bn_kron.c revision 296465 
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. */
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    /*-
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    /*
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    /*
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}
187