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PIR schemes with small download complexity and low storage requirements

22 September 2016
S. Blackburn
T. Etzion
Maura B. Paterson
ArXiv (abs)PDFHTML
Abstract

Shah, Rashmi and Ramchandran recently considered a model for Private Information Retrieval (PIR) where a user wishes to retrieve one of several RRR-bit messages from a set of nnn non-colluding servers. Their security model is information-theoretic. Their paper is the first to consider a model for PIR in which the database is not necessarily replicated, so allowing distributed storage techniques to be used. Shah et al. show that at least R+1R+1R+1 bits must be downloaded from servers, and describe a scheme with linear total storage (in RRR) that downloads between 2R2R2R and 3R3R3R bits. For any positive ϵ\epsilonϵ, we provide a construction with the same storage property, that requires at most (1+ϵ)R(1+\epsilon)R(1+ϵ)R bits to be downloaded; moreover one variant of our scheme only requires each server to store a bounded number of bits (in the sense of being bounded by a function that is independent of RRR). We also provide variants of a scheme of Shah et al which downloads exactly R+1R+1R+1 bits and has quadratic total storage. Finally, we simplify and generalise a lower bound due to Shah et al. on the download complexity a PIR scheme. In a natural model, we show that an nnn-server PIR scheme requires at least nR/(n−1)nR/(n-1)nR/(n−1) download bits in many cases, and provide a scheme that meets this bound.

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