Information retrieval in the cloud is common and convenient. Nevertheless, privacy concerns should not be ignored as the cloud is not fully trustable. Fully Homomorphic Encryption (FHE) allows arbitrary operations to be performed on encrypted data, where the decryption of the result of ciphertext operation equals that of the corresponding plaintext operation. Thus, FHE schemes can be utilized for private information retrieval (PIR) on encrypted data. In the FHE scheme proposed by Ducas and Micciancio (DM), only a single homomorphic NOT AND (NAND) operation is allowed between consecutive ciphertext refreshings. Aiming at this problem, an improved FHE scheme is proposed for efficient PIR where homomorphic additions and multiplications are based on linear operations on ciphertext vectors. Theoretical analysis shows that when compared with the DM scheme, the proposed scheme allows multiple homomorphic additions and a single homomorphic multiplication to be performed. The number of allowed homomorphic additions is determined by the ratio of the ciphertext modulus to the upper bound of initial ciphertext noise. Moreover, simulation results show that the proposed scheme is significantly faster than the DM scheme in the homomorphic evaluation for a series of algorithms.
(Batch) Fully Homomorphic Encryption over Integers for Non-Binary Message Spaces
