Multi-Server Weakly-Private Information Retrieval

TL;DR

This paper explores how relaxing perfect privacy in multi-server PIR protocols can improve efficiency metrics like download rate, introducing new schemes and bounds for weakly-private information retrieval with quantifiable privacy leakage.

Contribution

It introduces two novel WPIR schemes based on recent PIR protocols, optimizes their download rate, and establishes tight bounds for the maximum achievable rate under certain privacy metrics.

Findings

Scheme A achieves improved download rate over previous schemes.

The converse bound is tight for two servers and two files under MaxL.

Proposed schemes outperform existing methods under $\,epsilon$-privacy metric.

Abstract

Private information retrieval (PIR) protocols ensure that a user can download a file from a database without revealing any information on the identity of the requested file to the servers storing the database. While existing protocols strictly impose that no information is leaked on the file's identity, this work initiates the study of the tradeoffs that can be achieved by relaxing the perfect privacy requirement. We refer to such protocols as weakly-private information retrieval (WPIR) protocols. In particular, for the case of multiple noncolluding replicated servers, we study how the download rate, the upload cost, and the access complexity can be improved when relaxing the full privacy constraint. To quantify the information leakage on the requested file's identity we consider mutual information (MI), worst-case information leakage, and maximal leakage (MaxL). We present two WPIR schemes, denoted by Scheme A and Scheme B, based on two recent PIR protocols and show that the download rate of the former can be optimized by solving a convex optimization problem. We also show that Scheme A achieves an improved download rate compared to the recently proposed scheme by Samy et al. under the so-called $\epsilon$-privacy metric. Additionally, a family of schemes based on partitioning is presented. Moreover, we provide an information-theoretic converse bound for the maximum possible download rate for the MI and MaxL privacy metrics under a practical restriction on the alphabet size of queries and answers. For two servers and two files, the bound is tight under the MaxL metric, which settles the WPIR capacity in this particular case. Finally, we compare the performance of the proposed schemes and their gap to the converse bound.