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

TL;DR

This paper introduces a $k$-server Byzantine-Resistant PIR scheme that achieves optimal download rate and minimal file size, ensuring private and reliable retrieval even with colluding or malicious servers.

Contribution

It presents a novel PIR scheme that attains the asymptotic capacity with minimal file size, addressing a key open problem in the field.

Findings

Achieves the information-theoretic capacity for Byzantine-resistant PIR.

Proves the minimal file size needed for the fixed number of retrieved symbols.

Provides a scheme resilient to collusion and malicious server responses.

Abstract

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 for the fixed number of retrieved symbols, solving the problem pointed out by Banawan and Ulukus.