Private Information Retrieval from Transversal Designs

TL;DR

This paper introduces a new PIR protocol using incidence matrices of transversal designs that achieves low storage, efficient communication, and optimal server computation, with extensions for collusion resistance.

Contribution

It presents a novel database encoding based on transversal designs that balances privacy, storage, communication, and computational efficiency in PIR protocols.

Findings

Achieves low storage overhead and communication complexity.

Provides an efficient server-side decoding algorithm.

Extends to collusion-resistant PIR protocols.

Abstract

Private information retrieval (PIR) protocols allow a user to retrieve entries of a database without revealing the index of the desired item. Information-theoretical privacy can be achieved by the use of several servers and specific retrieval algorithms. Most of known PIR protocols focus on decreasing the number of bits exchanged between the client and the server(s) during the retrieval process. On another side, Fazeli et. al. introduced so-called PIR codes in order to reduce the storage overhead on the servers. However, only a few works address the issue of the computation complexity of the servers. In this paper, we show that a specific encoding of the database provides PIR protocols with reasonable communication complexity, low storage overhead and optimal computational complexity for the servers. This encoding is based on incidence matrices of transversal designs, from which a natural and efficient recovering algorithm is derived. We also present instances of our construction, making use of finite geometries and orthogonal arrays, and we finally give a generalisation of our main construction for resisting collusions of servers.