Single-database private information retrieval from fully homomorphic encryption

Private Information Retrieval (PIR) allows a user to retrieve the (i)th bit of an (n)-bit database without revealing to the database server the value of (i). In this paper, we present a PIR protocol with the communication complexity of (O(? n)) bits, where (?) is the ciphertext size. Furthermore, we extend the PIR protocol to a private block retrieval (PBR) protocol, a natural and more practical extension of PIR in which the user retrieves a block of bits, instead of retrieving single bit. Our protocols are built on the state-of-the-art fully homomorphic encryption (FHE) techniques and provide privacy for the user if the underlying FHE scheme is semantically secure. The total communication complexity of our PBR is (O(? m+? n/m)) bits, where (m) is the number of blocks. The total computation complexity of our PBR is (O(m\log m)) modular multiplications plus (O(n/2)) modular additions. In terms of total protocol execution time, our PBR protocol is more efficient than existing PBR protocols which usually require to compute (O(n/2)) modular multiplications when the size of a block in the database is large and a high-speed network is available.