openssl/crypto/bn/bn_recp.c

/* crypto/bn/bn_recp.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.]
 */

#include "internal/cryptlib.h"
#include "bn_lcl.h"

void BN_RECP_CTX_init(BN_RECP_CTX *recp)
{
    BN_init(&(recp->N));
    BN_init(&(recp->Nr));
    recp->num_bits = 0;
    recp->flags = 0;
}

BN_RECP_CTX *BN_RECP_CTX_new(void)
{
    BN_RECP_CTX *ret;

    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
        return (NULL);

    BN_RECP_CTX_init(ret);
    ret->flags = BN_FLG_MALLOCED;
    return (ret);
}

void BN_RECP_CTX_free(BN_RECP_CTX *recp)
{
    if (recp == NULL)
        return;

    BN_free(&(recp->N));
    BN_free(&(recp->Nr));
    if (recp->flags & BN_FLG_MALLOCED)
        OPENSSL_free(recp);
}

int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
{
    if (!BN_copy(&(recp->N), d))
        return 0;
    BN_zero(&(recp->Nr));
    recp->num_bits = BN_num_bits(d);
    recp->shift = 0;
    return (1);
}

int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
                          BN_RECP_CTX *recp, BN_CTX *ctx)
{
    int ret = 0;
    BIGNUM *a;
    const BIGNUM *ca;

    BN_CTX_start(ctx);
    if ((a = BN_CTX_get(ctx)) == NULL)
        goto err;
    if (y != NULL) {
        if (x == y) {
            if (!BN_sqr(a, x, ctx))
                goto err;
        } else {
            if (!BN_mul(a, x, y, ctx))
                goto err;
        }
        ca = a;
    } else
        ca = x;                 /* Just do the mod */

    ret = BN_div_recp(NULL, r, ca, recp, ctx);
 err:
    BN_CTX_end(ctx);
    bn_check_top(r);
    return (ret);
}

int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
                BN_RECP_CTX *recp, BN_CTX *ctx)
{
    int i, j, ret = 0;
    BIGNUM *a, *b, *d, *r;

    BN_CTX_start(ctx);
    a = BN_CTX_get(ctx);
    b = BN_CTX_get(ctx);
    if (dv != NULL)
        d = dv;
    else
        d = BN_CTX_get(ctx);
    if (rem != NULL)
        r = rem;
    else
        r = BN_CTX_get(ctx);
    if (a == NULL || b == NULL || d == NULL || r == NULL)
        goto err;

    if (BN_ucmp(m, &(recp->N)) < 0) {
        BN_zero(d);
        if (!BN_copy(r, m))
            return 0;
        BN_CTX_end(ctx);
        return (1);
    }

    /*
     * We want the remainder Given input of ABCDEF / ab we need multiply
     * ABCDEF by 3 digests of the reciprocal of ab
     */

    /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
    i = BN_num_bits(m);
    j = recp->num_bits << 1;
    if (j > i)
        i = j;

    /* Nr := round(2^i / N) */
    if (i != recp->shift)
        recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
    /* BN_reciprocal could have returned -1 for an error */
    if (recp->shift == -1)
        goto err;

    /*-
     * d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
     *    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
     *   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
     *    = |m/N|
     */
    if (!BN_rshift(a, m, recp->num_bits))
        goto err;
    if (!BN_mul(b, a, &(recp->Nr), ctx))
        goto err;
    if (!BN_rshift(d, b, i - recp->num_bits))
        goto err;
    d->neg = 0;

    if (!BN_mul(b, &(recp->N), d, ctx))
        goto err;
    if (!BN_usub(r, m, b))
        goto err;
    r->neg = 0;

    j = 0;
    while (BN_ucmp(r, &(recp->N)) >= 0) {
        if (j++ > 2) {
            BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL);
            goto err;
        }
        if (!BN_usub(r, r, &(recp->N)))
            goto err;
        if (!BN_add_word(d, 1))
            goto err;
    }

    r->neg = BN_is_zero(r) ? 0 : m->neg;
    d->neg = m->neg ^ recp->N.neg;
    ret = 1;
 err:
    BN_CTX_end(ctx);
    bn_check_top(dv);
    bn_check_top(rem);
    return (ret);
}

/*
 * len is the expected size of the result We actually calculate with an extra
 * word of precision, so we can do faster division if the remainder is not
 * required.
 */
/* r := 2^len / m */
int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
{
    int ret = -1;
    BIGNUM *t;

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

    if (!BN_set_bit(t, len))
        goto err;

    if (!BN_div(r, NULL, t, m, ctx))
        goto err;

    ret = len;
 err:
    bn_check_top(r);
    BN_CTX_end(ctx);
    return (ret);
}