This example generates a key pair for various public/private key algorithms. See also e197 Listing All Available Public/Private Key Generators. 
    try {
        // Generate a 1024-bit Digital Signature Algorithm (DSA) key pair
        KeyPairGenerator keyGen = KeyPairGenerator.getInstance("DSA");
        keyGen.initialize(1024);
        KeyPair keypair = keyGen.genKeyPair();
        PrivateKey privateKey = keypair.getPrivate();
        PublicKey publicKey = keypair.getPublic();
    
        // Generate a 576-bit DH key pair
        keyGen = KeyPairGenerator.getInstance("DH");
        keyGen.initialize(576);
        keypair = keyGen.genKeyPair();
        privateKey = keypair.getPrivate();
        publicKey = keypair.getPublic();
    
        // Generate a 1024-bit RSA key pair
        keyGen = KeyPairGenerator.getInstance("RSA");
        keyGen.initialize(1024);
        keypair = keyGen.genKeyPair();
        privateKey = keypair.getPrivate();
        publicKey = keypair.getPublic();
    } catch (java.security.NoSuchAlgorithmException e) {
    }