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