javamathmodulusdsaexponentiation

Modular Exponentiation in Java

I need a way to calculate:

(g^u * y^v) mod p

in Java.

I've found this algorithm for calculating (g^u) mod p:

int modulo(int a,int b,int c) {
    long x=1
    long y=a;
    while(b > 0){
        if(b%2 == 1){
            x=(x*y)%c;
        }
        y = (y*y)%c; // squaring the base
        b /= 2;
    }
    return (int) x%c;
}

and it works great, but I can't seem to find a way to do this for

(g^u * y^v) mod p

as my math skills are lackluster.

To put it in context, it's for a java implementation of a "reduced" DSA - the verifying part requires this to be solved.

Solution

  • Assuming that the two factors will not overflow, I believe you can simplify an expression like that in this way:

    (x * y) mod p = ( (x mod p)*(y mod p) ) mod p. I'm sure you can figure it out from there.