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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 */
27int 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 }
95Y4:
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}
143EXPORT_SYMBOL_GPL(mpi_invm);
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 */
28int 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 }
126Y4:
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
171cleanup:
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}