Weak Private Information Retrieval for Graph-based Storage

2026-07-23

AI Summary

This work addresses the problem of graph-structured weakly private information retrieval (G-WPIR), aiming to achieve a tunable trade-off between communication efficiency and privacy by relaxing the stringent requirement of perfect privacy. The study formally defines the G-WPIR model for the first time, presents a universal protocol applicable to arbitrary graphs, and develops optimized schemes tailored to complete graphs and complete bipartite graphs. By leveraging minimal subpacketization and probabilistic query mechanisms, and employing mutual information and max-leakage as privacy metrics, the paper rigorously characterizes the rate–privacy trade-off boundary. The proposed approach significantly reduces subpacketization overhead while achieving superior communication rates compared to conventional perfectly private schemes, and quantitatively demonstrates a smooth balance between privacy leakage and retrieval efficiency across diverse graph structures.

Abstract

A distributed storage system with graph-based replication consists of a collection of databases and the files they contain. The databases (or servers) are represented as the vertices of a graph, while each file is stored in a distinct pair of servers and is represented by an edge of this graph. Private information retrieval (G-PIR) on such a graph-based storage system involves a client which seeks to retrieve a desired file via a query-response protocol, without leaking the identity of the desired file index to any database. The goal of G-PIR is to maximize the rate (reciprocal of the total normalized download) under the privacy constraint. Prior work on G-PIR has involved perfect information-theoretic privacy (i.e., null leakage). However, if the privacy constraint is relaxed, then PIR protocols could be designed that have even higher rates. We term such protocols as Graph-based Weak Private Information Retrieval (G-WPIR) protocols and initiate their formal study in this work. We propose a G-WPIR scheme for arbitrary graphs, and identify the trade-offs it achieves between rate and privacy, under two well known leakage metrics: mutual information leakage and maximal leakage. Our protocol employs minimal subpacketization (representing a file-size constraint) and employs a simple probabilistic query realization to obtain the smooth trade-off. We extend this protocol with some modifications to two special classes of graphs, the complete graphs and the complete bipartite graphs, and identify the corresponding rate-privacy trade-offs achieved.

Problem

• Private Information Retrieval
• Graph-based Storage
• Weak Privacy
• Rate-Privacy Trade-off
• Information Leakage

Innovation

• Graph-based PIR
• Weak Privacy
• Rate-Privacy Trade-off
• Subpacketization
• Probabilistic Query