Single-Database private information retrieval from fully homomorphic encryption

Private Information Retrieval (PIR) allows a user to retrieve the ith 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(γ logn) bits, where -y 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(γ logm + γn/m) bits, where m is the number of blocks. The total computation complexity of our PBR is O(m logm) 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.