Secure Length-Saving ElGamal Encryption under the Computational Diffie-Hellman Assumption

Abstract

A design of secure and efficient public key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as the ElGamal-type encryption is concerned, some variants of the original ElGamal encryption scheme whose security depends on weaker computational assumption have been proposed: Although the security of the original ElGamal encryption is based on the decisional Diffie-Hellman assumption (DDH-A), the security of a recent scheme, such as Pointcheval’s ElGamal encryption variant, is based on the weaker assumption, the computational Diffie-Hellman assumption (CDH-A). In this paper, we propose a length-saving ElGamal encryption variant whose security is based on CDH-A and analyze its security in the random oracle model. The proposed scheme is length-efficient which provides a shorter ciphertext than that of Pointcheval’s scheme and provably secure against the chosen-ciphertext attack.