Toward single-server private information retrieval protocol via learning with errors

At FOCS2011 Brakerski and Vaikuntanathan proposed a single-server LWE-based private information retrieval (abbreviated as PIR) protocol with a security reduction to hard standard lattice problems and nearly optimal communication complexity. However, Brakerski just described a generic PIR protocol that utilized a somewhat homomorphic encryption and an arbitrary symmetric encryption as building blocks, he did not instantiate the generic construction. In this work, we first modify Brakerski's construction without the evaluating key and construct a new PIR model. Moreover, we instantiate our new model via matrix FHE first proposed by Ryo et al. at PKC2015 and vector symmetric encryption scheme proposed in this work as building block. Then we optimize the Response operations and several other aspects of the scheme.