Paper 2008/330

Chosen ciphertext secure public key encryption under DDH assumption with short ciphertext

Xianhui Lu, Xuejia Lai, and Dake He

Abstract

An efficient variant of the ElGamal public key encryption scheme is proposed which is provably secure against adaptive chosen ciphertext attacks(IND-CCA2) under the decisional Diffie-Hellman(DDH) assumption. Compared to the previously most efficient scheme under DDH assumption by Kurosawa and Desmedt [Crypto 2004] it has one group element shorter ciphertexts, 50\% shorter secret keys, 25\% shorter public keys and it is 28.6\% more efficient in terms of encryption speed, 33.3\% more efficient in terms of decryption speed. A new security proof logic is used, which shows directly that the decryption oracle will not help the adversary in the IND-CCA2 game. Compared to the previous security proof, the decryption simulation is not needed in the new logic. This makes the security proof simple and easy to understand.