Symmetric Private Information Retrieval (SPIR) on Graph-Based Replicated Systems

TL;DR

This paper studies symmetric private information retrieval on graph-modeled replicated databases, establishing capacity bounds and optimal schemes for specific graph classes, advancing understanding of privacy and efficiency in distributed data systems.

Contribution

It introduces a graph-based SPIR model with message-specific common randomness and derives exact capacity results for path and regular graphs.

Findings

Established a lower bound on SPIR capacity for general graphs.

Proved the minimum randomness size equals message size for feasibility.

Derived exact capacity for path and regular graph classes.

Abstract

We introduce the problem of symmetric private information retrieval (SPIR) on replicated databases modeled by a simple graph. In this model, each vertex corresponds to a server, and a message is replicated on two servers if and only if there is an edge between them. We consider the setting where the server-side common randomness necessary to accomplish SPIR is also replicated at the servers according to the graph, and we call this as message-specific common randomness. In this setting, we establish a lower bound on the SPIR capacity, i.e., the maximum download rate, for general graphs, by proposing an achievable SPIR scheme. Next, we prove that, for any SPIR scheme to be feasible, the minimum size of message-specific randomness should be equal to the size of a message. Finally, by providing matching upper bounds, we derive the exact SPIR capacity for the class of path and regular graphs.