98 lines
2.0 KiB
C
98 lines
2.0 KiB
C
// Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
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// SPDX-License-Identifier: Apache-2.0
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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)->width == 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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