2-Server PIR with sub-polynomial communication

TL;DR

This paper presents a new 2-server PIR scheme with sub-polynomial communication cost, improving over previous protocols by reducing the number of servers needed through algebraic techniques and polynomial interpolation.

Contribution

It introduces a 1-round 2-server PIR protocol with sub-polynomial communication, achieved by adapting matching vector code protocols with algebraic extensions.

Findings

Achieves $n^{O(\sqrt{rac{\log\log n}{\log n}})}$ communication complexity.

Reduces server count from 3 or 4 to 2 in PIR protocols.

Matches the communication efficiency of 3-server schemes.

Abstract

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. In this work we construct a 1-round 2-server PIR with total communication cost $n^{O({\sqrt{\log\log n/\log n}})}$. This improves over the currently known 2-server protocols which require $O(n^{1/3})$ communication and matches the communication cost of known 3-server PIR schemes. Our improvement comes from reducing the number of servers in existing protocols, based on Matching Vector Codes, from 3 or 4 servers to 2. This is achieved by viewing these protocols in an algebraic way (using polynomial interpolation) and extending them using partial derivatives.