Generalized ElGamal Public Key Cryptosystem Based on a New Diffie-Hellman Problem

This paper proposes a new generalized ElGamal public key encryption scheme based on a new Diffie-Hellman problem, so-called EDDH problem, which DDH problem can be reduced to. This scheme is one-way if and only if ECDH assumption holds and it is semantically secure in the standard model if and only if EDDH assumption holds. Since EDDH assumption still holds for generic bilinear groups, this encryption scheme adds to the growing toolkit of provable security primitives that can be used by the protocol designer looking to build complex secure systems with a sound basis.