crypto/bn/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 "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(BIGNUM *rnd, int bits,
                             const BIGNUM *add, const BIGNUM *rem,
                             BN_CTX *ctx);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add,
                                  const BIGNUM *rem, BN_CTX *ctx);

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);

    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 (!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);
    }
    if (mont != NULL)
        BN_MONT_CTX_free(mont);

    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, maxdelta;

 again:
    if (!BN_rand(rnd, bits, 1, 1))
        return (0);
    /* we now have a random number 'rand' to test. */
    for (i = 1; i < NUMPRIMES; i++)
        mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]);
    maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
    delta = 0;
 loop: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);
    bn_check_top(rnd);
    return (1);
}

static int 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);
}