Local Private Information Retrieval: A New Privacy Perspective for Graph-Based Replicated Systems

TL;DR

This paper introduces local user privacy in graph-based PIR systems, analyzing its capacity and demonstrating significant efficiency gains over traditional PIR in specific graph structures.

Contribution

It formalizes local user privacy, derives capacity bounds for various graph classes, and provides exact capacity results for cyclic and odd-path graphs.

Findings

Local PIR capacity is multiplicative for disjoint union of graphs.

Capacity bounds for edge-transitive and bipartite graphs exceed previous bounds.

Exact capacity determined for cyclic and odd-path graphs.

Abstract

We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, and introduce a novel setting where the user's privacy is governed by the servers' storage structure. In particular, while retrieving a message from a server, the user is concerned with hiding their desired message index from the server, only if the server stores the corresponding message. We coin this privacy requirement as local user privacy and the resulting PIR problem as local PIR on the graph. Our goal is to measure the gain in communication efficiency of local PIR, compared to that of canonical PIR, by establishing its capacity, i.e., the maximum number of message symbols retrieved, per downloaded symbol. To this end, we observe a remarkable gain in the local PIR capacity of graphs, that are disjoint union of distinct graphs, which is multiplicative, compared to the PIR capacity, when the individual graphs are identical. For connected graphs, we propose schemes to establish capacity lower bounds for edge-transitive and bipartite graphs, which are greater than the best-known PIR capacity bounds. Finally, we derive the exact local PIR capacity for the cyclic graph, and the path graph with an odd number of vertices.