Private Information Retrieval Schemes Using Cyclic Codes

TL;DR

This paper explores the use of cyclic codes in private information retrieval schemes, demonstrating they can offer more flexible parameters and potentially outperform Reed-Muller codes in certain scenarios.

Contribution

It introduces cyclic codes into PIR schemes, expanding the range of achievable parameters and showing they can outperform Reed-Muller codes in some cases.

Findings

Cyclic codes provide a larger set of PIR parameters.

Binary PIR schemes with cyclic codes can outperform Reed-Muller codes.

The approach enhances the flexibility of PIR scheme design.

Abstract

A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with colluding servers is considered in this work, namely the approach in [$t$-private information retrieval schemes using transitive codes, IEEE Trans. Inform. Theory, vol. 65, no. 4, pp. 2107-2118, 2019] which considers a storage and retrieval code with a transitive group and provides binary PIR schemes with the highest possible rate. Reed-Muller codes were considered in [$t$-private information retrieval schemes using transitive codes, IEEE Trans. Inform. Theory, vol. 65, no. 4, pp. 2107-2118, 2019]. In this work, we consider cyclic codes and we show that binary PIR schemes using cyclic codes provide a larger constellation of PIR parameters and they may outperform the ones coming from Reed-Muller codes in some cases.