RSA Encryption using modulus and exponent in Java

Question

I'm currently doing RSA encryption on Java and I have to use private and public modulus for the encryption. I currently Have the following:

private void createPublicKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String publicModulus = "d2c34017ef94f8ab6696dae66e3c0d1ad186bbd9ce4461b68d7cd017c15bda174045bfef36fbf048" +
                "73cfd6d09e3806af3949f99c3e09d6d3c37f6398d8c63f9a3e39b78a187809822e8bcf912f4c44a8" +
                "92fe6a65a477ddea9582738317317286a2610ba30b6b090c3b8c61ffb64207229b3f01afe928a960" +
                "c5a44c24b26f5f91";

        BigInteger keyInt = new BigInteger(publicModulus, 16);
        BigInteger exponentInt = new BigInteger("10001", 16);
        RSAPublicKeySpec keySpeck = new RSAPublicKeySpec(keyInt, exponentInt);
        KeyFactory keyFactory = KeyFactory.getInstance("RSA");
        publicKey = keyFactory.generatePublic(keySpeck);

    }

private void createPrivateKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String privateModulus = "6c97ab6369cf00dd174bacd7c37e6f661d04e5af10670d4d88d30148ec188e63227b8dac0c517cf9" +
                "67aa73cd23684c9165dc269f091bfab33b6c5c7db95b54130e348255c30aaaac1c7f09ef701e0d6f" +
                "6dc142d2e4ed78466cc104e28d50be7adf3863afc021dbdd8b5f0b968b7cd965242c7d8d4b32ee84" +
                "0fac3cad134344c1";
        BigInteger privateModulusInt = new BigInteger(privateModulus, 16);
        BigInteger exponentInt = new BigInteger("10001", 16);
        RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(privateModulusInt, exponentInt);
        KeyFactory factory = KeyFactory.getInstance("RSA");
        privateKey = factory.generatePrivate(privateKeySpec);
    }

In the main method I have the following:

        createPrivateKey();
        createPublicKey();

        String data = "12";

        Cipher cipher1 = Cipher.getInstance("RSA/ECB/NoPadding");
        cipher1.init(Cipher.ENCRYPT_MODE, publicKey);
        byte[] encryptedData = cipher1.doFinal(data.getBytes());

        Cipher cipher2 = Cipher.getInstance("RSA/ECB/NoPadding");
        cipher2.init(Cipher.DECRYPT_MODE,privateKey);
        byte[] decryptedData = cipher2.doFinal(encryptedData);
        System.out.println(new String(decryptedData));

In the console I get the following: ���.7���p;%kV�9y���xa�ɼ{ and not "12" If I make the String data = "12345";, I then get: javax.crypto.BadPaddingException: Message is larger than modulus

Firstly why is the encryption and decryption not working? Why am I not getting back "12". Secondly why can I not have data be greater than 2 characters?

Note I'm using the following website to get the modulus and exponent values.

Answer 1

There is an error creating the private key. You are providing the public exponent instead of private and (as commented @dave_thomsom_085) private exponent instead of modulus

Change createPrivateKey() with

private static PrivateKey createPrivateKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String publicModulus = "d2c34017ef94f8ab6696dae66e3c0d1ad186bbd9ce4461b68d7cd017c15bda174045bfef36fbf048" +
                "73cfd6d09e3806af3949f99c3e09d6d3c37f6398d8c63f9a3e39b78a187809822e8bcf912f4c44a8" +
                "92fe6a65a477ddea9582738317317286a2610ba30b6b090c3b8c61ffb64207229b3f01afe928a960" +
                "c5a44c24b26f5f91";
        String privateExponent = "6c97ab6369cf00dd174bacd7c37e6f661d04e5af10670d4d88d30148ec188e63227b8dac0c517cf9" +
                "67aa73cd23684c9165dc269f091bfab33b6c5c7db95b54130e348255c30aaaac1c7f09ef701e0d6f" +
                "6dc142d2e4ed78466cc104e28d50be7adf3863afc021dbdd8b5f0b968b7cd965242c7d8d4b32ee84" +
                "0fac3cad134344c1";
        BigInteger privateExponenInt = new BigInteger(privateExponent, 16);
        BigInteger keyInt = new BigInteger(publicModulus, 16);
        RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(keyInt, privateExponenInt);
        KeyFactory factory = KeyFactory.getInstance("RSA");
        return factory.generatePrivate(privateKeySpec);
    }

Also you should not use raw RSA without padding for security reasons. Use RSA/ECB/PKCS1Padding or the new OAEP padding RSA/ECB/OAEPWithSHA1AndMGF1Padding

According to this answer you can encrypt with PKCS1Padding data up to 11 bytes less than the key size. and using OAEP it must be less than the size of the key modulus – 41

Then, using your 1024 bits key:

• PKCS1: (1024 bits / 8) - 11 = 117 bytes
• OAEP: (1024 bits / 8) - 42 = 86 bytes

Also is recommended to use CRT instead of private exponent directly

RSAPrivateCrtKeySpec privateKeySpec = 
    new RSAPrivateCrtKeySpec(modulus, publicExponent, privateExponent, primeP, primeQ, primeExpP, primeExpQ, crtCoefficient);