/*************************************************************************

• Compilation: javac RSA.java
• Execution: java RSA N
• Generate an N-bit public and private RSA key and use to encrypt
• and decrypt a random message.
• % java RSA 50
• public = 65537
• private = 553699199426609
• modulus = 825641896390631
• message = 48194775244950
• encrpyted = 321340212160104
• decrypted = 48194775244950
• Known bugs (not addressed for simplicity)

• ---

• • It could be the case that the message >= modulus. To avoid, use
• a do-while loop to generate key until modulus happen to be exactly N bits.
• • It's possible that gcd(phi, publicKey) != 1 in which case
• the key generation fails. This will only happen if phi is a
• multiple of 65537. To avoid, use a do-while loop to generate
• keys until the gcd is 1.

*************************************************************************/

import java.math.BigInteger;
import java.security.SecureRandom;

public class RSA {
private final static BigInteger one = new BigInteger("1");
private final static SecureRandom random = new SecureRandom();

private BigInteger privateKey;
private BigInteger publicKey;
private BigInteger modulus;

// generate an N-bit (roughly) public and private key
RSA(int N) {
BigInteger p = BigInteger.probablePrime(N/2, random);
BigInteger q = BigInteger.probablePrime(N/2, random);
BigInteger phi = (p.subtract(one)).multiply(q.subtract(one));

  modulus    = p.multiply(q);                                  
  publicKey  = new BigInteger("65537");     // common value in practice = 2^16 + 1
  privateKey = publicKey.modInverse(phi);

}

BigInteger encrypt(BigInteger message) {
return message.modPow(publicKey, modulus);
}

BigInteger decrypt(BigInteger encrypted) {
return encrypted.modPow(privateKey, modulus);
}

public String toString() {
String s = "";
s += "public = " + publicKey + "\n";
s += "private = " + privateKey + "\n";
s += "modulus = " + modulus;
return s;
}

public static void main(String[] args) {
int N = 50;
RSA key = new RSA(N);
System.out.println(key);

  // create random message, encrypt and decrypt
  //BigInteger message = new BigInteger(N-1, random);
  BigInteger message = new BigInteger("3080152");
  //// create message by converting string to integer
  // String s = "test";
  // byte[] bytes = s.getBytes();
  // BigInteger message = new BigInteger(s);

  BigInteger encrypt = key.encrypt(message);
  BigInteger decrypt = key.decrypt(encrypt);
  System.out.println("message   = " + message);
  System.out.println("encrpyted = " + encrypt);
  System.out.println("decrypted = " + decrypt);

}
}