I've searched some information on ECC, but so far I have only found Diffie-Hellman key-exchange implementations using ECC, but I don't want to exchange keys, I want to encrypt & decrypt data like in ElGamal. I know that ElGamal with elliptic curves should be possible (Since ElGamal is based on DH), but I have no idea how. So, could anyone tell me how to implement ElGamal using elliptic curves. I think I do not need to much background information,
- What is the private, what is the public key?
- How to encrypt messages? and
- How to decrypt messages?
should be enough.