| Dmitry Kasatkin | 7e8dec9 | 2011-11-07 15:16:37 +0200 | [diff] [blame] | 1 | /* mpi-inv.c - MPI functions |
| 2 | * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc. |
| 3 | * |
| 4 | * This file is part of GnuPG. |
| 5 | * |
| 6 | * GnuPG is free software; you can redistribute it and/or modify |
| 7 | * it under the terms of the GNU General Public License as published by |
| 8 | * the Free Software Foundation; either version 2 of the License, or |
| 9 | * (at your option) any later version. |
| 10 | * |
| 11 | * GnuPG 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 General Public License for more details. |
| 15 | * |
| 16 | * You should have received a copy of the GNU General Public License |
| 17 | * along with this program; if not, write to the Free Software |
| 18 | * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA |
| 19 | */ |
| 20 | |
| 21 | #include "mpi-internal.h" |
| 22 | |
| 23 | /**************** |
| 24 | * Calculate the multiplicative inverse X of A mod N |
| 25 | * That is: Find the solution x for |
| 26 | * 1 = (a*x) mod n |
| 27 | */ |
| 28 | int mpi_invm(MPI x, const MPI a, const MPI n) |
| 29 | { |
| 30 | /* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X) |
| 31 | * modified according to Michael Penk's solution for Exercice 35 |
| 32 | * with further enhancement */ |
| 33 | MPI u = NULL, v = NULL; |
| 34 | MPI u1 = NULL, u2 = NULL, u3 = NULL; |
| 35 | MPI v1 = NULL, v2 = NULL, v3 = NULL; |
| 36 | MPI t1 = NULL, t2 = NULL, t3 = NULL; |
| 37 | unsigned k; |
| 38 | int sign; |
| 39 | int odd = 0; |
| 40 | int rc = -ENOMEM; |
| 41 | |
| 42 | if (mpi_copy(&u, a) < 0) |
| 43 | goto cleanup; |
| 44 | if (mpi_copy(&v, n) < 0) |
| 45 | goto cleanup; |
| 46 | |
| 47 | for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) { |
| 48 | if (mpi_rshift(u, u, 1) < 0) |
| 49 | goto cleanup; |
| 50 | if (mpi_rshift(v, v, 1) < 0) |
| 51 | goto cleanup; |
| 52 | } |
| 53 | odd = mpi_test_bit(v, 0); |
| 54 | |
| 55 | u1 = mpi_alloc_set_ui(1); |
| 56 | if (!u1) |
| 57 | goto cleanup; |
| 58 | if (!odd) { |
| 59 | u2 = mpi_alloc_set_ui(0); |
| 60 | if (!u2) |
| 61 | goto cleanup; |
| 62 | } |
| 63 | if (mpi_copy(&u3, u) < 0) |
| 64 | goto cleanup; |
| 65 | if (mpi_copy(&v1, v) < 0) |
| 66 | goto cleanup; |
| 67 | if (!odd) { |
| 68 | v2 = mpi_alloc(mpi_get_nlimbs(u)); |
| 69 | if (!v2) |
| 70 | goto cleanup; |
| 71 | if (mpi_sub(v2, u1, u) < 0) |
| 72 | goto cleanup; /* U is used as const 1 */ |
| 73 | } |
| 74 | if (mpi_copy(&v3, v) < 0) |
| 75 | goto cleanup; |
| 76 | if (mpi_test_bit(u, 0)) { /* u is odd */ |
| 77 | t1 = mpi_alloc_set_ui(0); |
| 78 | if (!t1) |
| 79 | goto cleanup; |
| 80 | if (!odd) { |
| 81 | t2 = mpi_alloc_set_ui(1); |
| 82 | if (!t2) |
| 83 | goto cleanup; |
| 84 | t2->sign = 1; |
| 85 | } |
| 86 | if (mpi_copy(&t3, v) < 0) |
| 87 | goto cleanup; |
| 88 | t3->sign = !t3->sign; |
| 89 | goto Y4; |
| 90 | } else { |
| 91 | t1 = mpi_alloc_set_ui(1); |
| 92 | if (!t1) |
| 93 | goto cleanup; |
| 94 | if (!odd) { |
| 95 | t2 = mpi_alloc_set_ui(0); |
| 96 | if (!t2) |
| 97 | goto cleanup; |
| 98 | } |
| 99 | if (mpi_copy(&t3, u) < 0) |
| 100 | goto cleanup; |
| 101 | } |
| 102 | do { |
| 103 | do { |
| 104 | if (!odd) { |
| 105 | if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) { /* one is odd */ |
| 106 | if (mpi_add(t1, t1, v) < 0) |
| 107 | goto cleanup; |
| 108 | if (mpi_sub(t2, t2, u) < 0) |
| 109 | goto cleanup; |
| 110 | } |
| 111 | if (mpi_rshift(t1, t1, 1) < 0) |
| 112 | goto cleanup; |
| 113 | if (mpi_rshift(t2, t2, 1) < 0) |
| 114 | goto cleanup; |
| 115 | if (mpi_rshift(t3, t3, 1) < 0) |
| 116 | goto cleanup; |
| 117 | } else { |
| 118 | if (mpi_test_bit(t1, 0)) |
| 119 | if (mpi_add(t1, t1, v) < 0) |
| 120 | goto cleanup; |
| 121 | if (mpi_rshift(t1, t1, 1) < 0) |
| 122 | goto cleanup; |
| 123 | if (mpi_rshift(t3, t3, 1) < 0) |
| 124 | goto cleanup; |
| 125 | } |
| 126 | Y4: |
| 127 | ; |
| 128 | } while (!mpi_test_bit(t3, 0)); /* while t3 is even */ |
| 129 | |
| 130 | if (!t3->sign) { |
| 131 | if (mpi_set(u1, t1) < 0) |
| 132 | goto cleanup; |
| 133 | if (!odd) |
| 134 | if (mpi_set(u2, t2) < 0) |
| 135 | goto cleanup; |
| 136 | if (mpi_set(u3, t3) < 0) |
| 137 | goto cleanup; |
| 138 | } else { |
| 139 | if (mpi_sub(v1, v, t1) < 0) |
| 140 | goto cleanup; |
| 141 | sign = u->sign; |
| 142 | u->sign = !u->sign; |
| 143 | if (!odd) |
| 144 | if (mpi_sub(v2, u, t2) < 0) |
| 145 | goto cleanup; |
| 146 | u->sign = sign; |
| 147 | sign = t3->sign; |
| 148 | t3->sign = !t3->sign; |
| 149 | if (mpi_set(v3, t3) < 0) |
| 150 | goto cleanup; |
| 151 | t3->sign = sign; |
| 152 | } |
| 153 | if (mpi_sub(t1, u1, v1) < 0) |
| 154 | goto cleanup; |
| 155 | if (!odd) |
| 156 | if (mpi_sub(t2, u2, v2) < 0) |
| 157 | goto cleanup; |
| 158 | if (mpi_sub(t3, u3, v3) < 0) |
| 159 | goto cleanup; |
| 160 | if (t1->sign) { |
| 161 | if (mpi_add(t1, t1, v) < 0) |
| 162 | goto cleanup; |
| 163 | if (!odd) |
| 164 | if (mpi_sub(t2, t2, u) < 0) |
| 165 | goto cleanup; |
| 166 | } |
| 167 | } while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */ |
| 168 | /* mpi_lshift( u3, k ); */ |
| 169 | rc = mpi_set(x, u1); |
| 170 | |
| 171 | cleanup: |
| 172 | mpi_free(u1); |
| 173 | mpi_free(v1); |
| 174 | mpi_free(t1); |
| 175 | if (!odd) { |
| 176 | mpi_free(u2); |
| 177 | mpi_free(v2); |
| 178 | mpi_free(t2); |
| 179 | } |
| 180 | mpi_free(u3); |
| 181 | mpi_free(v3); |
| 182 | mpi_free(t3); |
| 183 | |
| 184 | mpi_free(u); |
| 185 | mpi_free(v); |
| 186 | return rc; |
| 187 | } |