Verifiable single-server private information retrieval from LWE with binary errors

Abstract Private Information Retrieval (PIR) allows a client to privately retrieve some data from a public database. There exist two types of PIR: (computational) Single-server PIR (SPIR) and (information-theoretic) multi-server PIR. In this paper, we focus on exploring SPIR. We first propose a simple and efficient additively-homomorphic encryption scheme of which privacy is based on the learning with binary errors assumption that is known as an interesting candidate for practical lattice-based cryptography. Then, according to our proposed homomorphic encryption scheme, we give a Verifiable (single/multi-bit) SPIR (VSPIR) scheme for the single-query case under the malicious server model. To the best of our knowledge, our proposal is the first practical non-interactive VSPIR scheme employing an efficient probabilistic proof that can discover the forged result with overwhelming probability. The corresponding communication complexity and computational complexity are comparable with those of some typical SPIR schemes. Moreover, we extend our single-query VSPIR scheme to construct a non-interactive multi-query solution. In particular, the corresponding communication complexity and computational complexity are the same as those of the single-query scheme. Finally, we provide detailed implementation results to confirm efficiency of our proposals.

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