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0.13.1
Simple HTTP client with HTTP/1.1, HTTP/2, and HTTP/3 support
Security advisory:
This version has known vulnerabilities.
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c_src/boringssl/crypto/fipsmodule/bn/jacobi.cc.inc
// Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <openssl/bn.h>
#include <openssl/err.h>
#include "internal.h"
// least significant word
#define BN_lsw(n) (((n)->width == 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;
}
bssl::BN_CTXScope scope(ctx);
BIGNUM *A = BN_CTX_get(ctx);
BIGNUM *B = BN_CTX_get(ctx);
if (B == nullptr) {
return -2;
}
if (!BN_copy(A, a) ||
!BN_copy(B, b)) {
return -2;
}
// 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).
int ret = 1;
while (1) {
// Cohen's step 3:
// B is positive and odd
if (BN_is_zero(A)) {
return BN_is_one(B) ? ret : 0;
}
// now A is non-zero
int i = 0;
while (!BN_is_bit_set(A, i)) {
i++;
}
if (!BN_rshift(A, A, i)) {
return -2;
}
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)) {
return -2;
}
BIGNUM *tmp = A;
A = B;
B = tmp;
tmp->neg = 0;
}
}