Private Information Retrieval With Arbitrary Privacy Requirements for Graph-Based Storage

TL;DR

This paper introduces a flexible privacy model for graph-based private information retrieval, allowing arbitrary privacy requirements per server and analyzing capacity bounds for specific graph structures.

Contribution

It generalizes PIR privacy definitions to arbitrary sets, focusing on path and cyclic graphs, and derives capacity bounds for neighborhood-based privacy sets.

Findings

Derived capacity bounds for neighborhood privacy sets.

Analyzed privacy requirements in path and cyclic graph storage.

Transitioned from local PIR to general graph-replicated PIR.

Abstract

We reformulate the definition of privacy in the private information retrieval (PIR) problem to accommodate flexible privacy requirements. We focus on graph-replicated PIR, with a generalized privacy requirement, instead of requiring all messages to be private from all servers, during retrieval. Towards this, we define a privacy requirement set for each server, which can be an arbitrary subset of all message indices, as long as the stored message indices are in their privacy requirement set. Since both the storage and privacy requirement sets have many possibilities, we focus on two specific storage settings, namely the path and cyclic graphs. We consider several privacy settings for each of them, which are not necessarily the same, to give different examples for privacy sets. Of particular interest are the privacy sets that comprise the indices of messages stored at servers within a neighborhood range. The neighborhood range parameter allows a transition from the recently introduced local PIR [1] to the standard graph-replicated PIR. In these cases, we derive bounds on the capacity or find the exact capacity.