A note on a provable secure encryption scheme

A Cramer-Shoup scheme was modified in a variant way.The major advantage with respect to Kurosawa-Desmedt scheme is that it saves a key parameter and produces shorter ciphertext.The proof of security shows that our scheme can be instantiated with any computational secure key derivation and message authentication functions.Thus it extends the applicability of the Kurosawa-Desmedt scheme and improves its effciency.