On the Security of a Variation of Cramer-Shoup's Public Key Scheme

At Crypto’98, Cramer and Shoup [1] proposed a public key cryptosystem that is provably secure against the adaptive chosen ciphertext attacks. Recently, Zhu, Chan, and Deng [2] proposed a variation of Cramer and Shoup’s scheme (the Zhu-Chan-Deng scheme in short) which attempts to reduce Cramer and Shoup’s public key cryptosystem in terms of both the size of the ciphertext and the computation required for decryption. However, in this paper, we show that the Zhu-Chan-Deng scheme is insecure against the adaptive chosen ciphertext attacks. Moreover, we also show that the Zhu-Chan-Deng scheme doesn’t exhibit the non-malleability property, even under the weakest attack model  the chosen plaintext attack.