bn_prime.c

/* crypto/bn/bn_prime.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <stdio.h>
#include <time.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
#include <openssl/rand.h>

/*
 * NB: these functions have been "upgraded", the deprecated versions (which
 * are compatibility wrappers using these functions) are in bn_depr.c. -
 * Geoff
 */

/*
 * The quick sieve algorithm approach to weeding out primes is Philip
 * Zimmermann's, as implemented in PGP.  I have had a read of his comments
 * and implemented my own version.
 */
#include "bn_prime.h"

static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
                   const BIGNUM *a1_odd, int k, BN_CTX *ctx,
                   BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
                                  const BIGNUM *add, const BIGNUM *rem,
                                  BN_CTX *ctx);

static const int prime_offsets[480] = {
    13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
    89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
    167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
    233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
    299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
    373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
    437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
    503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
    571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
    641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
    703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
    773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
    841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
    907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
    977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
    1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
    1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
    1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
    1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
    1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
    1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
    1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
    1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
    1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
    1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
    1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
    1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
    1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
    1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
    1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
    1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
    1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
    2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
    2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
    2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
    2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
    2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
    2309, 2311
};

static const int prime_offset_count = 480;
static const int prime_multiplier = 2310;
static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
                                              * |prime_multiplier| */
static const int first_prime_index = 5;

int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
    /* No callback means continue */
    if (!cb)
        return 1;
    switch (cb->ver) {
    case 1:
        /* Deprecated-style callbacks */
        if (!cb->cb.cb_1)
            return 1;
        cb->cb.cb_1(a, b, cb->arg);
        return 1;
    case 2:
        /* New-style callbacks */
        return cb->cb.cb_2(a, b, cb);
    default:
        break;
    }
    /* Unrecognised callback type */
    return 0;
}

int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
                         const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
{
    BIGNUM *t;
    int found = 0;
    int i, j, c1 = 0;
    BN_CTX *ctx;
    int checks = BN_prime_checks_for_size(bits);

    if (bits < 2) {
        /* There are no prime numbers this small. */
        BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
        return 0;
    } else if (bits == 2 && safe) {
        /* The smallest safe prime (7) is three bits. */
        BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
        return 0;
    }

    ctx = BN_CTX_new();
    if (ctx == NULL)
        goto err;
    BN_CTX_start(ctx);
    t = BN_CTX_get(ctx);
    if (!t)
        goto err;
 loop:
    /* make a random number and set the top and bottom bits */
    if (add == NULL) {
        if (!probable_prime(ret, bits))
            goto err;
    } else {
        if (safe) {
            if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
                goto err;
        } else {
            if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
                goto err;
        }
    }
    /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
    if (!BN_GENCB_call(cb, 0, c1++))
        /* aborted */
        goto err;

    if (!safe) {
        i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
        if (i == -1)
            goto err;
        if (i == 0)
            goto loop;
    } else {
        /*
         * for "safe prime" generation, check that (p-1)/2 is prime. Since a
         * prime is odd, We just need to divide by 2
         */
        if (!BN_rshift1(t, ret))
            goto err;

        for (i = 0; i < checks; i++) {
            j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
            if (j == -1)
                goto err;
            if (j == 0)
                goto loop;

            j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
            if (j == -1)
                goto err;
            if (j == 0)
                goto loop;

            if (!BN_GENCB_call(cb, 2, c1 - 1))
                goto err;
            /* We have a safe prime test pass */
        }
    }
    /* we have a prime :-) */
    found = 1;
 err:
    if (ctx != NULL)
        BN_CTX_end(ctx);
    BN_CTX_free(ctx);
    bn_check_top(ret);
    return found;
}

int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
                   BN_GENCB *cb)
{
    return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
}

int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
                            int do_trial_division, BN_GENCB *cb)
{
    int i, j, ret = -1;
    int k;
    BN_CTX *ctx = NULL;
    BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
    BN_MONT_CTX *mont = NULL;
    const BIGNUM *A = NULL;

    if (BN_cmp(a, BN_value_one()) <= 0)
        return 0;

    if (checks == BN_prime_checks)
        checks = BN_prime_checks_for_size(BN_num_bits(a));

    /* first look for small factors */
    if (!BN_is_odd(a))
        /* a is even => a is prime if and only if a == 2 */
        return BN_is_word(a, 2);
    if (do_trial_division) {
        for (i = 1; i < NUMPRIMES; i++)
            if (BN_mod_word(a, primes[i]) == 0)
                return 0;
        if (!BN_GENCB_call(cb, 1, -1))
            goto err;
    }

    if (ctx_passed != NULL)
        ctx = ctx_passed;
    else if ((ctx = BN_CTX_new()) == NULL)
        goto err;
    BN_CTX_start(ctx);

    /* A := abs(a) */
    if (a->neg) {
        BIGNUM *t;
        if ((t = BN_CTX_get(ctx)) == NULL)
            goto err;
        BN_copy(t, a);
        t->neg = 0;
        A = t;
    } else
        A = a;
    A1 = BN_CTX_get(ctx);
    A1_odd = BN_CTX_get(ctx);
    check = BN_CTX_get(ctx);
    if (check == NULL)
        goto err;

    /* compute A1 := A - 1 */
    if (!BN_copy(A1, A))
        goto err;
    if (!BN_sub_word(A1, 1))
        goto err;
    if (BN_is_zero(A1)) {
        ret = 0;
        goto err;
    }

    /* write  A1  as  A1_odd * 2^k */
    k = 1;
    while (!BN_is_bit_set(A1, k))
        k++;
    if (!BN_rshift(A1_odd, A1, k))
        goto err;

    /* Montgomery setup for computations mod A */
    mont = BN_MONT_CTX_new();
    if (mont == NULL)
        goto err;
    if (!BN_MONT_CTX_set(mont, A, ctx))
        goto err;

    for (i = 0; i < checks; i++) {
        if (!BN_pseudo_rand_range(check, A1))
            goto err;
        if (!BN_add_word(check, 1))
            goto err;
        /* now 1 <= check < A */

        j = witness(check, A, A1, A1_odd, k, ctx, mont);
        if (j == -1)
            goto err;
        if (j) {
            ret = 0;
            goto err;
        }
        if (!BN_GENCB_call(cb, 1, i))
            goto err;
    }
    ret = 1;
 err:
    if (ctx != NULL) {
        BN_CTX_end(ctx);
        if (ctx_passed == NULL)
            BN_CTX_free(ctx);
    }
    BN_MONT_CTX_free(mont);

    return (ret);
}

int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
{
    int i;
    int ret = 0;

 loop:
    if (!BN_rand(rnd, bits, 0, 1))
        goto err;

    /* we now have a random number 'rand' to test. */

    for (i = 1; i < NUMPRIMES; i++) {
        /* check that rnd is a prime */
        if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
            goto loop;
        }
    }
    ret = 1;

 err:
    bn_check_top(rnd);
    return (ret);
}

int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
{
    int i;
    BIGNUM *offset_index;
    BIGNUM *offset_count;
    int ret = 0;

    OPENSSL_assert(bits > prime_multiplier_bits);

    BN_CTX_start(ctx);
    if ((offset_index = BN_CTX_get(ctx)) == NULL)
        goto err;
    if ((offset_count = BN_CTX_get(ctx)) == NULL)
        goto err;

    BN_add_word(offset_count, prime_offset_count);

 loop:
    if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1))
        goto err;
    if (BN_is_bit_set(rnd, bits))
        goto loop;
    if (!BN_rand_range(offset_index, offset_count))
        goto err;

    BN_mul_word(rnd, prime_multiplier);
    BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]);

    /* we now have a random number 'rand' to test. */

    /* skip coprimes */
    for (i = first_prime_index; i < NUMPRIMES; i++) {
        /* check that rnd is a prime */
        if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
            goto loop;
        }
    }
    ret = 1;

 err:
    BN_CTX_end(ctx);
    bn_check_top(rnd);
    return ret;
}

static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
                   const BIGNUM *a1_odd, int k, BN_CTX *ctx,
                   BN_MONT_CTX *mont)
{
    if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
        return -1;
    if (BN_is_one(w))
        return 0;               /* probably prime */
    if (BN_cmp(w, a1) == 0)
        return 0;               /* w == -1 (mod a), 'a' is probably prime */
    while (--k) {
        if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
            return -1;
        if (BN_is_one(w))
            return 1;           /* 'a' is composite, otherwise a previous 'w'
                                 * would have been == -1 (mod 'a') */
        if (BN_cmp(w, a1) == 0)
            return 0;           /* w == -1 (mod a), 'a' is probably prime */
    }
    /*
     * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
     * it is neither -1 nor +1 -- so 'a' cannot be prime
     */
    bn_check_top(w);
    return 1;
}

static int probable_prime(BIGNUM *rnd, int bits)
{
    int i;
    prime_t mods[NUMPRIMES];
    BN_ULONG delta;
    BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
    char is_single_word = bits <= BN_BITS2;

 again:
    if (!BN_rand(rnd, bits, 1, 1))
        return (0);
    /* we now have a random number 'rnd' to test. */
    for (i = 1; i < NUMPRIMES; i++)
        mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]);
    /*
     * If bits is so small that it fits into a single word then we
     * additionally don't want to exceed that many bits.
     */
    if (is_single_word) {
        BN_ULONG size_limit;
        
        if (bits == BN_BITS2) {
            /*
             * Shifting by this much has undefined behaviour so we do it a
             * different way
             */
            size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
        } else {
            size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
        }
        if (size_limit < maxdelta)
            maxdelta = size_limit;
    }
    delta = 0;
 loop:
    if (is_single_word) {
        BN_ULONG rnd_word = BN_get_word(rnd);

        /*-
         * In the case that the candidate prime is a single word then
         * we check that:
         *   1) It's greater than primes[i] because we shouldn't reject
         *      3 as being a prime number because it's a multiple of
         *      three.
         *   2) That it's not a multiple of a known prime. We don't
         *      check that rnd-1 is also coprime to all the known
         *      primes because there aren't many small primes where
         *      that's true.
         */
        for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
            if ((mods[i] + delta) % primes[i] == 0) {
                delta += 2;
                if (delta > maxdelta)
                    goto again;
                goto loop;
            }
        }
    } else {
        for (i = 1; i < NUMPRIMES; i++) {
            /*
             * check that rnd is not a prime and also that gcd(rnd-1,primes)
             * == 1 (except for 2)
             */
            if (((mods[i] + delta) % primes[i]) <= 1) {
                delta += 2;
                if (delta > maxdelta)
                    goto again;
                goto loop;
            }
        }
    }
    if (!BN_add_word(rnd, delta))
        return (0);
    if (BN_num_bits(rnd) != bits)
        goto again;
    bn_check_top(rnd);
    return (1);
}

int bn_probable_prime_dh(BIGNUM *rnd, int bits,
                         const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
{
    int i, ret = 0;
    BIGNUM *t1;

    BN_CTX_start(ctx);
    if ((t1 = BN_CTX_get(ctx)) == NULL)
        goto err;

    if (!BN_rand(rnd, bits, 0, 1))
        goto err;

    /* we need ((rnd-rem) % add) == 0 */

    if (!BN_mod(t1, rnd, add, ctx))
        goto err;
    if (!BN_sub(rnd, rnd, t1))
        goto err;
    if (rem == NULL) {
        if (!BN_add_word(rnd, 1))
            goto err;
    } else {
        if (!BN_add(rnd, rnd, rem))
            goto err;
    }

    /* we now have a random number 'rand' to test. */

 loop:
    for (i = 1; i < NUMPRIMES; i++) {
        /* check that rnd is a prime */
        if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
            if (!BN_add(rnd, rnd, add))
                goto err;
            goto loop;
        }
    }
    ret = 1;

 err:
    BN_CTX_end(ctx);
    bn_check_top(rnd);
    return (ret);
}

static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
                                  const BIGNUM *rem, BN_CTX *ctx)
{
    int i, ret = 0;
    BIGNUM *t1, *qadd, *q;

    bits--;
    BN_CTX_start(ctx);
    t1 = BN_CTX_get(ctx);
    q = BN_CTX_get(ctx);
    qadd = BN_CTX_get(ctx);
    if (qadd == NULL)
        goto err;

    if (!BN_rshift1(qadd, padd))
        goto err;

    if (!BN_rand(q, bits, 0, 1))
        goto err;

    /* we need ((rnd-rem) % add) == 0 */
    if (!BN_mod(t1, q, qadd, ctx))
        goto err;
    if (!BN_sub(q, q, t1))
        goto err;
    if (rem == NULL) {
        if (!BN_add_word(q, 1))
            goto err;
    } else {
        if (!BN_rshift1(t1, rem))
            goto err;
        if (!BN_add(q, q, t1))
            goto err;
    }

    /* we now have a random number 'rand' to test. */
    if (!BN_lshift1(p, q))
        goto err;
    if (!BN_add_word(p, 1))
        goto err;

 loop:
    for (i = 1; i < NUMPRIMES; i++) {
        /* check that p and q are prime */
        /*
         * check that for p and q gcd(p-1,primes) == 1 (except for 2)
         */
        if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) ||
            (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) {
            if (!BN_add(p, p, padd))
                goto err;
            if (!BN_add(q, q, qadd))
                goto err;
            goto loop;
        }
    }
    ret = 1;

 err:
    BN_CTX_end(ctx);
    bn_check_top(p);
    return (ret);
}