Question

I am carrying out the following modulo division operations from within a C program:

(5^6) mod 23 = 8

(5^15) mod 23 = 19

I am using the following function, for convenience:

int mod_func(int p, int g, int x) {
    return ((int)pow((double)g, (double)x)) % p;
}

But the result of the operations when calling the function is incorrect:

mod_func(23, 5, 6) //returns 8
mod_func(23, 5, 15) //returns -6

Does the modulo operator have some limit on the size of the operands?

Answer 1

5 to the power 15 is 30,517,578,125

The largest value you can store in an int is 2,147,483,647

You could use 64-bit integers, but beware you’ll have precision issues when converting from double eventually.

From memory, there is a rule from number theory about the calculation you are doing that means you don’t need to compute the full power expansion in order to determine the modulo result. But I could be wrong. Been too many years since I learned that stuff.

Ahh, here it is: Modular Exponentiation

Read that, and stop using double and pow =)

int mod_func(int p, int g, int x)
{
    int r = g;
    for( int i = 1; i < x; i++ ) {
        r = (r * g) % p;
    }
    return r;
}