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

2026-05-11

AI Summary

Traditional private information retrieval (PIR) schemes require hiding all messages from every server, which fails to accommodate flexible privacy requirements. This work proposes a PIR framework tailored for graph-based storage systems that supports arbitrary privacy constraints. By defining, for each server, a privacy set dynamically adjusted according to its neighborhood, the framework enables a smooth transition from local PIR to standard replicated-graph PIR. Leveraging a graph-replication storage model and information-theoretic capacity analysis, the study derives either exact capacities or tight upper bounds under various privacy configurations for path and ring graph topologies. The proposed approach effectively balances privacy flexibility with retrieval efficiency, offering a principled trade-off between customizable privacy guarantees and achievable download rates.

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.

Problem

• Private Information Retrieval
• Graph-based Storage
• Flexible Privacy Requirements
• Privacy Sets
• Neighborhood Range

Innovation

• Private Information Retrieval
• Graph-based Storage
• Flexible Privacy Requirements
• Neighborhood Privacy
• Capacity Bounds