bn_kron.c

Go to the documentation of this file.

/* crypto/bn/bn_kron.c */
/* ====================================================================
 * Copyright (c) 1998-2000 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
 *    [email protected].
 *
 * 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
 * ([email protected]).  This product includes software written by Tim
 * Hudson ([email protected]).
 *
 */

#include "cryptlib.h"
#include "bn_lcl.h"

/* least significant word */
#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])

/* Returns -2 for errors because both -1 and 0 are valid results. */
int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
    {
    int i;
    int ret = -2; /* avoid 'uninitialized' warning */
    int err = 0;
    BIGNUM *A, *B, *tmp;
    /* In 'tab', only odd-indexed entries are relevant:
     * For any odd BIGNUM n,
     *     tab[BN_lsw(n) & 7]
     * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
     * Note that the sign of n does not matter.
     */
    static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};

    bn_check_top(a);
    bn_check_top(b);

    BN_CTX_start(ctx);
    A = BN_CTX_get(ctx);
    B = BN_CTX_get(ctx);
    if (B == NULL) goto end;
    
    err = !BN_copy(A, a);
    if (err) goto end;
    err = !BN_copy(B, b);
    if (err) goto end;

    /*
     * Kronecker symbol, imlemented according to Henri Cohen,
     * "A Course in Computational Algebraic Number Theory"
     * (algorithm 1.4.10).
     */

    /* Cohen's step 1: */

    if (BN_is_zero(B))
        {
        ret = BN_abs_is_word(A, 1);
        goto end;
        }
    
    /* Cohen's step 2: */

    if (!BN_is_odd(A) && !BN_is_odd(B))
        {
        ret = 0;
        goto end;
        }

    /* now  B  is non-zero */
    i = 0;
    while (!BN_is_bit_set(B, i))
        i++;
    err = !BN_rshift(B, B, i);
    if (err) goto end;
    if (i & 1)
        {
        /* i is odd */
        /* (thus  B  was even, thus  A  must be odd!)  */

        /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
        ret = tab[BN_lsw(A) & 7];
        }
    else
        {
        /* i is even */
        ret = 1;
        }
    
    if (B->neg)
        {
        B->neg = 0;
        if (A->neg)
            ret = -ret;
        }

    /* now  B  is positive and odd, so what remains to be done is
     * to compute the Jacobi symbol  (A/B)  and multiply it by 'ret' */

    while (1)
        {
        /* Cohen's step 3: */

        /*  B  is positive and odd */

        if (BN_is_zero(A))
            {
            ret = BN_is_one(B) ? ret : 0;
            goto end;
            }

        /* now  A  is non-zero */
        i = 0;
        while (!BN_is_bit_set(A, i))
            i++;
        err = !BN_rshift(A, A, i);
        if (err) goto end;
        if (i & 1)
            {
            /* i is odd */
            /* multiply 'ret' by  $(-1)^{(B^2-1)/8}$ */
            ret = ret * tab[BN_lsw(B) & 7];
            }
    
        /* Cohen's step 4: */
        /* multiply 'ret' by  $(-1)^{(A-1)(B-1)/4}$ */
        if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2)
            ret = -ret;
        
        /* (A, B) := (B mod |A|, |A|) */
        err = !BN_nnmod(B, B, A, ctx);
        if (err) goto end;
        tmp = A; A = B; B = tmp;
        tmp->neg = 0;
        }
end:
    BN_CTX_end(ctx);
    if (err)
        return -2;
    else
        return ret;
    }