Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* ==================================================================== |
| 2 | * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. |
| 3 | * |
| 4 | * Redistribution and use in source and binary forms, with or without |
| 5 | * modification, are permitted provided that the following conditions |
| 6 | * are met: |
| 7 | * |
| 8 | * 1. Redistributions of source code must retain the above copyright |
| 9 | * notice, this list of conditions and the following disclaimer. |
| 10 | * |
| 11 | * 2. Redistributions in binary form must reproduce the above copyright |
| 12 | * notice, this list of conditions and the following disclaimer in |
| 13 | * the documentation and/or other materials provided with the |
| 14 | * distribution. |
| 15 | * |
| 16 | * 3. All advertising materials mentioning features or use of this |
| 17 | * software must display the following acknowledgment: |
| 18 | * "This product includes software developed by the OpenSSL Project |
| 19 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 20 | * |
| 21 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 22 | * endorse or promote products derived from this software without |
| 23 | * prior written permission. For written permission, please contact |
| 24 | * openssl-core@openssl.org. |
| 25 | * |
| 26 | * 5. Products derived from this software may not be called "OpenSSL" |
| 27 | * nor may "OpenSSL" appear in their names without prior written |
| 28 | * permission of the OpenSSL Project. |
| 29 | * |
| 30 | * 6. Redistributions of any form whatsoever must retain the following |
| 31 | * acknowledgment: |
| 32 | * "This product includes software developed by the OpenSSL Project |
| 33 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 34 | * |
| 35 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 36 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 37 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 38 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 39 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 40 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 41 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 42 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 43 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 44 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 45 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 46 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 47 | * ==================================================================== |
| 48 | * |
| 49 | * This product includes cryptographic software written by Eric Young |
| 50 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 51 | * Hudson (tjh@cryptsoft.com). */ |
| 52 | |
| 53 | #include <openssl/bn.h> |
| 54 | |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 55 | #include <openssl/err.h> |
| 56 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 57 | #include "internal.h" |
| 58 | |
| 59 | |
| 60 | /* least significant word */ |
| 61 | #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0]) |
| 62 | |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 63 | int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 64 | /* In 'tab', only odd-indexed entries are relevant: |
| 65 | * For any odd BIGNUM n, |
| 66 | * tab[BN_lsw(n) & 7] |
| 67 | * is $(-1)^{(n^2-1)/8}$ (using TeX notation). |
| 68 | * Note that the sign of n does not matter. */ |
| 69 | static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1}; |
| 70 | |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 71 | /* The Jacobi symbol is only defined for odd modulus. */ |
| 72 | if (!BN_is_odd(b)) { |
| 73 | OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); |
| 74 | return -2; |
| 75 | } |
| 76 | |
| 77 | /* Require b be positive. */ |
| 78 | if (BN_is_negative(b)) { |
| 79 | OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); |
| 80 | return -2; |
| 81 | } |
| 82 | |
| 83 | int ret = -2; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 84 | BN_CTX_start(ctx); |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 85 | BIGNUM *A = BN_CTX_get(ctx); |
| 86 | BIGNUM *B = BN_CTX_get(ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 87 | if (B == NULL) { |
| 88 | goto end; |
| 89 | } |
| 90 | |
| 91 | if (!BN_copy(A, a) || |
| 92 | !BN_copy(B, b)) { |
| 93 | goto end; |
| 94 | } |
| 95 | |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 96 | /* Adapted from logic to compute the Kronecker symbol, originally implemented |
| 97 | * according to Henri Cohen, "A Course in Computational Algebraic Number |
| 98 | * Theory" (algorithm 1.4.10). */ |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 99 | |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 100 | ret = 1; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 101 | |
| 102 | while (1) { |
| 103 | /* Cohen's step 3: */ |
| 104 | |
| 105 | /* B is positive and odd */ |
| 106 | if (BN_is_zero(A)) { |
| 107 | ret = BN_is_one(B) ? ret : 0; |
| 108 | goto end; |
| 109 | } |
| 110 | |
| 111 | /* now A is non-zero */ |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 112 | int i = 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 113 | while (!BN_is_bit_set(A, i)) { |
| 114 | i++; |
| 115 | } |
| 116 | if (!BN_rshift(A, A, i)) { |
Steven Valdez | e7531f0 | 2016-12-14 13:29:57 -0500 | [diff] [blame] | 117 | ret = -2; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 118 | goto end; |
| 119 | } |
| 120 | if (i & 1) { |
| 121 | /* i is odd */ |
| 122 | /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ |
| 123 | ret = ret * tab[BN_lsw(B) & 7]; |
| 124 | } |
| 125 | |
| 126 | /* Cohen's step 4: */ |
| 127 | /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ |
| 128 | if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) { |
| 129 | ret = -ret; |
| 130 | } |
| 131 | |
| 132 | /* (A, B) := (B mod |A|, |A|) */ |
| 133 | if (!BN_nnmod(B, B, A, ctx)) { |
| 134 | ret = -2; |
| 135 | goto end; |
| 136 | } |
Robert Sloan | 2424d84 | 2017-05-01 07:46:28 -0700 | [diff] [blame] | 137 | BIGNUM *tmp = A; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 138 | A = B; |
| 139 | B = tmp; |
| 140 | tmp->neg = 0; |
| 141 | } |
| 142 | |
| 143 | end: |
| 144 | BN_CTX_end(ctx); |
| 145 | return ret; |
| 146 | } |