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031e5cce SM |
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). | |
3e575651 SL |
53 | * |
54 | */ | |
55 | ||
031e5cce | 56 | #include "cryptlib.h" |
3e575651 SL |
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) | |
d3819813 MTL |
64 | { |
65 | int i; | |
66 | int ret = -2; /* avoid 'uninitialized' warning */ | |
67 | int err = 0; | |
68 | BIGNUM *A, *B, *tmp; | |
69 | /*- | |
70 | * In 'tab', only odd-indexed entries are relevant: | |
71 | * For any odd BIGNUM n, | |
72 | * tab[BN_lsw(n) & 7] | |
73 | * is $(-1)^{(n^2-1)/8}$ (using TeX notation). | |
74 | * Note that the sign of n does not matter. | |
75 | */ | |
76 | static const int tab[8] = { 0, 1, 0, -1, 0, -1, 0, 1 }; | |
77 | ||
78 | bn_check_top(a); | |
79 | bn_check_top(b); | |
80 | ||
81 | BN_CTX_start(ctx); | |
82 | A = BN_CTX_get(ctx); | |
83 | B = BN_CTX_get(ctx); | |
84 | if (B == NULL) | |
85 | goto end; | |
86 | ||
87 | err = !BN_copy(A, a); | |
88 | if (err) | |
89 | goto end; | |
90 | err = !BN_copy(B, b); | |
91 | if (err) | |
92 | goto end; | |
93 | ||
94 | /* | |
031e5cce | 95 | * Kronecker symbol, imlemented according to Henri Cohen, |
d3819813 MTL |
96 | * "A Course in Computational Algebraic Number Theory" |
97 | * (algorithm 1.4.10). | |
98 | */ | |
99 | ||
100 | /* Cohen's step 1: */ | |
101 | ||
102 | if (BN_is_zero(B)) { | |
103 | ret = BN_abs_is_word(A, 1); | |
104 | goto end; | |
105 | } | |
106 | ||
107 | /* Cohen's step 2: */ | |
108 | ||
109 | if (!BN_is_odd(A) && !BN_is_odd(B)) { | |
110 | ret = 0; | |
111 | goto end; | |
112 | } | |
113 | ||
114 | /* now B is non-zero */ | |
115 | i = 0; | |
116 | while (!BN_is_bit_set(B, i)) | |
117 | i++; | |
118 | err = !BN_rshift(B, B, i); | |
119 | if (err) | |
120 | goto end; | |
121 | if (i & 1) { | |
122 | /* i is odd */ | |
123 | /* (thus B was even, thus A must be odd!) */ | |
124 | ||
125 | /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ | |
126 | ret = tab[BN_lsw(A) & 7]; | |
127 | } else { | |
128 | /* i is even */ | |
129 | ret = 1; | |
130 | } | |
131 | ||
132 | if (B->neg) { | |
133 | B->neg = 0; | |
134 | if (A->neg) | |
135 | ret = -ret; | |
136 | } | |
137 | ||
138 | /* | |
139 | * now B is positive and odd, so what remains to be done is to compute | |
140 | * the Jacobi symbol (A/B) and multiply it by 'ret' | |
141 | */ | |
142 | ||
143 | while (1) { | |
144 | /* Cohen's step 3: */ | |
145 | ||
146 | /* B is positive and odd */ | |
147 | ||
148 | if (BN_is_zero(A)) { | |
149 | ret = BN_is_one(B) ? ret : 0; | |
150 | goto end; | |
151 | } | |
152 | ||
153 | /* now A is non-zero */ | |
154 | i = 0; | |
155 | while (!BN_is_bit_set(A, i)) | |
156 | i++; | |
157 | err = !BN_rshift(A, A, i); | |
158 | if (err) | |
159 | goto end; | |
160 | if (i & 1) { | |
161 | /* i is odd */ | |
162 | /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ | |
163 | ret = ret * tab[BN_lsw(B) & 7]; | |
164 | } | |
165 | ||
166 | /* Cohen's step 4: */ | |
167 | /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ | |
168 | if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) | |
169 | ret = -ret; | |
170 | ||
171 | /* (A, B) := (B mod |A|, |A|) */ | |
172 | err = !BN_nnmod(B, B, A, ctx); | |
173 | if (err) | |
174 | goto end; | |
175 | tmp = A; | |
176 | A = B; | |
177 | B = tmp; | |
178 | tmp->neg = 0; | |
179 | } | |
180 | end: | |
181 | BN_CTX_end(ctx); | |
182 | if (err) | |
183 | return -2; | |
184 | else | |
185 | return ret; | |
186 | } |