How to encrypt in RSA?

Question

I want to write my own RSA encrypter without libaries!

Code:

import java.util.Random;

public class Main {

public static void main(String[] args) {
    System.out.println(createPrime());
}

private static byte encrypt(byte message) {
    double p = createPrime();
    double q = createPrime();
    double e = 2 ^ new Random().nextInt(100) % (p * q);
    byte ciphered = Math.pow(message, e);
    return ciphered;
}

private static double createPrime() {
    double testPow;
    do {
    int test = new Random().nextInt(20);
    int power = new Random().nextInt(20);
    test += 1;
    power +=1;
    testPow = Math.pow(test, power);
    System.out.println("Double Math.pow: " + testPow);
    } while (!testPrime(testPow));
    return testPow;
}

private static Boolean testPrime(Double test) {
    int factor = 2;
    int lastFactor = 1;
    while (test > 1) {
        if (test % factor == 0) {
            lastFactor = factor;
            test /= factor;
            while (test % factor == 0) {
                test /= factor;
            }
        }
        factor++;
    }
    Boolean isPrime = false;
    if (test == lastFactor) {
        isPrime = true;
    }
    return isPrime;
 }
}

This is what I have for encrypting. I don't know what I should do to correct this, but I have pretty much done this by hand before trying this.

So I know that the equation to encrypt is c = m^e (mod N) and decryption m = c^d (mod N)

where p, q are prime numbers - m is message - c is ciphered text - e is totient of N - N is p times q - totient of N is (p-1)(q-1)

Any help is appreciated

Answer 1

I'd suggest reading/copying an existing implementation for reference, such as BouncyCastle: http://www.docjar.com/html/api/org/bouncycastle/crypto/engines/RSACoreEngine.java.html

By the way, if you want this to be at all secure, you should be using java.security.SecureRandom, not java.util.Random

Answer 2

Java has built-in encryption algorithms under the java.security package. Check this. So no need for external libraries. I see no production need to implement it yourself. Only if it is homework (which you didn't tag)

Answer 3

You didn't ask a real question, but I see a couple of problems anyways

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double e = 2 ^ new Random().nextInt(100) % (p * q);

I don't know what this is supposed to do, but it's wrong. Did you mean Math.Pow() rather than ^? In any case, usually you just use some small constant with very few set bits for e to make encryption fast. e=3 or e=65 would work fine.

You don't seem to be calculating the private key (d), or even storing the public key (e, p*q) at all.

When you start using large numbers, int and double (??) will not be able to hold them. Use BigInteger instead.

---

do {
    testPow = Math.pow(test, power);
} while (!testPrime(testPow));

If power > 1, testPow will never be prime...

---

I have not looked at testPrime(), but you should be able to write some quick unit tests to convince yourself whether or not it probably works.

Answer 4

The first thing to do is to have a look at the class java.math.BigInteger. This class will help you a lot to implement "School-book" RSA.