Current File : //data/down/eBOOKS//Handbook of Applied Cryptography/inverse.c
/*
Author: Pate Williams (c) 1997
2.142 Algorithm Computing multiplicative
inverses in Zn
See "Handbook of Applied Cryptography" by
Alfred J. Menezes et al page 71.
*/
#include <stdio.h>
void extended_euclid(long a, long b, long *x,
long *y, long *d)
/* calculates a * *x + b * *y = gcd(a, b) = *d */
{
long q, r, x1, x2, y1, y2;
if (b == 0) {
*d = a, *x = 1, *y = 0;
return;
}
x2 = 1, x1 = 0, y2 = 0, y1 = 1;
while (b > 0) {
q = a / b, r = a - q * b;
*x = x2 - q * x1, *y = y2 - q * y1;
a = b, b = r;
x2 = x1, x1 = *x, y2 = y1, y1 = *y;
}
*d = a, *x = x2, *y = y2;
}
long inverse(long a, long n)
/* computes the inverse of a modulo n */
{
long d, x, y;
extended_euclid(a, n, &x, &y, &d);
if (d == 1) return x;
return 0;
}
int main(void)
{
long a = 5, n = 7;
printf("the inverse of %ld modulo %2ld is %ld\n",
a, n, inverse(a, n));
a = 2, n = 12;
printf("the inverse of %ld modulo %2ld is %ld\n",
a, n, inverse(a, n));
return 0;
}
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