crypto/libressl/crypto/bn/bn_kron.c

   1 /* $OpenBSD: bn_kron.c,v 1.5 2014/07/11 08:44:48 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. */
  62 int
  63 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         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
 179 end:
 180         BN_CTX_end(ctx);
 181         if (err)
 182                 return -2;
 183         else
 184                 return ret;
 185 }