Java power exponentiation method keeps returning wrong value

Question

I am doing a small cryptography program and need a function to calculate power mod n

I wrote this method:

static int power(int x, int y, int p){
    int res = 1; // Initialize result
        
    x = x % p; // Update x if it is more than or equal to p
  
    while (y > 0) {
        res = ((res*x) % p)+p % p;
        y-=1;
    }
    return res;
}

But I have noticed it returns the wrong answer for certain cases. Example:

56295^779 mod 69997 should return 53580 but returns 20366 instead

43576^7116 mod 50087 should return 35712 but returns 40613 instead

It doesnt always return a wrong answer, so I am not sure why exactly this is happening. Any advice?

Answer 1

You are the victim of integer overflow.

        res = ((res*x) % p)+p % p;

This line could overflow. res * x is not guaranteed to fit into a signed 32-bit integer (but does fit into a signed 64-bit integer).

Examples:

2147483647 * 2 = -2
1147483647 * 22 = -525163542

To prevent this from happening, you can make res a long instead of int, and then cast back to int when returning from the function.

static int power(int x, int y, int p){
    long res = 1; // Initialize as long to prevent overflow!
        
    x = x % p;
  
    while (y > 0) {
        res = ((res*x) % p)+p % p; // No more overflow here!
        y-=1;
    }
    return (int) res; // Cast result back to int
}