1 #include <tommath.h>
2 #ifdef BN_FAST_MP_INVMOD_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
16 */
17
18 /* computes the modular inverse via binary extended euclidean algorithm,
19 * that is c = 1/a mod b
20 *
21 * Based on slow invmod except this is optimized for the case where b is
22 * odd as per HAC Note 14.64 on pp. 610
23 */
fast_mp_invmod(mp_int * a,mp_int * b,mp_int * c)24 int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
25 {
26 mp_int x, y, u, v, B, D;
27 int res, neg;
28
29 /* 2. [modified] b must be odd */
30 if (mp_iseven (b) == 1) {
31 return MP_VAL;
32 }
33
34 /* init all our temps */
35 if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
36 return res;
37 }
38
39 /* x == modulus, y == value to invert */
40 if ((res = mp_copy (b, &x)) != MP_OKAY) {
41 goto LBL_ERR;
42 }
43
44 /* we need y = |a| */
45 if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
46 goto LBL_ERR;
47 }
48
49 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
50 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
51 goto LBL_ERR;
52 }
53 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
54 goto LBL_ERR;
55 }
56 mp_set (&D, 1);
57
58 top:
59 /* 4. while u is even do */
60 while (mp_iseven (&u) == 1) {
61 /* 4.1 u = u/2 */
62 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
63 goto LBL_ERR;
64 }
65 /* 4.2 if B is odd then */
66 if (mp_isodd (&B) == 1) {
67 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
68 goto LBL_ERR;
69 }
70 }
71 /* B = B/2 */
72 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
73 goto LBL_ERR;
74 }
75 }
76
77 /* 5. while v is even do */
78 while (mp_iseven (&v) == 1) {
79 /* 5.1 v = v/2 */
80 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
81 goto LBL_ERR;
82 }
83 /* 5.2 if D is odd then */
84 if (mp_isodd (&D) == 1) {
85 /* D = (D-x)/2 */
86 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
87 goto LBL_ERR;
88 }
89 }
90 /* D = D/2 */
91 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
92 goto LBL_ERR;
93 }
94 }
95
96 /* 6. if u >= v then */
97 if (mp_cmp (&u, &v) != MP_LT) {
98 /* u = u - v, B = B - D */
99 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
100 goto LBL_ERR;
101 }
102
103 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
104 goto LBL_ERR;
105 }
106 } else {
107 /* v - v - u, D = D - B */
108 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
109 goto LBL_ERR;
110 }
111
112 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
113 goto LBL_ERR;
114 }
115 }
116
117 /* if not zero goto step 4 */
118 if (mp_iszero (&u) == 0) {
119 goto top;
120 }
121
122 /* now a = C, b = D, gcd == g*v */
123
124 /* if v != 1 then there is no inverse */
125 if (mp_cmp_d (&v, 1) != MP_EQ) {
126 res = MP_VAL;
127 goto LBL_ERR;
128 }
129
130 /* b is now the inverse */
131 neg = a->sign;
132 while (D.sign == MP_NEG) {
133 if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
134 goto LBL_ERR;
135 }
136 }
137 mp_exch (&D, c);
138 c->sign = neg;
139 res = MP_OKAY;
140
141 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
142 return res;
143 }
144 #endif
145
146 /* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
147 /* $Revision: 1.3 $ */
148 /* $Date: 2006/03/31 14:18:44 $ */
149