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
|
#include <tommath_private.h>
#ifdef BN_MP_EXTEUCLID_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, tstdenis82@gmail.com, http://libtom.org
*/
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
*/
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
int err;
if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
return err;
}
/* initialize, (u1,u2,u3) = (1,0,a) */
mp_set(&u1, 1);
if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto LBL_ERR; }
/* initialize, (v1,v2,v3) = (0,1,b) */
mp_set(&v2, 1);
if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto LBL_ERR; }
/* loop while v3 != 0 */
while (mp_iszero(&v3) == MP_NO) {
/* q = u3/v3 */
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto LBL_ERR; }
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto LBL_ERR; }
/* (u1,u2,u3) = (v1,v2,v3) */
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto LBL_ERR; }
/* (v1,v2,v3) = (t1,t2,t3) */
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto LBL_ERR; }
}
/* make sure U3 >= 0 */
if (u3.sign == MP_NEG) {
if ((err = mp_neg(&u1, &u1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_neg(&u2, &u2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_neg(&u3, &u3)) != MP_OKAY) { goto LBL_ERR; }
}
/* copy result out */
if (U1 != NULL) { mp_exch(U1, &u1); }
if (U2 != NULL) { mp_exch(U2, &u2); }
if (U3 != NULL) { mp_exch(U3, &u3); }
err = MP_OKAY;
LBL_ERR:
mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */
|
