Calculating pow(a,b) mod n

Question

I want to calculate a^b mod n for use in RSA decryption. My code (below) returns incorrect answers. What is wrong with it?

unsigned long i         


        

Answer 1

Here is another way. Remember that when we find modulo multiplicative inverse of a under mod m. Then

a and m must be coprime with each other.

We can use gcd extended for calculating modulo multiplicative inverse.

For computing a^b mod m when a and b can have more than 10⁵ digits then its tricky to compute the result.

Below code will do the computing part :

#include 
#include 
using namespace std;
/*
*   May this code live long.
*/
long pow(string,string,long long);
long pow(long long ,long long ,long long);
int main() {
    string _num,_pow;
    long long _mod;
    cin>>_num>>_pow>>_mod;
    //cout<<_num<<" "<<_pow<<" "<<_mod<0){
        if((p&1)==0){
            p/=2;
            a=(a*a)%mod;
        }
        else{
            p--;
            res=(res*a)%mod;
        }
    }
    return res;
}
 

This code works because a^b mod m can be written as (a mod m)^{b mod m-1} mod m.

Hope it helped { :)