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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 } | |
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