2 #ifdef BN_FAST_MP_INVMOD_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
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.
12 * The library is free for all purposes without any express
15 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
18 /* computes the modular inverse via binary extended euclidean algorithm,
19 * that is c = 1/a mod b
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
24 int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
26 mp_int x, y, u, v, B, D;
29 /* 2. [modified] b must be odd */
30 if (mp_iseven (b) == 1) {
34 /* init all our temps */
35 if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
39 /* x == modulus, y == value to invert */
40 if ((res = mp_copy (b, &x)) != MP_OKAY) {
45 if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
49 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
50 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
53 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
59 /* 4. while u is even do */
60 while (mp_iseven (&u) == 1) {
62 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
65 /* 4.2 if B is odd then */
66 if (mp_isodd (&B) == 1) {
67 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
72 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
77 /* 5. while v is even do */
78 while (mp_iseven (&v) == 1) {
80 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
83 /* 5.2 if D is odd then */
84 if (mp_isodd (&D) == 1) {
86 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
91 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
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) {
103 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
107 /* v - v - u, D = D - B */
108 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
112 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
117 /* if not zero goto step 4 */
118 if (mp_iszero (&u) == 0) {
122 /* now a = C, b = D, gcd == g*v */
124 /* if v != 1 then there is no inverse */
125 if (mp_cmp_d (&v, 1) != MP_EQ) {
130 /* b is now the inverse */
132 while (D.sign == MP_NEG) {
133 if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
141 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
146 /* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
147 /* $Revision: 1.3 $ */
148 /* $Date: 2006/03/31 14:18:44 $ */