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