GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libcrypto/bn/bn_kron.c Lines: 37 44 84.1 %
Date: 2017-11-07 Branches: 36 62 58.1 %

Line Branch Exec Source
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/* $OpenBSD: bn_kron.c,v 1.6 2015/02/09 15:49:22 jsing Exp $ */
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/* ====================================================================
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 * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
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 *
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 * Redistribution and use in source and binary forms, with or without
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 * modification, are permitted provided that the following conditions
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 * are met:
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 *
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 * 1. Redistributions of source code must retain the above copyright
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 *    notice, this list of conditions and the following disclaimer.
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 *
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 * 2. Redistributions in binary form must reproduce the above copyright
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 *    notice, this list of conditions and the following disclaimer in
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 *    the documentation and/or other materials provided with the
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 *    distribution.
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 *
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 * 3. All advertising materials mentioning features or use of this
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 *    software must display the following acknowledgment:
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 *    "This product includes software developed by the OpenSSL Project
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 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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 *
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 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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 *    endorse or promote products derived from this software without
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 *    prior written permission. For written permission, please contact
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 *    openssl-core@openssl.org.
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 *
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 * 5. Products derived from this software may not be called "OpenSSL"
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 *    nor may "OpenSSL" appear in their names without prior written
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 *    permission of the OpenSSL Project.
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 *
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 * 6. Redistributions of any form whatsoever must retain the following
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 *    acknowledgment:
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 *    "This product includes software developed by the OpenSSL Project
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 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 *
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 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
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 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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 * OF THE POSSIBILITY OF SUCH DAMAGE.
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 * ====================================================================
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 *
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 * This product includes cryptographic software written by Eric Young
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 * (eay@cryptsoft.com).  This product includes software written by Tim
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 * Hudson (tjh@cryptsoft.com).
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 *
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 */
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#include "bn_lcl.h"
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/* least significant word */
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#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
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/* Returns -2 for errors because both -1 and 0 are valid results. */
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int
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BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
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{
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	int i;
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	int ret = -2; /* avoid 'uninitialized' warning */
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	int err = 0;
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	BIGNUM *A, *B, *tmp;
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	/* In 'tab', only odd-indexed entries are relevant:
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	 * For any odd BIGNUM n,
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	 *     tab[BN_lsw(n) & 7]
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	 * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
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	 * Note that the sign of n does not matter.
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	 */
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	static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};
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	bn_check_top(a);
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	bn_check_top(b);
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1784
	BN_CTX_start(ctx);
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892
	if ((A = BN_CTX_get(ctx)) == NULL)
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		goto end;
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892
	if ((B = BN_CTX_get(ctx)) == NULL)
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		goto end;
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892
	err = !BN_copy(A, a);
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892
	if (err)
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		goto end;
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892
	err = !BN_copy(B, b);
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892
	if (err)
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		goto end;
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	/*
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	 * Kronecker symbol, imlemented according to Henri Cohen,
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	 * "A Course in Computational Algebraic Number Theory"
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	 * (algorithm 1.4.10).
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	 */
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	/* Cohen's step 1: */
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	if (BN_is_zero(B)) {
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		ret = BN_abs_is_word(A, 1);
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		goto end;
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	}
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	/* Cohen's step 2: */
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2682
	if (!BN_is_odd(A) && !BN_is_odd(B)) {
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		ret = 0;
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		goto end;
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	}
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	/* now  B  is non-zero */
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	i = 0;
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1784
	while (!BN_is_bit_set(B, i))
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		i++;
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892
	err = !BN_rshift(B, B, i);
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892
	if (err)
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		goto end;
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892
	if (i & 1) {
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		/* i is odd */
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		/* (thus  B  was even, thus  A  must be odd!)  */
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		/* set 'ret' to $(-1)^{(A^2-1)/8}$ */
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		ret = tab[BN_lsw(A) & 7];
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	} else {
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		/* i is even */
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		ret = 1;
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	}
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892
	if (B->neg) {
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600
		B->neg = 0;
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600
		if (A->neg)
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			ret = -ret;
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	}
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	/* now  B  is positive and odd, so what remains to be done is
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	 * to compute the Jacobi symbol  (A/B)  and multiply it by 'ret' */
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111614
	while (1) {
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		/* Cohen's step 3: */
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		/*  B  is positive and odd */
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112506
		if (BN_is_zero(A)) {
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3568
			ret = BN_is_one(B) ? ret : 0;
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892
			goto end;
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		}
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		/* now  A  is non-zero */
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		i = 0;
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474942
		while (!BN_is_bit_set(A, i))
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125857
			i++;
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111614
		err = !BN_rshift(A, A, i);
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111614
		if (err)
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			goto end;
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111614
		if (i & 1) {
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			/* i is odd */
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			/* multiply 'ret' by  $(-1)^{(B^2-1)/8}$ */
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121713
			ret = ret * tab[BN_lsw(B) & 7];
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40571
		}
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		/* Cohen's step 4: */
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		/* multiply 'ret' by  $(-1)^{(A-1)(B-1)/4}$ */
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669984
		if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2)
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27652
			ret = -ret;
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		/* (A, B) := (B mod |A|, |A|) */
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111614
		err = !BN_nnmod(B, B, A, ctx);
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111614
		if (err)
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			goto end;
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		tmp = A;
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		A = B;
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		B = tmp;
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111614
		tmp->neg = 0;
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	}
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end:
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892
	BN_CTX_end(ctx);
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892
	if (err)
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		return -2;
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	else
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892
		return ret;
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892
}