Jo,

there are asymmetric encryption schemes, like RSA, those use
public/private key pairs, i.e. one of both keys on each end, and there are
symmetric encryption schemes, like DES, those use the same key on both
ends. This is basic encryption know how, if you do not know this, you
should try to read a book about encryption before you try to code a Java
program using encryption, because chances are, that out of ignorance you
make it wrong, and hence your program wont be more secure than it would be
without using encryption.

However, if you use DES, then both sides have to use the same key, and in
Java you do not create a KeyPair from KeyPairGenerator and the feed the
private (or public) key of the pair to the DES Cipher, as you tried, but
instead you use a KeyGenerator, to create a Key, and you have to share
this key on both ends of your communication. However, anybody who
intercepts this shared key, can read your communication, so it is only as
secure, as your shared key is. But: it is easy to create a Cipher, that
enables a per byte encryption, and hence allows a Cipher*Stream to
transmit single bytes, just as you need it:

        KeyGenerator kg = KeyGenerator.getInstance("DES");
        kg.init(56);  //Key length
        Key k = kg.generateKey(); // that is the key to be shared!

        Cipher c = Cipher.getInstance("DES/CFB8/NoPadding");
        c.init(Cipher.ENCRYPT_MODE, k);
        System.out.println(c.getBlockSize());

        CipherOutputStream cos = new CipherOutputStream(System.out, c);
        cos.write('A');
        cos.flush();

To avoid this, asymmetric encryption schemes like RSA use public/private
key pairs, where you can freely distribute the public key, used for
encryption, while keeping the private key, the one used for decryption, to
yourself. Because you never transport your private key, it can never be
intercepted, and hence this scheme can be much more easily protected
against eavesdropper, than symmetric schemes. However, as you know by now,
you cannot create a asymmetric Cipher, that allows per byte encryption as
shown above. Hence such a Cipher used for a Cipher*Stream will only
transmit encrypted bytes, if either enough data has been written or the
stream is closed an the encryption scheme gets finalized. Also such
asymmetric Cipher are much much slower than symmetric Ciphers and are not
suitable to encrypt large amounts of data.

So in order to get both:

a) better secrecy of asymmetric encryption,

b) better speed and bytewise operation of symmetric encryption,

you have to combine them:

A) Create a KeyPair (e.g. for RSA). Keep the private key at the receiving
end, and transport the public key to the sender. (Well, if nothing else
works, put it in the newspaper, so the sender can read it there!)

B) Open a unencrypted Socket between Sender and Receiver.

C0) Create a Random symmetric Key (e.g. for DES) at the sending end.

C1) Convert this key to a sequence of bytes.

C2) encrypt this sequence of bytes using the public key and a (RSA)Cipher.
The result is again a sequence of now encrypted bytes.

C3) Transmit this encrypted bytes openly through the socket to the
receiving end.

C4) At the receiving end decrypt those bytes using the private key and  
(RSA) Cipher. You will get the same sequence of unencrypted bytes as in
C1, but now you have this sequence on both ends, that is you have
established a shared secret.

C5) At the receiving end create a symmetric Key but not random as in C0)
instead use the sequence of bytes as initialization data. You will now
have a Key-Object on both ends and both objects wil represent the same
symmetric key.

D) Now use the Key object to create a symmetric Cipher. (Dont forget to
tell it to use CFB8 or OFB8 mode!) And use this Cipher for your
Cipher*Streams.

E) You have now established a secure data transport from the sending
CipherOutputStream to the receiving CipherInputStream, which will actually
transmit data, if you flush it.

If you cannot build it from this explanation, then please refrain from
coding encryption part yourself and pay some expert to do it for you,
because using encryption in a wrong way, is often not better than using no
encryption at all. And if cou cannot do it with this explanation, then you
will probably do it wrong anyway.

cu