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/* ====================================================================
* 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 <openssl/bn.h>
#include <openssl/err.h>
#include "internal.h"
// least significant word
#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
// 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};
// The Jacobi symbol is only defined for odd modulus.
if (!BN_is_odd(b)) {
OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
return -2;
}
// Require b be positive.
if (BN_is_negative(b)) {
OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
return -2;
}
int ret = -2;
BN_CTX_start(ctx);
BIGNUM *A = BN_CTX_get(ctx);
BIGNUM *B = BN_CTX_get(ctx);
if (B == NULL) {
goto end;
}
if (!BN_copy(A, a) ||
!BN_copy(B, b)) {
goto end;
}
// Adapted from logic to compute the Kronecker symbol, originally implemented
// according to Henri Cohen, "A Course in Computational Algebraic Number
// Theory" (algorithm 1.4.10).
ret = 1;
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
int i = 0;
while (!BN_is_bit_set(A, i)) {
i++;
}
if (!BN_rshift(A, A, i)) {
ret = -2;
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|)
if (!BN_nnmod(B, B, A, ctx)) {
ret = -2;
goto end;
}
BIGNUM *tmp = A;
A = B;
B = tmp;
tmp->neg = 0;
}
end:
BN_CTX_end(ctx);
return ret;
}