Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns

TL;DR

This paper explores private information retrieval schemes for coded data with arbitrary collusion patterns among servers, extending previous models to more realistic scenarios with diverse collusion structures.

Contribution

It generalizes PIR rate results from uniform collusion models to arbitrary and partitioned collusion patterns, introducing new strategies for these complex scenarios.

Findings

Extended PIR rate bounds for arbitrary collusion patterns

Analyzed effectiveness of existing PIR strategies in new settings

Proposed new schemes for disjoint colluding groups

Abstract

In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several servers, subsets of which can collude to attempt to deduce the requested file. With the goal of studying the achievable PIR rates in realistic scenarios, we generalize results for coded data from the case of all subsets of servers of size $t$ colluding, to arbitrary subsets of the servers. We investigate the effectiveness of previous strategies in this new scenario, and present new results in the case where the servers are partitioned into disjoint colluding groups.