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
144
145
146
147
148
|
#include <tommath.h>
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
*/
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
* Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int fast_mp_invmod(mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, B, D;
int res, neg;
/* 2. [modified] b must be odd */
if (mp_iseven(b) == 1) {
return MP_VAL;
}
/* init all our temps */
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return res;
}
/* x == modulus, y == value to invert */
if ((res = mp_copy(b, &x)) != MP_OKAY) {
goto LBL_ERR;
}
/* we need y = |a| */
if ((res = mp_mod(a, b, &y)) != MP_OKAY) {
goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy(&x, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy(&y, &v)) != MP_OKAY) {
goto LBL_ERR;
}
mp_set(&D, 1);
top:
/* 4. while u is even do */
while (mp_iseven(&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2(&u, &u)) != MP_OKAY) {
goto LBL_ERR;
}
/* 4.2 if B is odd then */
if (mp_isodd(&B) == 1) {
if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* B = B/2 */
if ((res = mp_div_2(&B, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 5. while v is even do */
while (mp_iseven(&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2(&v, &v)) != MP_OKAY) {
goto LBL_ERR;
}
/* 5.2 if D is odd then */
if (mp_isodd(&D) == 1) {
/* D = (D-x)/2 */
if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* D = D/2 */
if ((res = mp_div_2(&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
if (mp_cmp(&u, &v) != MP_LT) {
/* u = u - v, B = B - D */
if ((res = mp_sub(&u, &v, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub(&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, D = D - B */
if ((res = mp_sub(&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub(&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero(&u) == 0) {
goto top;
}
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d(&v, 1) != MP_EQ) {
res = MP_VAL;
goto LBL_ERR;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add(&D, b, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_exch(&D, c);
c->sign = neg;
res = MP_OKAY;
LBL_ERR:mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
return res;
}
#endif
/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
/* $Revision: 1.4 $ */
/* $Date: 2006/12/28 01:25:13 $ */
|
