crypto/bn/bn_prime.c

   1 /*
   2  * WARNING: do not edit!
   3  * Generated by crypto/bn/bn_prime.pl
   4  * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
   5  *
   6  * Licensed under the OpenSSL license (the "License").  You may not use
   7  * this file except in compliance with the License.  You can obtain a copy
   8  * in the file LICENSE in the source distribution or at
   9  * https://www.openssl.org/source/license.html
  10  */
  11
  12 #include <stdio.h>
  13 #include <time.h>
  14 #include "internal/cryptlib.h"
  15 #include "bn_lcl.h"
  16
  17 /*
  18  * The quick sieve algorithm approach to weeding out primes is Philip
  19  * Zimmermann's, as implemented in PGP.  I have had a read of his comments
  20  * and implemented my own version.
  21  */
  22 #include "bn_prime.h"
  23
  24 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
  25                    const BIGNUM *a1_odd, int k, BN_CTX *ctx,
  26                    BN_MONT_CTX *mont);
  27 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
  28 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
  29                                   const BIGNUM *add, const BIGNUM *rem,
  30                                   BN_CTX *ctx);
  31
  32 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
  33 {
  34     /* No callback means continue */
  35     if (!cb)
  36         return 1;
  37     switch (cb->ver) {
  38     case 1:
  39         /* Deprecated-style callbacks */
  40         if (!cb->cb.cb_1)
  41             return 1;
  42         cb->cb.cb_1(a, b, cb->arg);
  43         return 1;
  44     case 2:
  45         /* New-style callbacks */
  46         return cb->cb.cb_2(a, b, cb);
  47     default:
  48         break;
  49     }
  50     /* Unrecognised callback type */
  51     return 0;
  52 }
  53
  54 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
  55                          const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
  56 {
  57     BIGNUM *t;
  58     int found = 0;
  59     int i, j, c1 = 0;
  60     BN_CTX *ctx = NULL;
  61     prime_t *mods = NULL;
  62     int checks = BN_prime_checks_for_size(bits);
  63
  64     if (bits < 2) {
  65         /* There are no prime numbers this small. */
  66         BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
  67         return 0;
  68     } else if (bits == 2 && safe) {
  69         /* The smallest safe prime (7) is three bits. */
  70         BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
  71         return 0;
  72     }
  73
  74     mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
  75     if (mods == NULL)
  76         goto err;
  77
  78     ctx = BN_CTX_new();
  79     if (ctx == NULL)
  80         goto err;
  81     BN_CTX_start(ctx);
  82     t = BN_CTX_get(ctx);
  83     if (!t)
  84         goto err;
  85  loop:
  86     /* make a random number and set the top and bottom bits */
  87     if (add == NULL) {
  88         if (!probable_prime(ret, bits, mods))
  89             goto err;
  90     } else {
  91         if (safe) {
  92             if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
  93                 goto err;
  94         } else {
  95             if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
  96                 goto err;
  97         }
  98     }
  99
 100     if (!BN_GENCB_call(cb, 0, c1++))
 101         /* aborted */
 102         goto err;
 103
 104     if (!safe) {
 105         i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
 106         if (i == -1)
 107             goto err;
 108         if (i == 0)
 109             goto loop;
 110     } else {
 111         /*
 112          * for "safe prime" generation, check that (p-1)/2 is prime. Since a
 113          * prime is odd, We just need to divide by 2
 114          */
 115         if (!BN_rshift1(t, ret))
 116             goto err;
 117
 118         for (i = 0; i < checks; i++) {
 119             j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
 120             if (j == -1)
 121                 goto err;
 122             if (j == 0)
 123                 goto loop;
 124
 125             j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
 126             if (j == -1)
 127                 goto err;
 128             if (j == 0)
 129                 goto loop;
 130
 131             if (!BN_GENCB_call(cb, 2, c1 - 1))
 132                 goto err;
 133             /* We have a safe prime test pass */
 134         }
 135     }
 136     /* we have a prime :-) */
 137     found = 1;
 138  err:
 139     OPENSSL_free(mods);
 140     if (ctx != NULL)
 141         BN_CTX_end(ctx);
 142     BN_CTX_free(ctx);
 143     bn_check_top(ret);
 144     return found;
 145 }
 146
 147 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 148                    BN_GENCB *cb)
 149 {
 150     return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
 151 }
 152
 153 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 154                             int do_trial_division, BN_GENCB *cb)
 155 {
 156     int i, j, ret = -1;
 157     int k;
 158     BN_CTX *ctx = NULL;
 159     BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 160     BN_MONT_CTX *mont = NULL;
 161
 162     if (BN_cmp(a, BN_value_one()) <= 0)
 163         return 0;
 164
 165     if (checks == BN_prime_checks)
 166         checks = BN_prime_checks_for_size(BN_num_bits(a));
 167
 168     /* first look for small factors */
 169     if (!BN_is_odd(a))
 170         /* a is even => a is prime if and only if a == 2 */
 171         return BN_is_word(a, 2);
 172     if (do_trial_division) {
 173         for (i = 1; i < NUMPRIMES; i++) {
 174             BN_ULONG mod = BN_mod_word(a, primes[i]);
 175             if (mod == (BN_ULONG)-1)
 176                 goto err;
 177             if (mod == 0)
 178                 return BN_is_word(a, primes[i]);
 179         }
 180         if (!BN_GENCB_call(cb, 1, -1))
 181             goto err;
 182     }
 183
 184     if (ctx_passed != NULL)
 185         ctx = ctx_passed;
 186     else if ((ctx = BN_CTX_new()) == NULL)
 187         goto err;
 188     BN_CTX_start(ctx);
 189
 190     A1 = BN_CTX_get(ctx);
 191     A1_odd = BN_CTX_get(ctx);
 192     check = BN_CTX_get(ctx);
 193     if (check == NULL)
 194         goto err;
 195
 196     /* compute A1 := a - 1 */
 197     if (!BN_copy(A1, a))
 198         goto err;
 199     if (!BN_sub_word(A1, 1))
 200         goto err;
 201     if (BN_is_zero(A1)) {
 202         ret = 0;
 203         goto err;
 204     }
 205
 206     /* write  A1  as  A1_odd * 2^k */
 207     k = 1;
 208     while (!BN_is_bit_set(A1, k))
 209         k++;
 210     if (!BN_rshift(A1_odd, A1, k))
 211         goto err;
 212
 213     /* Montgomery setup for computations mod a */
 214     mont = BN_MONT_CTX_new();
 215     if (mont == NULL)
 216         goto err;
 217     if (!BN_MONT_CTX_set(mont, a, ctx))
 218         goto err;
 219
 220     for (i = 0; i < checks; i++) {
 221         if (!BN_pseudo_rand_range(check, A1))
 222             goto err;
 223         if (!BN_add_word(check, 1))
 224             goto err;
 225         /* now 1 <= check < a */
 226
 227         j = witness(check, a, A1, A1_odd, k, ctx, mont);
 228         if (j == -1)
 229             goto err;
 230         if (j) {
 231             ret = 0;
 232             goto err;
 233         }
 234         if (!BN_GENCB_call(cb, 1, i))
 235             goto err;
 236     }
 237     ret = 1;
 238  err:
 239     if (ctx != NULL) {
 240         BN_CTX_end(ctx);
 241         if (ctx_passed == NULL)
 242             BN_CTX_free(ctx);
 243     }
 244     BN_MONT_CTX_free(mont);
 245
 246     return (ret);
 247 }
 248
 249 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 250                    const BIGNUM *a1_odd, int k, BN_CTX *ctx,
 251                    BN_MONT_CTX *mont)
 252 {
 253     if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
 254         return -1;
 255     if (BN_is_one(w))
 256         return 0;               /* probably prime */
 257     if (BN_cmp(w, a1) == 0)
 258         return 0;               /* w == -1 (mod a), 'a' is probably prime */
 259     while (--k) {
 260         if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 261             return -1;
 262         if (BN_is_one(w))
 263             return 1;           /* 'a' is composite, otherwise a previous 'w'
 264                                  * would have been == -1 (mod 'a') */
 265         if (BN_cmp(w, a1) == 0)
 266             return 0;           /* w == -1 (mod a), 'a' is probably prime */
 267     }
 268     /*
 269      * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
 270      * it is neither -1 nor +1 -- so 'a' cannot be prime
 271      */
 272     bn_check_top(w);
 273     return 1;
 274 }
 275
 276 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
 277 {
 278     int i;
 279     BN_ULONG delta;
 280     BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
 281     char is_single_word = bits <= BN_BITS2;
 282
 283  again:
 284     if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
 285         return (0);
 286     /* we now have a random number 'rnd' to test. */
 287     for (i = 1; i < NUMPRIMES; i++) {
 288         BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 289         if (mod == (BN_ULONG)-1)
 290             return 0;
 291         mods[i] = (prime_t) mod;
 292     }
 293     /*
 294      * If bits is so small that it fits into a single word then we
 295      * additionally don't want to exceed that many bits.
 296      */
 297     if (is_single_word) {
 298         BN_ULONG size_limit;
 299
 300         if (bits == BN_BITS2) {
 301             /*
 302              * Shifting by this much has undefined behaviour so we do it a
 303              * different way
 304              */
 305             size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
 306         } else {
 307             size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
 308         }
 309         if (size_limit < maxdelta)
 310             maxdelta = size_limit;
 311     }
 312     delta = 0;
 313  loop:
 314     if (is_single_word) {
 315         BN_ULONG rnd_word = BN_get_word(rnd);
 316
 317         /*-
 318          * In the case that the candidate prime is a single word then
 319          * we check that:
 320          *   1) It's greater than primes[i] because we shouldn't reject
 321          *      3 as being a prime number because it's a multiple of
 322          *      three.
 323          *   2) That it's not a multiple of a known prime. We don't
 324          *      check that rnd-1 is also coprime to all the known
 325          *      primes because there aren't many small primes where
 326          *      that's true.
 327          */
 328         for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
 329             if ((mods[i] + delta) % primes[i] == 0) {
 330                 delta += 2;
 331                 if (delta > maxdelta)
 332                     goto again;
 333                 goto loop;
 334             }
 335         }
 336     } else {
 337         for (i = 1; i < NUMPRIMES; i++) {
 338             /*
 339              * check that rnd is not a prime and also that gcd(rnd-1,primes)
 340              * == 1 (except for 2)
 341              */
 342             if (((mods[i] + delta) % primes[i]) <= 1) {
 343                 delta += 2;
 344                 if (delta > maxdelta)
 345                     goto again;
 346                 goto loop;
 347             }
 348         }
 349     }
 350     if (!BN_add_word(rnd, delta))
 351         return (0);
 352     if (BN_num_bits(rnd) != bits)
 353         goto again;
 354     bn_check_top(rnd);
 355     return (1);
 356 }
 357
 358 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
 359                          const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
 360 {
 361     int i, ret = 0;
 362     BIGNUM *t1;
 363
 364     BN_CTX_start(ctx);
 365     if ((t1 = BN_CTX_get(ctx)) == NULL)
 366         goto err;
 367
 368     if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
 369         goto err;
 370
 371     /* we need ((rnd-rem) % add) == 0 */
 372
 373     if (!BN_mod(t1, rnd, add, ctx))
 374         goto err;
 375     if (!BN_sub(rnd, rnd, t1))
 376         goto err;
 377     if (rem == NULL) {
 378         if (!BN_add_word(rnd, 1))
 379             goto err;
 380     } else {
 381         if (!BN_add(rnd, rnd, rem))
 382             goto err;
 383     }
 384
 385     /* we now have a random number 'rand' to test. */
 386
 387  loop:
 388     for (i = 1; i < NUMPRIMES; i++) {
 389         /* check that rnd is a prime */
 390         BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
 391         if (mod == (BN_ULONG)-1)
 392             goto err;
 393         if (mod <= 1) {
 394             if (!BN_add(rnd, rnd, add))
 395                 goto err;
 396             goto loop;
 397         }
 398     }
 399     ret = 1;
 400
 401  err:
 402     BN_CTX_end(ctx);
 403     bn_check_top(rnd);
 404     return (ret);
 405 }
 406
 407 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
 408                                   const BIGNUM *rem, BN_CTX *ctx)
 409 {
 410     int i, ret = 0;
 411     BIGNUM *t1, *qadd, *q;
 412
 413     bits--;
 414     BN_CTX_start(ctx);
 415     t1 = BN_CTX_get(ctx);
 416     q = BN_CTX_get(ctx);
 417     qadd = BN_CTX_get(ctx);
 418     if (qadd == NULL)
 419         goto err;
 420
 421     if (!BN_rshift1(qadd, padd))
 422         goto err;
 423
 424     if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
 425         goto err;
 426
 427     /* we need ((rnd-rem) % add) == 0 */
 428     if (!BN_mod(t1, q, qadd, ctx))
 429         goto err;
 430     if (!BN_sub(q, q, t1))
 431         goto err;
 432     if (rem == NULL) {
 433         if (!BN_add_word(q, 1))
 434             goto err;
 435     } else {
 436         if (!BN_rshift1(t1, rem))
 437             goto err;
 438         if (!BN_add(q, q, t1))
 439             goto err;
 440     }
 441
 442     /* we now have a random number 'rand' to test. */
 443     if (!BN_lshift1(p, q))
 444         goto err;
 445     if (!BN_add_word(p, 1))
 446         goto err;
 447
 448  loop:
 449     for (i = 1; i < NUMPRIMES; i++) {
 450         /* check that p and q are prime */
 451         /*
 452          * check that for p and q gcd(p-1,primes) == 1 (except for 2)
 453          */
 454         BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
 455         BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
 456         if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
 457             goto err;
 458         if (pmod == 0 || qmod == 0) {
 459             if (!BN_add(p, p, padd))
 460                 goto err;
 461             if (!BN_add(q, q, qadd))
 462                 goto err;
 463             goto loop;
 464         }
 465     }
 466     ret = 1;
 467
 468  err:
 469     BN_CTX_end(ctx);
 470     bn_check_top(p);
 471     return (ret);
 472 }