Simulation-based receiver selective opening CCA secure PKE from standard computational assumptions

Abstract

In the situation where there are one sender and multiple receivers and the sender transmits ciphertexts of correlated plaintexts, a receiver selective opening (RSO) attack for a public key encryption (PKE) scheme considers adversaries that can corrupt some of the receivers and get their secret keys and plaintexts. Security against RSO attacks for a PKE scheme ensures confidentiality of ciphertexts of uncorrupted receivers. Simulation-based RSO security against chosen ciphertext attacks (SIM-RSO-CCA) is the strongest security notion in all RSO attack scenarios. Jia, Lu, and Li (2016) [19] proposed the first SIM-RSO-CCA secure PKE scheme. However, their scheme used indistinguishability obfuscation, which is not known to be constructed from any standard computational assumption. In this paper, we give two contributions for constructing SIM-RSO-CCA secure PKE from standard computational assumptions. Firstly, we propose a generic construction of SIM-RSO-CCA secure PKE using an IND-CPA secure PKE scheme and a non-interactive zero-knowledge proof system satisfying one-time simulation soundness. Secondly, we propose an efficient and concrete construction of SIM-RSO-CCA secure PKE based on the decisional Diffie-Hellman (DDH) assumption. Moreover, we give a method for efficiently expanding the plaintext space of the DDH-based construction. By applying this method to the construction, we obtain the first DDH-based SIM-RSO-CCA secure PKE scheme supporting a super-polynomially large plaintext space with compact ciphertexts.