Lifting Private Information Retrieval from Two to any Number of Messages

TL;DR

This paper introduces a lifting method that extends PIR schemes from two messages to any number, improving download rates for coded data with colluding servers and simplifying existing schemes.

Contribution

The paper presents a novel lifting operation that generalizes PIR schemes from two messages to multiple messages, enhancing efficiency and understanding.

Findings

New PIR schemes with better download rates for MDS coded data

Simplified description of optimal PIR schemes on replicated data

Applicable to colluding server scenarios

Abstract

We study private information retrieval (PIR) on coded data with possibly colluding servers. Devising PIR schemes with optimal download rate in the case of collusion and coded data is still open in general. We provide a lifting operation that can transform what we call one-shot PIR schemes for two messages into schemes for any number of messages. We apply this lifting operation on existing PIR schemes and describe two immediate implications. First, we obtain novel PIR schemes with improved download rate in the case of MDS coded data and server collusion. Second, we provide a simplified description of existing optimal PIR schemes on replicated data as lifted secret sharing based PIR.