Extended Euclid’s Algorithm C Code

$GCD(a, b) = d = ax + by$
In addition to calculating a GCD, it calculates coefficients x and y such that satisfies the above equation. These coefficients x and y are important for calculating modular multiplicative inverses. The Extended Euclid’s algorithm is used in a much practical application specifically in cryptography.

The following C code presents an efficient algorithm to solve the Extended Euclid’s algorithm. The code is also available on GitHub.

#include <stdio.h>
#include <math.h>

typedef struct {
int d;
int x;
int y;
} EE;

EE extended_euclid(int a, int b) {
EE ee1, ee2, ee3;
if (b == 0) {
ee1.d = a;
ee1.x = 1;
ee1.y = 0;
printf("%d %d %d %d %d\n", a, b, ee1.d, ee1.x, ee1.y);
return ee1;
} else {
ee2 = extended_euclid(b, a % b);
ee3.d = ee2.d;
ee3.x = ee2.y;
ee3.y = ee2.x - floor(a / b) * ee2.y;
printf("%d %d %d %d %d\n", a, b, ee3.d, ee3.x, ee3.y);
return ee3;
}
}

int main(int argc, char* argv[]) {
int a = 287, b = 288;
EE ee = extended_euclid(a, b);
printf("GCD = %d\n", ee.d);
printf("x = %d\n", ee.x);
printf("y = %d\n", ee.y);
return 0;
}
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