Diffie-Hellman crack with partial info known

Question

This is school work.

I'm given the problem of finding the private keys of both parties in a DH exchange. The numbers involved in the tests aren't big enough and the task is basically brute-force. In the task, I can get the prime p, generator g and Alice's public key A. I'm also given the methods to encrypt a message and decrypt a message with a custom key.

Right now I've only gotten a by simply looping through integers i=1...p and checking if g^i mod p == g^A mod p and promptly returning the first value that meets the requirement.

However, my solution isn't always true according to automated tests. Anyone know how or even if it's possible to fins a and b with the given info?

Answer 1

Thanks to a third party, I managed to crack the DH code:

public Integer crackAlice() {
        // TODO
        Integer alicePrivate = 0;

        int p = session.getP();
        int g = session.getG();
        int A = session.getAlicesPublicKey();
        // A = g^a mod p


        System.out.println("Alice public A: "+A);
        String message = String.valueOf(156215);

        for (int i = 1; i < p; i++) {
            if (BigInteger.valueOf(g).pow(i).mod(BigInteger.valueOf(p)).equals(BigInteger.valueOf(A))) {
                //System.out.println("\t\t\t\t"+BigInteger.valueOf(g).pow(i));
                alicePrivate = i;
                System.out.println("Potential Alice private a: "+i);
                //break;
            }
        }
        return alicePrivate;
    }

and

public Integer crackBob() {
        // TODO

        Integer bobPrivate = 0;
        Integer a = crackAlice();
        int p = session.getP();
        int g = session.getG();
        int A = session.getAlicesPublicKey();
        String mainMessage = "teade";

        String msg = null;
        try {
            msg = session.getEncrypted(mainMessage);
        } catch (Exception e) {
            e.printStackTrace();
        }

        for (int i = 1; i < p; i++) {
            int ai = a*i;
            int Ai = A*i;
            //System.out.println("a*b = "+ai);
            BigInteger bigintP = BigInteger.valueOf(p);
            if (((BigInteger.valueOf(g).pow(a).mod(bigintP)).pow(i)).mod(bigintP)
                    .equals(((BigInteger.valueOf(g).pow(i).mod(bigintP)).pow(a)).mod(bigintP))) {
                String decrypt = null;
                try {
                    decrypt = session.getDecryptedWithCustomKey(msg, BigInteger.valueOf(g).pow(a*i).mod(bigintP).intValue());
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (decrypt != null && decrypt.trim().equals(mainMessage)) {
                    bobPrivate = i;
                    break;
                }
            }
        }
        return bobPrivate;
    }

I hope this will help out other with a similar problem.