Homomorphic encryption supporting logical operations

Homomorphic encryption is a form of encryption that allows computations to be carried out on ciphertext and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. The feature of homomorphic encryption is used in modern communication system architectures and cryptosystems. In view of the previous works, most of homomorphic encryptions support additive or multiplicative homomorphism. There is few homomorphic encryption schemes tailored for logical operations. In this paper, we propose a homomorphic encryption scheme that supports logical operations. Additionally, our proposed scheme can be applied to 2-DNF and k-CNF. Furthermore, the security of the proposed scheme is based on the subgroup decision assumption.