Staircase-PIR: Universally Robust Private Information Retrieval

TL;DR

This paper introduces Staircase-PIR schemes that provide universally robust private information retrieval, maintaining capacity despite unknown or varying numbers of slow or unresponsive servers, by linking PIR robustness to secret sharing efficiency.

Contribution

The paper proposes Staircase-PIR schemes that are universally robust, achieving PIR capacity under any number of stragglers, and establishes a novel equivalence with communication efficient secret sharing.

Findings

Staircase-PIR schemes are proven to be universally robust.

Achieves PIR capacity asymptotically in the number of files.

Establishes an equivalence between robust PIR and secret sharing efficiency.

Abstract

We consider the problem of designing private information retrieval (PIR) schemes on data of $m$ files replicated on $n$ servers that can possibly collude. We focus on devising robust PIR schemes that can tolerate stragglers, i.e., slow or unresponsive servers. In many settings, the number of stragglers is not known a priori or may change with time. We define universally robust PIR as schemes that achieve PIR capacity asymptotically in $m$ and simultaneously for any number of stragglers up to a given threshold. We introduce Staircase-PIR schemes and prove that they are universally robust. Towards that end, we establish an equivalence between robust PIR and communication efficient secret sharing.