#include <iostream>
#include <cmath>
#include <vector>
#include <numeric>

using namespace std;

int MyPow(int base, int exp, int n) {
   int answer = base;

   int i;

   for(i = 2; i <= exp; i++) {
       answer = answer * base;
       answer = answer % n;
   }

   return answer;
}

int FindD(int  e, int n) {
   int i;

   i = 1;
   while (i < n and (e*i) % n !=1) {
       ++i;
   }

   return i;
}


int main() {
    // select two distinct prime numbers
    int p {61},
        q {53};

    // compute n
    int n = p * q;
   
    // compute lambdaN, lcm(p-1, q-1)
    int lambdaN {lcm(p-1, q-1)};

    // e is selected so it is coprime to lambdaN
    int e {17};
    // d is the modular multiplicative inverse if e mod lambdaN
    int d {FindD(e, (p-1)*(q-1))}; 

    int plainText, cipherText;
    vector<int> code;

    cout << "p = " << p << endl;
    cout << "q = " << q << endl;
    cout << "n = " << n << endl;
    cout << "lambda N = " << lambdaN << endl;

    cout << endl;

    cout << "The public key is ("  << n << ", " << e << ")" << endl;
    cout << "The private key is ("  << n << ", " << d << ")" << endl;

/*
    cout << "C(d,C(e, i)) " << endl;
    // c(m) = m^e % n
    // d(m) = m^d % n
    for(char i = 65; i < 91; ++i) {
      cipherText = MyPow(i, e, n);
      plainText = MyPow(cipherText, d, n);
      cout << char(i) << " " << cipherText  << " " << char(plainText) << endl;
    }
*/

/*
 * cout << endl << endl;
    cout << "C(e,C(d, i)) " << endl;
    for(char i = 65; i < 91; ++i) {
      plainText = MyPow(i, d, n);
      cipherText = MyPow(plainText, e, n);
      cout << char(i) << " " << plainText  << " " << char(cipherText) << endl;
    }
*/

    cout << endl;

    cout << "Encoding Hello World, with public key" << endl;
    for(auto ch : "HELLO WORLD") {
       cipherText = MyPow(ch,e, n);
       code.push_back(cipherText);
    }
    code.pop_back();

    for(auto num: code){
       cout << num  << " ";
    }
    cout << endl;

    cout << "Decoding  with private key: " ;
    for(auto num: code) {
       cout << char(MyPow(num, d, n));
    }

    cout << endl;

    code.clear();

    cout << "Encoding Hello World, with private key" << endl;
    for(auto ch : "HELLO WORLD") {
       cipherText = MyPow(ch,d, n);
       code.push_back(cipherText);
    }
    code.pop_back();

    for(auto num: code){
       cout << num  << " ";
    }
    cout << endl << endl;

    cout << "Decoding  with public key: " ;
    for(auto num: code) {
       cout << char(MyPow(num, e, n));
    }

    cout << endl;

    return 0;
}