1 /* crypto/bn/bn_kron.c */
2 /* ====================================================================
3 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
59 /* least significant word */
60 #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
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
)
66 int ret
= -2; /* avoid 'uninitialized' warning */
69 /* In 'tab', only odd-indexed entries are relevant:
70 * For any odd BIGNUM n,
72 * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
73 * Note that the sign of n does not matter.
75 static const int tab
[8] = {0, 1, 0, -1, 0, -1, 0, 1};
83 if (B
== NULL
) goto end
;
91 * Kronecker symbol, imlemented according to Henri Cohen,
92 * "A Course in Computational Algebraic Number Theory"
100 ret
= BN_abs_is_word(A
, 1);
104 /* Cohen's step 2: */
106 if (!BN_is_odd(A
) && !BN_is_odd(B
))
112 /* now B is non-zero */
114 while (!BN_is_bit_set(B
, i
))
116 err
= !BN_rshift(B
, B
, i
);
121 /* (thus B was even, thus A must be odd!) */
123 /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
124 ret
= tab
[BN_lsw(A
) & 7];
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' */
144 /* Cohen's step 3: */
146 /* B is positive and odd */
150 ret
= BN_is_one(B
) ? ret
: 0;
154 /* now A is non-zero */
156 while (!BN_is_bit_set(A
, i
))
158 err
= !BN_rshift(A
, A
, i
);
163 /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */
164 ret
= ret
* tab
[BN_lsw(B
) & 7];
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)
172 /* (A, B) := (B mod |A|, |A|) */
173 err
= !BN_nnmod(B
, B
, A
, ctx
);
175 tmp
= A
; A
= B
; B
= tmp
;