OSX/libsecurity_apple_csp/open_ssl/bn/bn_prime.c

   1 /*
   2  * Copyright (c) 2000-2001,2011,2014 Apple 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     BN_init(&t);
 161
 162         ctx=BN_CTX_new();
 163         if (ctx == NULL) goto err;
 164         if (ret == NULL)
 165                 {
 166                 if ((rnd=BN_new()) == NULL) goto err;
 167                 }
 168         else
 169                 rnd=ret;
 170 loop:
 171         /* make a random number and set the top and bottom bits */
 172         if (add == NULL)
 173                 {
 174                 if (!probable_prime(rnd,bits)) goto err;
 175                 }
 176         else
 177                 {
 178                 if (safe)
 179                         {
 180                         if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
 181                                  goto err;
 182                         }
 183                 else
 184                         {
 185                         if (!probable_prime_dh(rnd,bits,add,rem,ctx))
 186                                 goto err;
 187                         }
 188                 }
 189         /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
 190         if (callback != NULL) callback(0,c1++,cb_arg);
 191
 192         if (!safe)
 193                 {
 194                 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
 195                 if (i == -1) goto err;
 196                 if (i == 0) goto loop;
 197                 }
 198         else
 199                 {
 200                 /* for "safe prime" generation,
 201                  * check that (p-1)/2 is prime.
 202                  * Since a prime is odd, We just
 203                  * need to divide by 2 */
 204                 if (!BN_rshift1(&t,rnd)) goto err;
 205
 206                 for (i=0; i<checks; i++)
 207                         {
 208                         j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
 209                         if (j == -1) goto err;
 210                         if (j == 0) goto loop;
 211
 212                         j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
 213                         if (j == -1) goto err;
 214                         if (j == 0) goto loop;
 215
 216                         if (callback != NULL) callback(2,c1-1,cb_arg);
 217                         /* We have a safe prime test pass */
 218                         }
 219                 }
 220         /* we have a prime :-) */
 221         found = 1;
 222 err:
 223         if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
 224         BN_free(&t);
 225         if (ctx != NULL) BN_CTX_free(ctx);
 226         return(found ? rnd : NULL);
 227         }
 228
 229 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
 230         BN_CTX *ctx_passed, void *cb_arg)
 231         {
 232         return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
 233         }
 234
 235 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
 236                 void (*callback)(int,int,void *),
 237                 BN_CTX *ctx_passed, void *cb_arg,
 238                 int do_trial_division)
 239         {
 240         int i, j, ret = -1;
 241         int k;
 242         BN_CTX *ctx = NULL;
 243         BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 244         BN_MONT_CTX *mont = NULL;
 245         const BIGNUM *A = NULL;
 246
 247         if (checks == BN_prime_checks)
 248                 checks = BN_prime_checks_for_size(BN_num_bits(a));
 249
 250         /* first look for small factors */
 251         if (!BN_is_odd(a))
 252                 return(0);
 253         if (do_trial_division)
 254                 {
 255                 for (i = 1; i < NUMPRIMES; i++)
 256                         if (BN_mod_word(a, primes[i]) == 0)
 257                                 return 0;
 258                 if (callback != NULL) callback(1, -1, cb_arg);
 259                 }
 260
 261         if (ctx_passed != NULL)
 262                 ctx = ctx_passed;
 263         else
 264                 if ((ctx=BN_CTX_new()) == NULL)
 265                         goto err;
 266         BN_CTX_start(ctx);
 267
 268         /* A := abs(a) */
 269         if (a->neg)
 270                 {
 271                 BIGNUM *t;
 272                 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
 273                 BN_copy(t, a);
 274                 t->neg = 0;
 275                 A = t;
 276                 }
 277         else
 278                 A = a;
 279         A1 = BN_CTX_get(ctx);
 280         A1_odd = BN_CTX_get(ctx);
 281         check = BN_CTX_get(ctx);
 282         if (check == NULL) goto err;
 283
 284         /* compute A1 := A - 1 */
 285         if (!BN_copy(A1, A))
 286                 goto err;
 287         if (!BN_sub_word(A1, 1))
 288                 goto err;
 289         if (BN_is_zero(A1))
 290                 {
 291                 ret = 0;
 292                 goto err;
 293                 }
 294
 295         /* write  A1  as  A1_odd * 2^k */
 296         k = 1;
 297         while (!BN_is_bit_set(A1, k))
 298                 k++;
 299         if (!BN_rshift(A1_odd, A1, k))
 300                 goto err;
 301
 302         /* Montgomery setup for computations mod A */
 303         mont = BN_MONT_CTX_new();
 304         if (mont == NULL)
 305                 goto err;
 306         if (!BN_MONT_CTX_set(mont, A, ctx))
 307                 goto err;
 308
 309         for (i = 0; i < checks; i++)
 310                 {
 311                 if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0))
 312                         goto err;
 313                 if (BN_cmp(check, A1) >= 0)
 314                         if (!BN_sub(check, check, A1))
 315                                 goto err;
 316                 if (!BN_add_word(check, 1))
 317                         goto err;
 318                 /* now 1 <= check < A */
 319
 320                 j = witness(check, A, A1, A1_odd, k, ctx, mont);
 321                 if (j == -1) goto err;
 322                 if (j)
 323                         {
 324                         ret=0;
 325                         goto err;
 326                         }
 327                 if (callback != NULL) callback(1,i,cb_arg);
 328                 }
 329         ret=1;
 330 err:
 331         if (ctx != NULL)
 332                 {
 333                 BN_CTX_end(ctx);
 334                 if (ctx_passed == NULL)
 335                         BN_CTX_free(ctx);
 336                 }
 337         if (mont != NULL)
 338                 BN_MONT_CTX_free(mont);
 339
 340         return(ret);
 341         }
 342
 343 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 344         const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
 345         {
 346         if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
 347                 return -1;
 348         if (BN_is_one(w))
 349                 return 0; /* probably prime */
 350         if (BN_cmp(w, a1) == 0)
 351                 return 0; /* w == -1 (mod a),  'a' is probably prime */
 352         while (--k)
 353                 {
 354                 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 355                         return -1;
 356                 if (BN_is_one(w))
 357                         return 1; /* 'a' is composite, otherwise a previous 'w' would
 358                                    * have been == -1 (mod 'a') */
 359                 if (BN_cmp(w, a1) == 0)
 360                         return 0; /* w == -1 (mod a), 'a' is probably prime */
 361                 }
 362         /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
 363          * and it is neither -1 nor +1 -- so 'a' cannot be prime */
 364         return 1;
 365         }
 366
 367 static int probable_prime(BIGNUM *rnd, int bits)
 368         {
 369         int i;
 370         BN_ULONG mods[NUMPRIMES];
 371         BN_ULONG delta,d;
 372
 373 again:
 374         if (!BN_rand(rnd,bits,1,1)) return(0);
 375         /* we now have a random number 'rand' to test. */
 376         for (i=1; i<NUMPRIMES; i++)
 377                 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
 378         delta=0;
 379         loop: for (i=1; i<NUMPRIMES; i++)
 380                 {
 381                 /* check that rnd is not a prime and also
 382                  * that gcd(rnd-1,primes) == 1 (except for 2) */
 383                 if (((mods[i]+delta)%primes[i]) <= 1)
 384                         {
 385                         d=delta;
 386                         delta+=2;
 387                         /* perhaps need to check for overflow of
 388                          * delta (but delta can be up to 2^32)
 389                          * 21-May-98 eay - added overflow check */
 390                         if (delta < d) goto again;
 391                         goto loop;
 392                         }
 393                 }
 394         if (!BN_add_word(rnd,delta)) return(0);
 395         return(1);
 396         }
 397
 398 static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
 399              BN_CTX *ctx)
 400         {
 401         int i,ret=0;
 402         BIGNUM *t1;
 403
 404         BN_CTX_start(ctx);
 405         if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
 406
 407         if (!BN_rand(rnd,bits,0,1)) goto err;
 408
 409         /* we need ((rnd-rem) % add) == 0 */
 410
 411         if (!BN_mod(t1,rnd,add,ctx)) goto err;
 412         if (!BN_sub(rnd,rnd,t1)) goto err;
 413         if (rem == NULL)
 414                 { if (!BN_add_word(rnd,1)) goto err; }
 415         else
 416                 { if (!BN_add(rnd,rnd,rem)) goto err; }
 417
 418         /* we now have a random number 'rand' to test. */
 419
 420         loop: for (i=1; i<NUMPRIMES; i++)
 421                 {
 422                 /* check that rnd is a prime */
 423                 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
 424                         {
 425                         if (!BN_add(rnd,rnd,add)) goto err;
 426                         goto loop;
 427                         }
 428                 }
 429         ret=1;
 430 err:
 431         BN_CTX_end(ctx);
 432         return(ret);
 433         }
 434
 435 static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
 436              BIGNUM *rem, BN_CTX *ctx)
 437         {
 438         int i,ret=0;
 439         BIGNUM *t1,*qadd,*q;
 440
 441         bits--;
 442         BN_CTX_start(ctx);
 443         t1 = BN_CTX_get(ctx);
 444         q = BN_CTX_get(ctx);
 445         qadd = BN_CTX_get(ctx);
 446         if (qadd == NULL) goto err;
 447
 448         if (!BN_rshift1(qadd,padd)) goto err;
 449
 450         if (!BN_rand(q,bits,0,1)) goto err;
 451
 452         /* we need ((rnd-rem) % add) == 0 */
 453         if (!BN_mod(t1,q,qadd,ctx)) goto err;
 454         if (!BN_sub(q,q,t1)) goto err;
 455         if (rem == NULL)
 456                 { if (!BN_add_word(q,1)) goto err; }
 457         else
 458                 {
 459                 if (!BN_rshift1(t1,rem)) goto err;
 460                 if (!BN_add(q,q,t1)) goto err;
 461                 }
 462
 463         /* we now have a random number 'rand' to test. */
 464         if (!BN_lshift1(p,q)) goto err;
 465         if (!BN_add_word(p,1)) goto err;
 466
 467         loop: for (i=1; i<NUMPRIMES; i++)
 468                 {
 469                 /* check that p and q are prime */
 470                 /* check that for p and q
 471                  * gcd(p-1,primes) == 1 (except for 2) */
 472                 if (    (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
 473                         (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
 474                         {
 475                         if (!BN_add(p,p,padd)) goto err;
 476                         if (!BN_add(q,q,qadd)) goto err;
 477                         goto loop;
 478                         }
 479                 }
 480         ret=1;
 481 err:
 482         BN_CTX_end(ctx);
 483         return(ret);
 484         }