lib/mpi/mpi-inv.c

   1 /* mpi-inv.c  -  MPI functions
   2  *      Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
   3  *
   4  * This file is part of Libgcrypt.
   5  *
   6  * Libgcrypt is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as
   8  * published by the Free Software Foundation; either version 2.1 of
   9  * the License, or (at your option) any later version.
  10  *
  11  * Libgcrypt is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public
  17  * License along with this program; if not, see <http://www.gnu.org/licenses/>.
  18  */
  19
  20 #include "mpi-internal.h"
  21
  22 /****************
  23  * Calculate the multiplicative inverse X of A mod N
  24  * That is: Find the solution x for
  25  *              1 = (a*x) mod n
  26  */
  27 int mpi_invm(MPI x, MPI a, MPI n)
  28 {
  29         /* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
  30          * modified according to Michael Penk's solution for Exercise 35
  31          * with further enhancement
  32          */
  33         MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
  34         unsigned int k;
  35         int sign;
  36         int odd;
  37
  38         if (!mpi_cmp_ui(a, 0))
  39                 return 0; /* Inverse does not exists.  */
  40         if (!mpi_cmp_ui(n, 1))
  41                 return 0; /* Inverse does not exists.  */
  42
  43         u = mpi_copy(a);
  44         v = mpi_copy(n);
  45
  46         for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
  47                 mpi_rshift(u, u, 1);
  48                 mpi_rshift(v, v, 1);
  49         }
  50         odd = mpi_test_bit(v, 0);
  51
  52         u1 = mpi_alloc_set_ui(1);
  53         if (!odd)
  54                 u2 = mpi_alloc_set_ui(0);
  55         u3 = mpi_copy(u);
  56         v1 = mpi_copy(v);
  57         if (!odd) {
  58                 v2 = mpi_alloc(mpi_get_nlimbs(u));
  59                 mpi_sub(v2, u1, u); /* U is used as const 1 */
  60         }
  61         v3 = mpi_copy(v);
  62         if (mpi_test_bit(u, 0)) { /* u is odd */
  63                 t1 = mpi_alloc_set_ui(0);
  64                 if (!odd) {
  65                         t2 = mpi_alloc_set_ui(1);
  66                         t2->sign = 1;
  67                 }
  68                 t3 = mpi_copy(v);
  69                 t3->sign = !t3->sign;
  70                 goto Y4;
  71         } else {
  72                 t1 = mpi_alloc_set_ui(1);
  73                 if (!odd)
  74                         t2 = mpi_alloc_set_ui(0);
  75                 t3 = mpi_copy(u);
  76         }
  77
  78         do {
  79                 do {
  80                         if (!odd) {
  81                                 if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {
  82                                         /* one is odd */
  83                                         mpi_add(t1, t1, v);
  84                                         mpi_sub(t2, t2, u);
  85                                 }
  86                                 mpi_rshift(t1, t1, 1);
  87                                 mpi_rshift(t2, t2, 1);
  88                                 mpi_rshift(t3, t3, 1);
  89                         } else {
  90                                 if (mpi_test_bit(t1, 0))
  91                                         mpi_add(t1, t1, v);
  92                                 mpi_rshift(t1, t1, 1);
  93                                 mpi_rshift(t3, t3, 1);
  94                         }
  95 Y4:
  96                         ;
  97                 } while (!mpi_test_bit(t3, 0)); /* while t3 is even */
  98
  99                 if (!t3->sign) {
 100                         mpi_set(u1, t1);
 101                         if (!odd)
 102                                 mpi_set(u2, t2);
 103                         mpi_set(u3, t3);
 104                 } else {
 105                         mpi_sub(v1, v, t1);
 106                         sign = u->sign; u->sign = !u->sign;
 107                         if (!odd)
 108                                 mpi_sub(v2, u, t2);
 109                         u->sign = sign;
 110                         sign = t3->sign; t3->sign = !t3->sign;
 111                         mpi_set(v3, t3);
 112                         t3->sign = sign;
 113                 }
 114                 mpi_sub(t1, u1, v1);
 115                 if (!odd)
 116                         mpi_sub(t2, u2, v2);
 117                 mpi_sub(t3, u3, v3);
 118                 if (t1->sign) {
 119                         mpi_add(t1, t1, v);
 120                         if (!odd)
 121                                 mpi_sub(t2, t2, u);
 122                 }
 123         } while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
 124         /* mpi_lshift( u3, k ); */
 125         mpi_set(x, u1);
 126
 127         mpi_free(u1);
 128         mpi_free(v1);
 129         mpi_free(t1);
 130         if (!odd) {
 131                 mpi_free(u2);
 132                 mpi_free(v2);
 133                 mpi_free(t2);
 134         }
 135         mpi_free(u3);
 136         mpi_free(v3);
 137         mpi_free(t3);
 138
 139         mpi_free(u);
 140         mpi_free(v);
 141         return 1;
 142 }
 143 EXPORT_SYMBOL_GPL(mpi_invm);