/* 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@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
* Based on mp_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] if a,b are both even then return an error!
*
* That is if gcd(a,b) = 2**k * q then obviously there is no inverse.
*/
if (mp_iseven (a) == 1 && 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 __ERR;
}
/* we need y = |a| */
if ((res = mp_abs (a, &y)) != MP_OKAY) {
goto __ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __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 __ERR;
}
/* 4.2 if B is odd then */
if (mp_isodd (&B) == 1) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __ERR;
}
}
/* B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __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 __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 __ERR;
}
}
/* D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __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 __ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __ERR;
}
} else {
/* v - v - u, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __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 __ERR;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
goto __ERR;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
