crypto/openssl-0.9/crypto/bn/bn_kron.c

   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. */
  63 int 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_check_top(a);
  78         bn_check_top(b);
  79
  80         BN_CTX_start(ctx);
  81         A = BN_CTX_get(ctx);
  82         B = BN_CTX_get(ctx);
  83         if (B == NULL) goto end;
  84
  85         err = !BN_copy(A, a);
  86         if (err) goto end;
  87         err = !BN_copy(B, b);
  88         if (err) goto end;
  89
  90         /*
  91          * Kronecker symbol, imlemented according to Henri Cohen,
  92          * "A Course in Computational Algebraic Number Theory"
  93          * (algorithm 1.4.10).
  94          */
  95
  96         /* Cohen's step 1: */
  97
  98         if (BN_is_zero(B))
  99                 {
 100                 ret = BN_abs_is_word(A, 1);
 101                 goto end;
 102                 }
 103
 104         /* Cohen's step 2: */
 105
 106         if (!BN_is_odd(A) && !BN_is_odd(B))
 107                 {
 108                 ret = 0;
 109                 goto end;
 110                 }
 111
 112         /* now  B  is non-zero */
 113         i = 0;
 114         while (!BN_is_bit_set(B, i))
 115                 i++;
 116         err = !BN_rshift(B, B, i);
 117         if (err) goto end;
 118         if (i & 1)
 119                 {
 120                 /* i is odd */
 121                 /* (thus  B  was even, thus  A  must be odd!)  */
 122
 123                 /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
 124                 ret = tab[BN_lsw(A) & 7];
 125                 }
 126         else
 127                 {
 128                 /* i is even */
 129                 ret = 1;
 130                 }
 131
 132         if (B->neg)
 133                 {
 134                 B->neg = 0;
 135                 if (A->neg)
 136                         ret = -ret;
 137                 }
 138
 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' */
 141
 142         while (1)
 143                 {
 144                 /* Cohen's step 3: */
 145
 146                 /*  B  is positive and odd */
 147
 148                 if (BN_is_zero(A))
 149                         {
 150                         ret = BN_is_one(B) ? ret : 0;
 151                         goto end;
 152                         }
 153
 154                 /* now  A  is non-zero */
 155                 i = 0;
 156                 while (!BN_is_bit_set(A, i))
 157                         i++;
 158                 err = !BN_rshift(A, A, i);
 159                 if (err) goto end;
 160                 if (i & 1)
 161                         {
 162                         /* i is odd */
 163                         /* multiply 'ret' by  $(-1)^{(B^2-1)/8}$ */
 164                         ret = ret * tab[BN_lsw(B) & 7];
 165                         }
 166
 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)
 170                         ret = -ret;
 171
 172                 /* (A, B) := (B mod |A|, |A|) */
 173                 err = !BN_nnmod(B, B, A, ctx);
 174                 if (err) goto end;
 175                 tmp = A; A = B; B = tmp;
 176                 tmp->neg = 0;
 177                 }
 178 end:
 179         BN_CTX_end(ctx);
 180         if (err)
 181                 return -2;
 182         else
 183                 return ret;
 184         }