k-server Byzantine-Resistant PIR Scheme with Optimal Download Rate and Optimal File Size

02/04/2023

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by   Stanislav Kruglik, et al.

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We consider the problem of designing a Private Information Retrieval (PIR) scheme on m files replicated on k servers that can collude or, even worse, can return incorrect answers. Our goal is to correctly retrieve a specific message while keeping its identity private from the database servers. We consider the asymptotic information-theoretic capacity of this problem defined as the maximum ratio of the number of correctly retrieved symbols to the downloaded one for a large enough number of stored files. We propose an achievable scheme with a small file size and prove that such a file size is minimal, solving the problem pointed out by Banawan and Ulukus.