A New Public-Key Encryption Scheme

This paper proposes a new public-key encryption scheme which removes oneelement from the public-key tuple of the original Cramer-Shoup scheme.As a result, a ciphertext is not a quadruple but a triple at the cost ofa strong assumption, the third version of knowledge of exponentassumption (KEA3). Under assumptions of KEA3, a decision Diffie-Hellman(DDH) and a variant of target collision resistance (TCRv), the new scheme isproved secure against indistinguishable adaptive chosen ciphertextattack (IND-CCA2). This scheme is as efficient as Damg\aard ElGamal (DEG)scheme when it makes use of a well-known algorithm for productof exponentiations. The DEG scheme is recently proved IND-CCA1 secureby Bellare and Palacio in ASIACRYPT 2004 under another strongassumption. In addition to our IND-CCA2 secured scheme, we also believethat the security proof procedure itself provides a well insight forElGamal-based encryption schemes which are secure in real world.