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 */
mpi_invm(MPI x,MPI a,MPI n)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);
144