147 lines
4.5 KiB
C
147 lines
4.5 KiB
C
/* ====================================================================
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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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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include "internal.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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int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
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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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static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};
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// The Jacobi symbol is only defined for odd modulus.
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if (!BN_is_odd(b)) {
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OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
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return -2;
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}
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// Require b be positive.
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if (BN_is_negative(b)) {
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OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
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return -2;
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}
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int ret = -2;
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BN_CTX_start(ctx);
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BIGNUM *A = BN_CTX_get(ctx);
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BIGNUM *B = BN_CTX_get(ctx);
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if (B == NULL) {
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goto end;
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}
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if (!BN_copy(A, a) ||
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!BN_copy(B, b)) {
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goto end;
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}
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// Adapted from logic to compute the Kronecker symbol, originally implemented
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// according to Henri Cohen, "A Course in Computational Algebraic Number
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// Theory" (algorithm 1.4.10).
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ret = 1;
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while (1) {
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// Cohen's step 3:
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// B is positive and odd
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if (BN_is_zero(A)) {
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ret = BN_is_one(B) ? ret : 0;
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goto end;
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}
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// now A is non-zero
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int i = 0;
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while (!BN_is_bit_set(A, i)) {
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i++;
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}
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if (!BN_rshift(A, A, i)) {
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ret = -2;
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goto end;
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}
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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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ret = ret * tab[BN_lsw(B) & 7];
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}
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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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if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) {
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ret = -ret;
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}
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// (A, B) := (B mod |A|, |A|)
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if (!BN_nnmod(B, B, A, ctx)) {
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ret = -2;
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goto end;
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}
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BIGNUM *tmp = A;
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A = B;
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B = tmp;
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tmp->neg = 0;
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}
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end:
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BN_CTX_end(ctx);
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return ret;
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}
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