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-rw-r--r--src/lib/libcrypto/bn/bn_kron.c185
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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/* $OpenBSD: bn_kron.c,v 1.6 2015/02/09 15:49:22 jsing Exp $ */
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/* least significant word */
59#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
60
61/* Returns -2 for errors because both -1 and 0 are valid results. */
62int
63BN_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
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 if ((A = BN_CTX_get(ctx)) == NULL)
83 goto end;
84 if ((B = BN_CTX_get(ctx)) == 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 /*
95 * Kronecker symbol, imlemented according to Henri Cohen,
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 /* now B is positive and odd, so what remains to be done is
139 * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */
140
141 while (1) {
142 /* Cohen's step 3: */
143
144 /* B is positive and odd */
145
146 if (BN_is_zero(A)) {
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)
157 goto end;
158 if (i & 1) {
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)
172 goto end;
173 tmp = A;
174 A = B;
175 B = tmp;
176 tmp->neg = 0;
177 }
178
179end:
180 BN_CTX_end(ctx);
181 if (err)
182 return -2;
183 else
184 return ret;
185}
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