Public-Key Encryption Schemes with Bounded CCA Security and Optimal Ciphertext Length Based on the CDH and HDH Assumptions

In Cramer et al. (2007, Bounded CCA2-Secure Encryption. In Kurosawa, K. (ed.), Advances in Cryptology – ASIACRYPT 2007, Kuching, Malaysia, December 2–6, Lecture Notes in Computer Science, Vol. 4833, pp. 502–518. Springer, Berlin, Germany) proposed a public-key encryption scheme secure against adversaries with a bounded number of decryption queries based on the decisional Diffie–Hellman problem. In this paper, we show that the same result can be obtained based on weaker computational assumptions, namely: the computational Diffie–Hellman and the hashed Diffie–Hellman assumptions.