| /* ==================================================================== |
| * 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; |
| } |