Cryptanalysis of a Lattice-Based PIR Scheme for Arbitrary Database Sizes

TL;DR

This paper introduces a new, efficient lattice-based attack on a PIR scheme, compromising its security for databases of any size within minutes using standard hardware.

Contribution

It extends previous lattice-based attacks to arbitrary database sizes using a novel binary-search-like preprocessing technique.

Findings

The attack can break the scheme in minutes on a laptop.

The method significantly reduces the number of lattice problems needed.

Analytical proofs and experiments validate the attack's effectiveness.

Abstract

Private Information Retrieval (PIR) schemes enable users to securely retrieve files from a server without disclosing the content of their queries, thereby preserving their privacy. In 2008, Melchor and Gaborit proposed a PIR scheme that achieves a balance between communication overhead and server-side computational cost. However, for particularly small databases, Liu and Bi identified a vulnerability in the scheme using lattice-based methods. Nevertheless, the rapid increase in computational cost associated with the attack limited its practical applicability, leaving the scheme's overall security largely intact. In this paper, we present a novel two-stage attack that extends the work of Liu and Bi to databases of arbitrary sizes. To this end, we employ a binary-search-like preprocessing technique, which enables a significant reduction in the number of lattice problems that need to be considered. Specifically, we demonstrate how to compromise the scheme in a matter of minutes using an ordinary laptop. Our findings are substantiated through both rigorous analytical proofs and comprehensive numerical experiments.