//        p = 5, q = 11
//        RSA-Modul N = p * q = 55
//        Phi(N) = Phi(p)*Phi(q) | weil eigenschaft eulersche phi funktion und p,q teilerfremd
//    = (p-1)*(q-1) | p,q primzahlen, daher nur durch 1 und sich selbst teilbar und alle anderen teilerfremd
//                = 4*10 = 40
//        e: 1 < e < Phi(N) und ggT(e, Phi(N)) = 1
//        e elem aus {3,..} => e = 3
//                (e,N) = (3, 55) public key
//    -----
//        d: e*d kongr 1 mod Phi(N) => e*d mod Phi(N) = 1
//                3*d mod 40 = 1
//        Durch probieren: d=27 => (27, 55) private key
//
//    ----
//        Verschlüsseln
//    13
//        c = m^e (mod N) => 13^3 (mod 55) = 52 = c
//    ----
//        Entschlüsseln
//                m = c^d (mod N) => 52^27 (mod 55) = 13 = m

import java.math.BigInteger;

public class RSA {
    private int bitLength;
    private BigInteger p;
    private BigInteger q;
    private BigInteger n;
    private BigInteger phiP;
    private BigInteger phiQ;
    private BigInteger phiN;
    private BigInteger e;
    private BigInteger d;

    public RSA (int bitLength) {
        this.bitLength = bitLength;
        this.p = Prime.generate(bitLength);
        this.q = Prime.generate(bitLength);
        this.n = p.multiply(q);
        this.phiP = p.subtract(BigInteger.ONE);
        this.phiQ = q.subtract(BigInteger.ONE);
        this.phiN = phiP.multiply(phiQ);
    }

    private void findPublicKey () {
        BigInteger check;
        do {
            this.e = Prime.generate(this.bitLength*2/3);
            check = this.e.gcd(phiN);
        } while (!check.equals(BigInteger.ONE));
    }

    private void findPrivateKey () {
        this.d = e.modInverse(phiN);
    }

    private void endKeyCreation () {
        this.p = BigInteger.ZERO;
        this.q = BigInteger.ZERO;
        this.phiP = BigInteger.ZERO;
        this.phiQ = BigInteger.ZERO;
        this.phiN = BigInteger.ZERO;
    }

    public void createKeys() {
        this.findPublicKey();
        this.findPrivateKey();
        this.endKeyCreation();
    }

    public BigInteger getPublicKey () {
        return e;
    }

    public BigInteger getPrivateKey () {
        return d;
    }

    public BigInteger getRSAModule() {
        return n;
    }

    static BigInteger cipher (BigInteger message, BigInteger key, BigInteger module) {
        return message.modPow(key, module);
    }
}