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authorcvs2svn <admin@example.com>2007-03-01 16:29:10 +0000
committercvs2svn <admin@example.com>2007-03-01 16:29:10 +0000
commitd92cde8050488a0c87c357c4756a89026b6659ee (patch)
tree737670254ff24eff6f6dddb0b97cae8c0ba8c571 /src/lib/libcrypto/bn/bn_kron.c
parent9c4b4ca341957016adebec4e1eb2446cf0261241 (diff)
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diff --git a/src/lib/libcrypto/bn/bn_kron.c b/src/lib/libcrypto/bn/bn_kron.c
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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 "bn_lcl.h"
57
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. */
63int 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_CTX_start(ctx);
78 A = BN_CTX_get(ctx);
79 B = BN_CTX_get(ctx);
80 if (B == NULL) goto end;
81
82 err = !BN_copy(A, a);
83 if (err) goto end;
84 err = !BN_copy(B, b);
85 if (err) goto end;
86
87 /*
88 * Kronecker symbol, imlemented according to Henri Cohen,
89 * "A Course in Computational Algebraic Number Theory"
90 * (algorithm 1.4.10).
91 */
92
93 /* Cohen's step 1: */
94
95 if (BN_is_zero(B))
96 {
97 ret = BN_abs_is_word(A, 1);
98 goto end;
99 }
100
101 /* Cohen's step 2: */
102
103 if (!BN_is_odd(A) && !BN_is_odd(B))
104 {
105 ret = 0;
106 goto end;
107 }
108
109 /* now B is non-zero */
110 i = 0;
111 while (!BN_is_bit_set(B, i))
112 i++;
113 err = !BN_rshift(B, B, i);
114 if (err) goto end;
115 if (i & 1)
116 {
117 /* i is odd */
118 /* (thus B was even, thus A must be odd!) */
119
120 /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
121 ret = tab[BN_lsw(A) & 7];
122 }
123 else
124 {
125 /* i is even */
126 ret = 1;
127 }
128
129 if (B->neg)
130 {
131 B->neg = 0;
132 if (A->neg)
133 ret = -ret;
134 }
135
136 /* now B is positive and odd, so what remains to be done is
137 * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */
138
139 while (1)
140 {
141 /* Cohen's step 3: */
142
143 /* B is positive and odd */
144
145 if (BN_is_zero(A))
146 {
147 ret = BN_is_one(B) ? ret : 0;
148 goto end;
149 }
150
151 /* now A is non-zero */
152 i = 0;
153 while (!BN_is_bit_set(A, i))
154 i++;
155 err = !BN_rshift(A, A, i);
156 if (err) goto end;
157 if (i & 1)
158 {
159 /* i is odd */
160 /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */
161 ret = ret * tab[BN_lsw(B) & 7];
162 }
163
164 /* Cohen's step 4: */
165 /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */
166 if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2)
167 ret = -ret;
168
169 /* (A, B) := (B mod |A|, |A|) */
170 err = !BN_nnmod(B, B, A, ctx);
171 if (err) goto end;
172 tmp = A; A = B; B = tmp;
173 tmp->neg = 0;
174 }
175
176 end:
177 BN_CTX_end(ctx);
178 if (err)
179 return -2;
180 else
181 return ret;
182 }
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