Necessary and Sufficient Conditions for Capacity-Achieving Private Information Retrieval with Adversarial Servers

TL;DR

This paper establishes the exact conditions under which private information retrieval schemes can achieve maximum efficiency in the presence of adversarial servers, addressing a key gap in systematic construction methods.

Contribution

It provides the necessary and sufficient conditions for designing capacity-achieving PIR schemes with adversarial servers, enabling systematic construction.

Findings

Derived the necessary and sufficient conditions for capacity-achieving PIR schemes.

Clarified the query conditions needed for optimal PIR performance.

Facilitated systematic design of PIR schemes meeting theoretical bounds.

Abstract

Private information retrieval (PIR) is a mechanism for efficiently downloading messages while keeping the index of the desired message secret from the servers. PIR schemes have been extended to various scenarios with adversarial servers: PIR schemes where some servers are unresponsive or return noisy responses are called robust PIR and Byzantine PIR, respectively; PIR schemes where some servers collude to reveal the index are called colluding PIR. The information-theoretic upper bound on the download efficiency of these PIR schemes has been proved in previous studies. However, systematic ways to construct PIR schemes that achieve the upper bound are not known. In order to construct a capacity-achieving PIR schemes systematically, it is necessary to clarify the conditions that the queries should satisfy. This paper proves the necessary and sufficient conditions for capacity-achieving PIR schemes.