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/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm, that is c = 1/a mod b */
int
fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, B, D;
int res, neg;
if ((res = mp_init (&x)) != MP_OKAY) {
goto __ERR;
}
if ((res = mp_init (&y)) != MP_OKAY) {
goto __X;
}
if ((res = mp_init (&u)) != MP_OKAY) {
goto __Y;
}
if ((res = mp_init (&v)) != MP_OKAY) {
goto __U;
}
if ((res = mp_init (&B)) != MP_OKAY) {
goto __V;
}
if ((res = mp_init (&D)) != MP_OKAY) {
goto __B;
}
/* x == modulus, y == value to invert */
if ((res = mp_copy (b, &x)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (a, &y)) != MP_OKAY) {
goto __D;
}
if ((res = mp_abs (&y, &y)) != MP_OKAY) {
goto __D;
}
/* 2. [modified] if x,y are both even then return an error! */
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
goto __D;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __D;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto __D;
}
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 __D;
}
/* 4.2 if A or B is odd then */
if (mp_iseven (&B) == 0) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto __D;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* 5.2 if C,D are even then */
if (mp_iseven (&D) == 0) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto __D;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto __D;
}
}
/* 6. if u >= v then */
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, A = A - C, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto __D;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto __D;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto __D;
}
}
/* 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 __D;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
goto __D;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
__D:mp_clear (&D);
__B:mp_clear (&B);
__V:mp_clear (&v);
__U:mp_clear (&u);
__Y:mp_clear (&y);
__X:mp_clear (&x);
__ERR:
return res;
}
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