/* 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

 *    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 "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. */

EXPORT_C 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;

	}