On the Security of a Variant of ElGamal Encryption Scheme

Abstract

Recently, based on the Paillier cryptosystem [1] , Yi et al. outline a distributed ElGamal cryptosystem which allows for both a much simpler distributed key generation procedure and a more efficient distributed decryption of messages from a large plaintext domain [2] . In this paper, we analyze the security of their proposed variant of ElGamal encryption scheme and demonstrate that their proposed variant is not secure as claimed. Thus, whether an additively homomorphic cryptosytem satisfying the desired properties exists remains an open question.