import java.lang.Math;
import java.math.BigInteger;
import java.util.Random;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;

public class RSA {
	
	final static BigInteger m =
          new BigInteger("91011121314151617181920212223242526272829",10);
	BigInteger p = new BigInteger("0",10);
	BigInteger q = new BigInteger("0",10);
	BigInteger phi = new BigInteger("0",10);
	BigInteger e = new BigInteger("0",10);
	BigInteger sha = new BigInteger("0",10);
	BigInteger n = new BigInteger("0",10);
	BigInteger d = new BigInteger("0",10);
	
	BigInteger encrypted		= new BigInteger("0",10);
	BigInteger decrypted		= new BigInteger("0",10);

    //Generates a PrimNumber
	private BigInteger genPrim(int bitlen){
		BigInteger p = BigInteger.probablePrime(bitlen, new Random());
		if(!p.isProbablePrime(100000)){
			throw new RuntimeException();
		}
		return p;
	}
	
	//Generates an E using phi
	private void genE(BigInteger phi){
		e = genPrim(256);		
		
		if(!phi.gcd(e).equals(BigInteger.ONE)){
			genE(phi);
		}
	}
	
    //Encrypt-Funktion
	public void encrypt(){
        q = genPrim(256); //get q
		p = genPrim(256); //get p
		
		if(p.equals(q)){ //ensure p!=q
			encrypt();
		}
		
		phi = p.subtract(BigInteger.ONE).multiply(
                        q.subtract(BigInteger.ONE)); //phi=(p - 1)(q - 1)
		
		n = p.multiply(q); //n = p*q
        
        genE(phi); //get e
		
		SHA256(); //calculate Hash of m
		
		encrypted = expModuloN(sha, e, n); // hash^e mod n
	}
	
    //Decrypt Function (you need 2 run encrypt first)
	public void decrypt(){
		
		d = extEuklid(e, phi); //calculate d
		
		decrypted = expModuloN(encrypted, d, n); //decrypt
	
	}
	
    //extended Euklid-Algorithm
	private BigInteger extEuklid(BigInteger a, BigInteger b){
		
        //Ancor
		if(b.equals(BigInteger.ZERO)){
			return BigInteger.ONE;
		}
		
        //Initialize vars
		BigInteger x1 = new BigInteger("0",10);
		BigInteger x2 = new BigInteger("1",10);
		BigInteger y = new BigInteger("1",10);
		BigInteger y1 = new BigInteger("1",10);
		BigInteger y2 = new BigInteger("0",10);
        BigInteger r = new BigInteger("0",10);
        BigInteger q = new BigInteger("0",10);
        BigInteger x = new BigInteger("0",10);
		
		while(b.compareTo(BigInteger.ZERO) == 1){
			q = a.divide(b);
			r = a.mod(b);
			x = x2.subtract(q.multiply(x1));
			y = y2.subtract(q.multiply(y1));
			a = b;
			b = r;
			x2 = x1;
			x1 = x;
			y2 = y1;
			y1 = y;
		}
        
		if(x2.compareTo(BigInteger.ZERO) == -1){
			x2 = phi.add(x2);
		}
		
		return x2; //only x2 is needed
		
	}
	
	
	//Efficient m^e mod n
	private BigInteger expModuloN(BigInteger m, BigInteger e, BigInteger n){
		
        BigInteger b = m;
		BigInteger r = BigInteger.ONE;
		
		for(int i = 0; i <= e.bitLength(); i++){
        
			if(e.testBit(i)){
				r = r.multiply(b).mod(n);
			}
            
			b = b.multiply(b).mod(n);				
		}

		return r;	
	}
    
    //Converts a byte to a HexString
    public String BytetoHex(byte b) {
           int value = (b & 0x7F) + (b < 0 ? 128 : 0);
       
            String ret = (value < 16 ? "0" : "");
            ret += Integer.toHexString(value).toUpperCase();
        
        return ret;
      }
      
    //Converts SHA-byte-array to HexString
    public String SHAtoHex(byte[] d)
    {
        StringBuffer buf = new StringBuffer();
        
          for (int i = 0; i < d.length; i++) {
              buf.append(BytetoHex(d[i]));
        }
           
        return buf.toString();      
     }

    
    //Calculates SHA256 of m
    private void SHA256(){
        try {
            MessageDigest l = MessageDigest.getInstance("SHA-256");
            l.reset();
            l.update(m.toByteArray());
            sha = new BigInteger(SHAtoHex(l.digest()), 16);        
        } catch (NoSuchAlgorithmException e) {
            throw new RuntimeException();
        }
    }
	
	public static void main(String[] args) {
		
		RSA r = new RSA();		
		
		r.encrypt(); //calculate all
		r.decrypt();
		
        //Print all
		System.out.println("\nKey public:");
		System.out.println("\t e: " + r.e);
		System.out.println("\t n: " + r.n);
		System.out.println("\nKey private:");
		System.out.println("\t d: " + r.d);
		System.out.println("\nHashvalue:");
		System.out.println("\t sha: " + r.sha);
		System.out.println("\nSignature:");
		System.out.println("\t Enc.: " + r.encrypted);
		System.out.println("\nDecrypted:");
		System.out.println("\t Dec.: " + r.decrypted);
		System.out.println("\nSHA = Decrypted:");
		System.out.println(r.decrypted.equals(r.sha));
		
	}	

}