A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers

TL;DR

This paper presents a new private information retrieval scheme that is storage-efficient, robust against Byzantine faults, and has lower locality by leveraging multiplicity codes' geometric properties, reducing redundancy and improving efficiency.

Contribution

It introduces a Byzantine robust PIR scheme using multiplicity codes that reduces database replication and achieves lower locality compared to traditional locally decodable codes.

Findings

Reduces global redundancy by avoiding full database replication.

Achieves lower locality in PIR than in LDC contexts.

Utilizes geometric properties of multiplicity codes for improved PIR performance.

Abstract

Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000, it is well-known that information the-oretically secure private information retrieval schemes can be built using locally decodable codes. In this paper, we construct a Byzantine ro-bust PIR scheme using the multiplicity codes introduced by Kopparty et al. Our main contributions are on the one hand to avoid full replica-tion of the database on each server; this significantly reduces the global redundancy. On the other hand, to have a much lower locality in the PIR context than in the LDC context. This shows that there exists two different notions: LDC-locality and PIR-locality. This is made possible by exploiting geometric properties of multiplicity codes.