prime :-) */
 203         found = 1;
 204 err:
 205         if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
 206         BN_free(&t);
 207         if (ctx != NULL) BN_CTX_free(ctx);
 208         return(found ? rnd : NULL);
 209         }
 210
 211 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
 212         BN_CTX *ctx_passed, void *cb_arg)
 213         {
 214         return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
 215         }
 216
 217 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
 218                 void (*callback)(int,int,void *),
 219                 BN_CTX *ctx_passed, void *cb_arg,
 220                 int do_trial_division)
 221         {
 222         int i, j, ret = -1;
 223         int k;
 224         BN_CTX *ctx = NULL;
 225         BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 226         BN_MONT_CTX *mont = NULL;
 227         const BIGNUM *A = NULL;
 228
 229         if (BN_cmp(a, BN_value_one) <= 0)
 230                 return 0;
 231
 232         if (checks == BN_prime_checks)
 233                 checks = BN_prime_checks_for_size(BN_num_bits(a));
 234
 235         /* first look for small factors */
 236         if (!BN_is_odd(a))
 237                 return 0;
 238         if (do_trial_division)
 239                 {
 240                 for (i = 1; i < NUMPRIMES; i++)
 241                         if (BN_mod_word(a, primes[i]) == 0)
 242                                 return 0;
 243                 if (callback != NULL) callback(1, -1, cb_arg);
 244                 }
 245
 246         if (ctx_passed != NULL)
 247                 ctx = ctx_passed;
 248         else
 249                 if ((ctx=BN_CTX_new()) == NULL)
 250                         goto err;
 251         BN_CTX_start(ctx);
 252
 253         /* A := abs(a) */
 254         if (a->neg)
 255                 {
 256                 BIGNUM *t;
 257                 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
 258                 BN_copy(t, a);
 259                 t->neg = 0;
 260                 A = t;
 261                 }
 262         else
 263                 A = a;
 264         A1 = BN_CTX_get(ctx);
 265         A1_odd = BN_CTX_get(ctx);
 266         check = BN_CTX_get(ctx);
 267         if (check == NULL) goto err;
 268
 269         /* compute A1 := A - 1 */
 270         if (!BN_copy(A1, A))
 271                 goto err;
 272         if (!BN_sub_word(A1, 1))
 273                 goto err;
 274         if (BN_is_zero(A1))
 275                 {
 276                 ret = 0;
 277                 goto err;
 278                 }
 279
 280         /* write  A1  as  A1_odd * 2^k */
 281         k = 1;
 282         while (!BN_is_bit_set(A1, k))
 283                 k++;
 284         if (!BN_rshift(A1_odd, A1, k))
 285                 goto err;
 286
 287         /* Montgomery setup for computations mod A */
 288         mont = BN_MONT_CTX_new();
 289         if (mont == NULL)
 290                 goto err;
 291         if (!BN_MONT_CTX_set(mont, A, ctx))
 292                 goto err;
 293
 294         for (i = 0; i < checks; i++)
 295                 {
 296                 if (!BN_pseudo_rand_range(check, A1))
 297                         goto err;
 298                 if (!BN_add_word(check, 1))
 299                         goto err;
 300                 /* now 1 <= check < A */
 301
 302                 j = witness(check, A, A1, A1_odd, k, ctx, mont);
 303                 if (j == -1) goto err;
 304                 if (j)
 305                         {
 306                         ret=0;
 307                         goto err;
 308                         }
 309                 if (callback != NULL) callback(1,i,cb_arg);
 310                 }
 311         ret=1;
 312 err:
 313         if (ctx != NULL)
 314                 {
 315                 BN_CTX_end(ctx);
 316                 if (ctx_passed == NULL)
 317                         BN_CTX_free(ctx);
 318                 }
 319         if (mont != NULL)
 320                 BN_MONT_CTX_free(mont);
 321
 322         return(ret);
 323         }
 324
 325 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 326         const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
 327         {
 328         if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
 329                 return -1;
 330         if (BN_is_one(w))
 331                 return 0; /* probably prime */
 332         if (BN_cmp(w, a1) == 0)
 333                 return 0; /* w == -1 (mod a),  'a' is probably prime */
 334         while (--k)
 335                 {
 336                 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 337                         return -1;
 338                 if (BN_is_one(w))
 339                         return 1; /* 'a' is composite, otherwise a previous 'w' would
 340                                    * have been == -1 (mod 'a') */
 341                 if (BN_cmp(w, a1) == 0)
 342                         return 0; /* w == -1 (mod a), 'a' is probably prime */
 343                 }
 344         /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
 345          * and it is neither -1 nor +1 -- so 'a' cannot be prime */
 346         return 1;
 347         }
 348
 349 static int probable_prime(BIGNUM *rnd, int bits)
 350         {
 351         int i;
 352         BN_ULONG mods[NUMPRIMES];
 353         BN_ULONG delta,d;
 354
 355 again:
 356         if (!BN_rand(rnd,bits,1,1)) return(0);
 357         /* we now have a random number 'rand' to test. */
 358         for (i=1; i<NUMPRIMES; i++)
 359                 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
 360         delta=0;
 361         loop: for (i=1; i<NUMPRIMES; i++)
 362                 {
 363                 /* check that rnd is not a prime and also
 364                  * that gcd(rnd-1,primes) == 1 (except for 2) */
 365                 if (((mods[i]+delta)%primes[i]) <= 1)
 366                         {
 367                         d=delta;
 368                         delta+=2;
 369                         /* perhaps need to check for overflow of
 370                          * delta (but delta can be up to 2^32)
 371                          * 21-May-98 eay - added overflow check */
 372                         if (delta < d) goto again;
 373                         goto loop;
 374                         }
 375                 }
 376         if (!BN_add_word(rnd,delta)) return(0);
 377         return(1);
 378         }
 379
 380 static int probable_prime_dh(BIGNUM *rnd, int bits,
 381         const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
 382         {
 383         int i,ret=0;
 384         BIGNUM *t1;
 385
 386         BN_CTX_start(ctx);
 387         if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
 388
 389         if (!BN_rand(rnd,bits,0,1)) goto err;
 390
 391         /* we need ((rnd-rem) % add) == 0 */
 392
 393         if (!BN_mod(t1,rnd,add,ctx)) goto err;
 394         if (!BN_sub(rnd,rnd,t1)) goto err;
 395         if (rem == NULL)
 396                 { if (!BN_add_word(rnd,1)) goto err; }
 397         else
 398                 { if (!BN_add(rnd,rnd,rem)) goto err; }
 399
 400         /* we now have a random number 'rand' to test. */
 401
 402         loop: for (i=1; i<NUMPRIMES; i++)
 403                 {
 404                 /* check that rnd is a prime */
 405                 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
 406                         {
 407                         if (!BN_add(rnd,rnd,add)) goto err;
 408                         goto loop;
 409                         }
 410                 }
 411         ret=1;
 412 err:
 413         BN_CTX_end(ctx);
 414         return(ret);
 415         }
 416
 417 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
 418         const BIGNUM *rem, BN_CTX *ctx)
 419         {
 420         int i,ret=0;
 421         BIGNUM *t1,*qadd,*q;
 422
 423         bits--;
 424         BN_CTX_start(ctx);
 425         t1 = BN_CTX_get(ctx);
 426         q = BN_CTX_get(ctx);
 427         qadd = BN_CTX_get(ctx);
 428         if (qadd == NULL) goto err;
 429
 430         if (!BN_rshift1(qadd,padd)) goto err;
 431
 432         if (!BN_rand(q,bits,0,1)) goto err;
 433
 434         /* we need ((rnd-rem) % add) == 0 */
 435         if (!BN_mod(t1,q,qadd,ctx)) goto err;
 436         if (!BN_sub(q,q,t1)) goto err;
 437         if (rem == NULL)
 438                 { if (!BN_add_word(q,1)) goto err; }
 439         else
 440                 {
 441                 if (!BN_rshift1(t1,rem)) goto err;
 442                 if (!BN_add(q,q,t1)) goto err;
 443                 }
 444
 445         /* we now have a random number 'rand' to test. */
 446         if (!BN_lshift1(p,q)) goto err;
 447         if (!BN_add_word(p,1)) goto err;
 448
 449         loop: for (i=1; i<NUMPRIMES; i++)
 450                 {
 451                 /* check that p and q are prime */
 452                 /* check that for p and q
 453                  * gcd(p-1,primes) == 1 (except for 2) */
 454                 if (    (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
 455                         (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
 456                         {
 457                         if (!BN_add(p,p,padd)) goto err;
 458                         if (!BN_add(q,q,qadd)) goto err;
 459                         goto loop;
 460                         }
 461                 }
 462         ret=1;
 463 err:
 464         BN_CTX_end(ctx);
 465         return(ret);
 466         }