Paper 2020/1068

An Efficient Transformation Capabilities of Single Database Private Block Retrieval

Radhakrishna Bhat and N R Sunitha

Abstract

Private Information Retrieval (PIR) is one of the promising techniques to preserve user privacy in the presence of trusted-but- curious servers. The information-theoretically private query construction assures the highest user privacy over curious and unbounded computation servers. Therefore, the need for information-theoretic private retrieval was fulfilled by various schemes in a variety of PIR settings. To augment previous work, we propose a combination of new bit connection methods called rail-shape and signal-shape and new quadratic residuosity assumption based family of trapdoor functions for generic single database Private Block Retrieval (PBR). The main goal of this work is to show that the possibility of mapping from computationally bounded privacy to information-theoretic privacy or vice-versa in a single database setting using newly constructed bit connection and trapdoor function combinations. The proposed bit connection and trapdoor function combinations have achieved the following results. • Single Database information-theoretic PBR (SitPBR): The proposed combinations are used to construct SitPBR in which the user privacy is preserved through the generation of information-theoretic queries and data privacy is preserved using quadratic residuosity assumption. • Single Database computationally bounded PBR (ScPBR): The proposed combinations are used to construct ScPBR in which both user privacy and data privacy are preserved using a well-known intractability assumption called quadratic residuosity assumption. • Map(SitPBR)→ScPBR: The proposed combinations can be used to transform (or map) SitPBR into ScPBR scheme by choosing appropriate function parameters. • Map(ScPBR)→SitPBR: The proposed combinations can be used to transform (or map) ScPBR into SitPBR scheme by choosing appropriate function parameters. All the proposed schemes are single round, memoryless and plain database schemes (at their basic constructions).

Note: The main goal of this work is to show that the possibility of mapping from computationally bounded privacy to information-theoretic privacy or vice-versa in a single database setting using newly constructed bit connection and trapdoor function combinations.