Improved Weakly Private Information Retrieval Codes

TL;DR

This paper introduces a novel code construction for weakly private information retrieval that reduces privacy leakage by optimizing retrieval patterns, achieving significant improvements over previous methods with explicit solutions.

Contribution

The paper presents a new W-PIR code construction that improves privacy leakage bounds by enabling a better retrieval pattern, with explicit solutions unlike prior numerical-only approaches.

Findings

Significant reduction in privacy leakage metrics.

Explicit code solutions provided.

Improved retrieval efficiency in W-PIR.

Abstract

We study the problem of weakly private information retrieval (W-PIR), where a user wishes to retrieve a desired message from $N$ non-colluding servers in a way that the privacy leakage regarding the desired message's identity is less than or equal to a threshold. We propose a new code construction which significantly improves upon the best known result in the literature, based on the following critical observation. In previous constructions, for the extreme case of minimum download, the retrieval pattern is to download the message directly from $N-1$ servers; however this causes leakage to all these $N-1$ servers, and a better retrieval pattern for this extreme case is to download the message directly from a single server. The proposed code construction allows a natural transition to such a pattern, and for both the maximal leakage metric and the mutual information leakage metric, significant improvements can be obtained. We provide explicit solutions, in contrast to a previous work by Lin et al., where only numerical solutions were obtained.