crypto/bn/bn_x931p.c

/*
 * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the Apache License 2.0 (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#include <stdio.h>
#include <openssl/bn.h>
#include "bn_local.h"

/* X9.31 routines for prime derivation */

/*
 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
 * q1, q2) from a parameter Xpi by checking successive odd integers.
 */

static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
                             BN_GENCB *cb)
{
    int i = 0, is_prime;
    if (!BN_copy(pi, Xpi))
        return 0;
    if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
        return 0;
    for (;;) {
        i++;
        BN_GENCB_call(cb, 0, i);
        /* NB 27 MR is specified in X9.31 */
        is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
        if (is_prime < 0)
            return 0;
        if (is_prime)
            break;
        if (!BN_add_word(pi, 2))
            return 0;
    }
    BN_GENCB_call(cb, 2, i);
    return 1;
}

/*
 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
 * will be returned too: this is needed for testing.
 */

int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
                            const BIGNUM *Xp, const BIGNUM *Xp1,
                            const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
                            BN_GENCB *cb)
{
    int ret = 0;

    BIGNUM *t, *p1p2, *pm1;

    /* Only even e supported */
    if (!BN_is_odd(e))
        return 0;

    BN_CTX_start(ctx);
    if (p1 == NULL)
        p1 = BN_CTX_get(ctx);

    if (p2 == NULL)
        p2 = BN_CTX_get(ctx);

    t = BN_CTX_get(ctx);

    p1p2 = BN_CTX_get(ctx);

    pm1 = BN_CTX_get(ctx);

    if (pm1 == NULL)
        goto err;

    if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
        goto err;

    if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
        goto err;

    if (!BN_mul(p1p2, p1, p2, ctx))
        goto err;

    /* First set p to value of Rp */

    if (!BN_mod_inverse(p, p2, p1, ctx))
        goto err;

    if (!BN_mul(p, p, p2, ctx))
        goto err;

    if (!BN_mod_inverse(t, p1, p2, ctx))
        goto err;

    if (!BN_mul(t, t, p1, ctx))
        goto err;

    if (!BN_sub(p, p, t))
        goto err;

    if (p->neg && !BN_add(p, p, p1p2))
        goto err;

    /* p now equals Rp */

    if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
        goto err;

    if (!BN_add(p, p, Xp))
        goto err;

    /* p now equals Yp0 */

    for (;;) {
        int i = 1;
        BN_GENCB_call(cb, 0, i++);
        if (!BN_copy(pm1, p))
            goto err;
        if (!BN_sub_word(pm1, 1))
            goto err;
        if (!BN_gcd(t, pm1, e, ctx))
            goto err;
        if (BN_is_one(t)) {
            /*
             * X9.31 specifies 8 MR and 1 Lucas test or any prime test
             * offering similar or better guarantees 50 MR is considerably
             * better.
             */
            int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
            if (r < 0)
                goto err;
            if (r)
                break;
        }
        if (!BN_add(p, p, p1p2))
            goto err;
    }

    BN_GENCB_call(cb, 3, 0);

    ret = 1;

 err:

    BN_CTX_end(ctx);

    return ret;
}

/*
 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
 * parameter is sum of number of bits in both.
 */

int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
{
    BIGNUM *t;
    int i;
    /*
     * Number of bits for each prime is of the form 512+128s for s = 0, 1,
     * ...
     */
    if ((nbits < 1024) || (nbits & 0xff))
        return 0;
    nbits >>= 1;
    /*
     * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
     * - 1. By setting the top two bits we ensure that the lower bound is
     * exceeded.
     */
    if (!BN_priv_rand_ex(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, ctx))
        goto err;

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

    for (i = 0; i < 1000; i++) {
        if (!BN_priv_rand_ex(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY,
                             ctx))
            goto err;

        /* Check that |Xp - Xq| > 2^(nbits - 100) */
        if (!BN_sub(t, Xp, Xq))
            goto err;
        if (BN_num_bits(t) > (nbits - 100))
            break;
    }

    BN_CTX_end(ctx);

    if (i < 1000)
        return 1;

    return 0;

 err:
    BN_CTX_end(ctx);
    return 0;
}

/*
 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
 * previous function and supplied as input.
 */

int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
                              BIGNUM *Xp1, BIGNUM *Xp2,
                              const BIGNUM *Xp,
                              const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
{
    int ret = 0;

    BN_CTX_start(ctx);
    if (Xp1 == NULL)
        Xp1 = BN_CTX_get(ctx);
    if (Xp2 == NULL)
        Xp2 = BN_CTX_get(ctx);
    if (Xp1 == NULL || Xp2 == NULL)
        goto error;

    if (!BN_priv_rand_ex(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx))
        goto error;
    if (!BN_priv_rand_ex(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, ctx))
        goto error;
    if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
        goto error;

    ret = 1;

 error:
    BN_CTX_end(ctx);

    return ret;

}