Dynamic and efficient joint encryption scheme in the plain public key model

In this paper, we propose a joint encryption scheme (JES) based on discrete logarithms in the plain public key model, in which a sender can easily encrypt messages under the public keys of a group of recipients, so that only by collaborating together can all the recipients recover messages. Neither the size of the ciphertext nor the encryption computation depends on the number of the recipients. We show that the JES scheme is semantically secure against adaptive chosen ciphertext attacks in the random oracle model under the assumption of Computational Diffie-Hellman problems.