AppleCSP/open_ssl/bn/bn_prime.c

   1 /*
   2  * Copyright (c) 2000-2001 Apple Computer, Inc. All Rights Reserved.
   3  *
   4  * The contents of this file constitute Original Code as defined in and are
   5  * subject to the Apple Public Source License Version 1.2 (the 'License').
   6  * You may not use this file except in compliance with the License. Please obtain
   7  * a copy of the License at http://www.apple.com/publicsource and read it before
   8  * using this file.
   9  *
  10  * This Original Code and all software distributed under the License are
  11  * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS
  12  * OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, INCLUDING WITHOUT
  13  * LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
  14  * PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. Please see the License for the
  15  * specific language governing rights and limitations under the License.
  16  */
  17
  18
  19 /* crypto/bn/bn_prime.c */
  20 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
  21  * All rights reserved.
  22  *
  23  * This package is an SSL implementation written
  24  * by Eric Young (eay@cryptsoft.com).
  25  * The implementation was written so as to conform with Netscapes SSL.
  26  *
  27  * This library is free for commercial and non-commercial use as long as
  28  * the following conditions are aheared to.  The following conditions
  29  * apply to all code found in this distribution, be it the RC4, RSA,
  30  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
  31  * included with this distribution is covered by the same copyright terms
  32  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
  33  *
  34  * Copyright remains Eric Young's, and as such any Copyright notices in
  35  * the code are not to be removed.
  36  * If this package is used in a product, Eric Young should be given attribution
  37  * as the author of the parts of the library used.
  38  * This can be in the form of a textual message at program startup or
  39  * in documentation (online or textual) provided with the package.
  40  *
  41  * Redistribution and use in source and binary forms, with or without
  42  * modification, are permitted provided that the following conditions
  43  * are met:
  44  * 1. Redistributions of source code must retain the copyright
  45  *    notice, this list of conditions and the following disclaimer.
  46  * 2. Redistributions in binary form must reproduce the above copyright
  47  *    notice, this list of conditions and the following disclaimer in the
  48  *    documentation and/or other materials provided with the distribution.
  49  * 3. All advertising materials mentioning features or use of this software
  50  *    must display the following acknowledgement:
  51  *    "This product includes cryptographic software written by
  52  *     Eric Young (eay@cryptsoft.com)"
  53  *    The word 'cryptographic' can be left out if the rouines from the library
  54  *    being used are not cryptographic related :-).
  55  * 4. If you include any Windows specific code (or a derivative thereof) from
  56  *    the apps directory (application code) you must include an acknowledgement:
  57  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
  58  *
  59  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
  60  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  61  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  62  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  63  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  64  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  65  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  66  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  67  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  68  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  69  * SUCH DAMAGE.
  70  *
  71  * The licence and distribution terms for any publically available version or
  72  * derivative of this code cannot be changed.  i.e. this code cannot simply be
  73  * copied and put under another distribution licence
  74  * [including the GNU Public Licence.]
  75  */
  76 /* ====================================================================
  77  * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
  78  *
  79  * Redistribution and use in source and binary forms, with or without
  80  * modification, are permitted provided that the following conditions
  81  * are met:
  82  *
  83  * 1. Redistributions of source code must retain the above copyright
  84  *    notice, this list of conditions and the following disclaimer.
  85  *
  86  * 2. Redistributions in binary form must reproduce the above copyright
  87  *    notice, this list of conditions and the following disclaimer in
  88  *    the documentation and/or other materials provided with the
  89  *    distribution.
  90  *
  91  * 3. All advertising materials mentioning features or use of this
  92  *    software must display the following acknowledgment:
  93  *    "This product includes software developed by the OpenSSL Project
  94  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  95  *
  96  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  97  *    endorse or promote products derived from this software without
  98  *    prior written permission. For written permission, please contact
  99  *    openssl-core@openssl.org.
 100  *
 101  * 5. Products derived from this software may not be called "OpenSSL"
 102  *    nor may "OpenSSL" appear in their names without prior written
 103  *    permission of the OpenSSL Project.
 104  *
 105  * 6. Redistributions of any form whatsoever must retain the following
 106  *    acknowledgment:
 107  *    "This product includes software developed by the OpenSSL Project
 108  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 109  *
 110  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 111  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 112  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 113  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 114  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 115  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 116  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 117  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 118  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 119  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 120  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 121  * OF THE POSSIBILITY OF SUCH DAMAGE.
 122  * ====================================================================
 123  *
 124  * This product includes cryptographic software written by Eric Young
 125  * (eay@cryptsoft.com).  This product includes software written by Tim
 126  * Hudson (tjh@cryptsoft.com).
 127  *
 128  */
 129
 130 #include <stdio.h>
 131 #include <time.h>
 132 #include "cryptlib.h"
 133 #include "bn_lcl.h"
 134 #include <openssl/rand.h>
 135
 136 /* The quick sieve algorithm approach to weeding out primes is
 137  * Philip Zimmermann's, as implemented in PGP.  I have had a read of
 138  * his comments and implemented my own version.
 139  */
 140 #include "bn_prime.h"
 141
 142 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 143         const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
 144 static int probable_prime(BIGNUM *rnd, int bits);
 145 static int probable_prime_dh(BIGNUM *rnd, int bits,
 146         BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
 147 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
 148         BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
 149
 150 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
 151              BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
 152         {
 153         BIGNUM *rnd=NULL;
 154         BIGNUM t;
 155         int found=0;
 156         int i,j,c1=0;
 157         BN_CTX *ctx;
 158         int checks = BN_prime_checks_for_size(bits);
 159
 160         ctx=BN_CTX_new();
 161         if (ctx == NULL) goto err;
 162         if (ret == NULL)
 163                 {
 164                 if ((rnd=BN_new()) == NULL) goto err;
 165                 }
 166         else
 167                 rnd=ret;
 168         BN_init(&t);
 169 loop:
 170         /* make a random number and set the top and bottom bits */
 171         if (add == NULL)
 172                 {
 173                 if (!probable_prime(rnd,bits)) goto err;
 174                 }
 175         else
 176                 {
 177                 if (safe)
 178                         {
 179                         if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
 180                                  goto err;
 181                         }
 182                 else
 183                         {
 184                         if (!probable_prime_dh(rnd,bits,add,rem,ctx))
 185                                 goto err;
 186                         }
 187                 }
 188         /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
 189         if (callback != NULL) callback(0,c1++,cb_arg);
 190
 191         if (!safe)
 192                 {
 193                 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
 194                 if (i == -1) goto err;
 195                 if (i == 0) goto loop;
 196                 }
 197         else
 198                 {
 199                 /* for "safe prime" generation,
 200                  * check that (p-1)/2 is prime.
 201                  * Since a prime is odd, We just
 202                  * need to divide by 2 */
 203                 if (!BN_rshift1(&t,rnd)) goto err;
 204
 205                 for (i=0; i<checks; i++)
 206                         {
 207                         j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
 208                         if (j == -1) goto err;
 209                         if (j == 0) goto loop;
 210
 211                         j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
 212                         if (j == -1) goto err;
 213                         if (j == 0) goto loop;
 214
 215                         if (callback != NULL) callback(2,c1-1,cb_arg);
 216                         /* We have a safe prime test pass */
 217                         }
 218                 }
 219         /* we have a prime :-) */
 220         found = 1;
 221 err:
 222         if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
 223         BN_free(&t);
 224         if (ctx != NULL) BN_CTX_free(ctx);
 225         return(found ? rnd : NULL);
 226         }
 227
 228 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
 229         BN_CTX *ctx_passed, void *cb_arg)
 230         {
 231         return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
 232         }
 233
 234 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
 235                 void (*callback)(int,int,void *),
 236                 BN_CTX *ctx_passed, void *cb_arg,
 237                 int do_trial_division)
 238         {
 239         int i, j, ret = -1;
 240         int k;
 241         BN_CTX *ctx = NULL;
 242         BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 243         BN_MONT_CTX *mont = NULL;
 244         const BIGNUM *A = NULL;
 245
 246         if (checks == BN_prime_checks)
 247                 checks = BN_prime_checks_for_size(BN_num_bits(a));
 248
 249         /* first look for small factors */
 250         if (!BN_is_odd(a))
 251                 return(0);
 252         if (do_trial_division)
 253                 {
 254                 for (i = 1; i < NUMPRIMES; i++)
 255                         if (BN_mod_word(a, primes[i]) == 0)
 256                                 return 0;
 257                 if (callback != NULL) callback(1, -1, cb_arg);
 258                 }
 259
 260         if (ctx_passed != NULL)
 261                 ctx = ctx_passed;
 262         else
 263                 if ((ctx=BN_CTX_new()) == NULL)
 264                         goto err;
 265         BN_CTX_start(ctx);
 266
 267         /* A := abs(a) */
 268         if (a->neg)
 269                 {
 270                 BIGNUM *t;
 271                 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
 272                 BN_copy(t, a);
 273                 t->neg = 0;
 274                 A = t;
 275                 }
 276         else
 277                 A = a;
 278         A1 = BN_CTX_get(ctx);
 279         A1_odd = BN_CTX_get(ctx);
 280         check = BN_CTX_get(ctx);
 281         if (check == NULL) goto err;
 282
 283         /* compute A1 := A - 1 */
 284         if (!BN_copy(A1, A))
 285                 goto err;
 286         if (!BN_sub_word(A1, 1))
 287                 goto err;
 288         if (BN_is_zero(A1))
 289                 {
 290                 ret = 0;
 291                 goto err;
 292                 }
 293
 294         /* write  A1  as  A1_odd * 2^k */
 295         k = 1;
 296         while (!BN_is_bit_set(A1, k))
 297                 k++;
 298         if (!BN_rshift(A1_odd, A1, k))
 299                 goto err;
 300
 301         /* Montgomery setup for computations mod A */
 302         mont = BN_MONT_CTX_new();
 303         if (mont == NULL)
 304                 goto err;
 305         if (!BN_MONT_CTX_set(mont, A, ctx))
 306                 goto err;
 307
 308         for (i = 0; i < checks; i++)
 309                 {
 310                 if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0))
 311                         goto err;
 312                 if (BN_cmp(check, A1) >= 0)
 313                         if (!BN_sub(check, check, A1))
 314                                 goto err;
 315                 if (!BN_add_word(check, 1))
 316                         goto err;
 317                 /* now 1 <= check < A */
 318
 319                 j = witness(check, A, A1, A1_odd, k, ctx, mont);
 320                 if (j == -1) goto err;
 321                 if (j)
 322                         {
 323                         ret=0;
 324                         goto err;
 325                         }
 326                 if (callback != NULL) callback(1,i,cb_arg);
 327                 }
 328         ret=1;
 329 err:
 330         if (ctx != NULL)
 331                 {
 332                 BN_CTX_end(ctx);
 333                 if (ctx_passed == NULL)
 334                         BN_CTX_free(ctx);
 335                 }
 336         if (mont != NULL)
 337                 BN_MONT_CTX_free(mont);
 338
 339         return(ret);
 340         }
 341
 342 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 343         const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
 344         {
 345         if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
 346                 return -1;
 347         if (BN_is_one(w))
 348                 return 0; /* probably prime */
 349         if (BN_cmp(w, a1) == 0)
 350                 return 0; /* w == -1 (mod a),  'a' is probably prime */
 351         while (--k)
 352                 {
 353                 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 354                         return -1;
 355                 if (BN_is_one(w))
 356                         return 1; /* 'a' is composite, otherwise a previous 'w' would
 357                                    * have been == -1 (mod 'a') */
 358                 if (BN_cmp(w, a1) == 0)
 359                         return 0; /* w == -1 (mod a), 'a' is probably prime */
 360                 }
 361         /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
 362          * and it is neither -1 nor +1 -- so 'a' cannot be prime */
 363         return 1;
 364         }
 365
 366 static int probable_prime(BIGNUM *rnd, int bits)
 367         {
 368         int i;
 369         BN_ULONG mods[NUMPRIMES];
 370         BN_ULONG delta,d;
 371
 372 again:
 373         if (!BN_rand(rnd,bits,1,1)) return(0);
 374         /* we now have a random number 'rand' to test. */
 375         for (i=1; i<NUMPRIMES; i++)
 376                 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
 377         delta=0;
 378         loop: for (i=1; i<NUMPRIMES; i++)
 379                 {
 380                 /* check that rnd is not a prime and also
 381                  * that gcd(rnd-1,primes) == 1 (except for 2) */
 382                 if (((mods[i]+delta)%primes[i]) <= 1)
 383                         {
 384                         d=delta;
 385                         delta+=2;
 386                         /* perhaps need to check for overflow of
 387                          * delta (but delta can be up to 2^32)
 388                          * 21-May-98 eay - added overflow check */
 389                         if (delta < d) goto again;
 390                         goto loop;
 391                         }
 392                 }
 393         if (!BN_add_word(rnd,delta)) return(0);
 394         return(1);
 395         }
 396
 397 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
 398              BN_CTX *ctx)
 399         {
 400         int i,ret=0;
 401         BIGNUM *t1;
 402
 403         BN_CTX_start(ctx);
 404         if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
 405
 406         if (!BN_rand(rnd,bits,0,1)) goto err;
 407
 408         /* we need ((rnd-rem) % add) == 0 */
 409
 410         if (!BN_mod(t1,rnd,add,ctx)) goto err;
 411         if (!BN_sub(rnd,rnd,t1)) goto err;
 412         if (rem == NULL)
 413                 { if (!BN_add_word(rnd,1)) goto err; }
 414         else
 415                 { if (!BN_add(rnd,rnd,rem)) goto err; }
 416
 417         /* we now have a random number 'rand' to test. */
 418
 419         loop: for (i=1; i<NUMPRIMES; i++)
 420                 {
 421                 /* check that rnd is a prime */
 422                 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
 423                         {
 424                         if (!BN_add(rnd,rnd,add)) goto err;
 425                         goto loop;
 426                         }
 427                 }
 428         ret=1;
 429 err:
 430         BN_CTX_end(ctx);
 431         return(ret);
 432         }
 433
 434 static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
 435              BIGNUM *rem, BN_CTX *ctx)
 436         {
 437         int i,ret=0;
 438         BIGNUM *t1,*qadd,*q;
 439
 440         bits--;
 441         BN_CTX_start(ctx);
 442         t1 = BN_CTX_get(ctx);
 443         q = BN_CTX_get(ctx);
 444         qadd = BN_CTX_get(ctx);
 445         if (qadd == NULL) goto err;
 446
 447         if (!BN_rshift1(qadd,padd)) goto err;
 448
 449         if (!BN_rand(q,bits,0,1)) goto err;
 450
 451         /* we need ((rnd-rem) % add) == 0 */
 452         if (!BN_mod(t1,q,qadd,ctx)) goto err;
 453         if (!BN_sub(q,q,t1)) goto err;
 454         if (rem == NULL)
 455                 { if (!BN_add_word(q,1)) goto err; }
 456         else
 457                 {
 458                 if (!BN_rshift1(t1,rem)) goto err;
 459                 if (!BN_add(q,q,t1)) goto err;
 460                 }
 461
 462         /* we now have a random number 'rand' to test. */
 463         if (!BN_lshift1(p,q)) goto err;
 464         if (!BN_add_word(p,1)) goto err;
 465
 466         loop: for (i=1; i<NUMPRIMES; i++)
 467                 {
 468                 /* check that p and q are prime */
 469                 /* check that for p and q
 470                  * gcd(p-1,primes) == 1 (except for 2) */
 471                 if (    (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
 472                         (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
 473                         {
 474                         if (!BN_add(p,p,padd)) goto err;
 475                         if (!BN_add(q,q,qadd)) goto err;
 476                         goto loop;
 477                         }
 478                 }
 479         ret=1;
 480 err:
 481         BN_CTX_end(ctx);
 482         return(ret);
 483         }