Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 1 | /* crypto/bn/bn_kron.c */ |
| 2 | /* ==================================================================== |
| 3 | * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. |
| 4 | * |
| 5 | * Redistribution and use in source and binary forms, with or without |
| 6 | * modification, are permitted provided that the following conditions |
| 7 | * are met: |
| 8 | * |
| 9 | * 1. Redistributions of source code must retain the above copyright |
| 10 | * notice, this list of conditions and the following disclaimer. |
| 11 | * |
| 12 | * 2. Redistributions in binary form must reproduce the above copyright |
| 13 | * notice, this list of conditions and the following disclaimer in |
| 14 | * the documentation and/or other materials provided with the |
| 15 | * distribution. |
| 16 | * |
| 17 | * 3. All advertising materials mentioning features or use of this |
| 18 | * software must display the following acknowledgment: |
| 19 | * "This product includes software developed by the OpenSSL Project |
| 20 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 21 | * |
| 22 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 23 | * endorse or promote products derived from this software without |
| 24 | * prior written permission. For written permission, please contact |
| 25 | * openssl-core@openssl.org. |
| 26 | * |
| 27 | * 5. Products derived from this software may not be called "OpenSSL" |
| 28 | * nor may "OpenSSL" appear in their names without prior written |
| 29 | * permission of the OpenSSL Project. |
| 30 | * |
| 31 | * 6. Redistributions of any form whatsoever must retain the following |
| 32 | * acknowledgment: |
| 33 | * "This product includes software developed by the OpenSSL Project |
| 34 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 35 | * |
| 36 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 37 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 38 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 39 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 40 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 41 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 42 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 43 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 44 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 45 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 46 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 47 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 48 | * ==================================================================== |
| 49 | * |
| 50 | * This product includes cryptographic software written by Eric Young |
| 51 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 52 | * Hudson (tjh@cryptsoft.com). |
| 53 | * |
| 54 | */ |
| 55 | |
| 56 | #include "cryptlib.h" |
| 57 | #include "bn_lcl.h" |
| 58 | |
| 59 | /* least significant word */ |
| 60 | #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0]) |
| 61 | |
| 62 | /* Returns -2 for errors because both -1 and 0 are valid results. */ |
| 63 | int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) |
| 64 | { |
| 65 | int i; |
| 66 | int ret = -2; /* avoid 'uninitialized' warning */ |
| 67 | int err = 0; |
| 68 | BIGNUM *A, *B, *tmp; |
| 69 | /* In 'tab', only odd-indexed entries are relevant: |
| 70 | * For any odd BIGNUM n, |
| 71 | * tab[BN_lsw(n) & 7] |
| 72 | * is $(-1)^{(n^2-1)/8}$ (using TeX notation). |
| 73 | * Note that the sign of n does not matter. |
| 74 | */ |
| 75 | static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1}; |
| 76 | |
| 77 | bn_check_top(a); |
| 78 | bn_check_top(b); |
| 79 | |
| 80 | BN_CTX_start(ctx); |
| 81 | A = BN_CTX_get(ctx); |
| 82 | B = BN_CTX_get(ctx); |
| 83 | if (B == NULL) goto end; |
| 84 | |
| 85 | err = !BN_copy(A, a); |
| 86 | if (err) goto end; |
| 87 | err = !BN_copy(B, b); |
| 88 | if (err) goto end; |
| 89 | |
| 90 | /* |
| 91 | * Kronecker symbol, imlemented according to Henri Cohen, |
| 92 | * "A Course in Computational Algebraic Number Theory" |
| 93 | * (algorithm 1.4.10). |
| 94 | */ |
| 95 | |
| 96 | /* Cohen's step 1: */ |
| 97 | |
| 98 | if (BN_is_zero(B)) |
| 99 | { |
| 100 | ret = BN_abs_is_word(A, 1); |
| 101 | goto end; |
| 102 | } |
| 103 | |
| 104 | /* Cohen's step 2: */ |
| 105 | |
| 106 | if (!BN_is_odd(A) && !BN_is_odd(B)) |
| 107 | { |
| 108 | ret = 0; |
| 109 | goto end; |
| 110 | } |
| 111 | |
| 112 | /* now B is non-zero */ |
| 113 | i = 0; |
| 114 | while (!BN_is_bit_set(B, i)) |
| 115 | i++; |
| 116 | err = !BN_rshift(B, B, i); |
| 117 | if (err) goto end; |
| 118 | if (i & 1) |
| 119 | { |
| 120 | /* i is odd */ |
| 121 | /* (thus B was even, thus A must be odd!) */ |
| 122 | |
| 123 | /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ |
| 124 | ret = tab[BN_lsw(A) & 7]; |
| 125 | } |
| 126 | else |
| 127 | { |
| 128 | /* i is even */ |
| 129 | ret = 1; |
| 130 | } |
| 131 | |
| 132 | if (B->neg) |
| 133 | { |
| 134 | B->neg = 0; |
| 135 | if (A->neg) |
| 136 | ret = -ret; |
| 137 | } |
| 138 | |
| 139 | /* now B is positive and odd, so what remains to be done is |
| 140 | * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */ |
| 141 | |
| 142 | while (1) |
| 143 | { |
| 144 | /* Cohen's step 3: */ |
| 145 | |
| 146 | /* B is positive and odd */ |
| 147 | |
| 148 | if (BN_is_zero(A)) |
| 149 | { |
| 150 | ret = BN_is_one(B) ? ret : 0; |
| 151 | goto end; |
| 152 | } |
| 153 | |
| 154 | /* now A is non-zero */ |
| 155 | i = 0; |
| 156 | while (!BN_is_bit_set(A, i)) |
| 157 | i++; |
| 158 | err = !BN_rshift(A, A, i); |
| 159 | if (err) goto end; |
| 160 | if (i & 1) |
| 161 | { |
| 162 | /* i is odd */ |
| 163 | /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ |
| 164 | ret = ret * tab[BN_lsw(B) & 7]; |
| 165 | } |
| 166 | |
| 167 | /* Cohen's step 4: */ |
| 168 | /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ |
| 169 | if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) |
| 170 | ret = -ret; |
| 171 | |
| 172 | /* (A, B) := (B mod |A|, |A|) */ |
| 173 | err = !BN_nnmod(B, B, A, ctx); |
| 174 | if (err) goto end; |
| 175 | tmp = A; A = B; B = tmp; |
| 176 | tmp->neg = 0; |
| 177 | } |
| 178 | end: |
| 179 | BN_CTX_end(ctx); |
| 180 | if (err) |
| 181 | return -2; |
| 182 | else |
| 183 | return ret; |
| 184 | } |