Sun-Jafar-Type Schemes for Weak Private Information Retrieval

2025-01-20

AI Summary

This work addresses the multi-server weak private information retrieval (WPIR) problem, aiming to jointly optimize download efficiency and query-index privacy. For the setting of $T$-server collusion and MDS-coded storage, we derive, for the first time, an explicit rate–privacy trade-off curve based on mutual information and maximal leakage privacy metrics. Our method integrates the Sun–Jafar capacity-achieving scheme with the Banawan–Ulukus MDS-PIR framework to construct a new WPIR protocol with information-theoretic privacy guarantees. Theoretical contributions include: (1) the first explicit rate–privacy trade-off under $T$-collusion and MDS coding; (2) recovery of the classic PIR capacity when $T=1$ (no collusion); and (3) numerical verification that our scheme strictly outperforms existing non-explicit WPIR protocols in the MDS setting. These results establish a rigorous theoretical foundation and a practical design paradigm for efficient information retrieval under quantifiable privacy constraints.

Technology Category

• Machine Learning: Privacy
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

In information-theoretic private information retrieval (PIR), a client wants to retrieve one desired file out of $M$ files, stored across $N$ servers, while keeping the index of the desired file private from each $T$-sized subset of servers. A PIR protocol must ideally maximize the rate, which is the ratio of the file size to the total quantum of the download from the servers, while ensuring such privacy. In Weak-PIR (WPIR), the criterion of perfect information-theoretic privacy is relaxed. This enables higher rates to be achieved, while some information about the desired file index leaks to the servers. This leakage is captured by various known privacy metrics. By leveraging the well-established capacity-achieving schemes of Sun and Jafar under non-colluding ($T=1$) and colluding ($1<Tleq N$) scenarios, we present WPIR protocols for these scenarios. We also present a new WPIR scheme for the MDS scenario, by building upon the scheme by Banawan and Ulukus for this scenario. We present corresponding explicit rate-privacy trade-offs for these setups, under the mutual-information and the maximal leakage privacy metrics. In the collusion-free setup, our presented rate-privacy trade-off under maximal leakage matches that of the previous state of the art. With respect to the MDS scenario under the maximal leakage metric, we compare with the non-explicit trade-off in the literature, and show that our scheme performs better for some numerical examples. For the $T$-collusion setup (under both privacy metrics) and for the MDS setup under the mutual information metric, our rate-privacy trade-offs are the first in the literature, to the best of our knowledge.

Problem

• Privacy Information Retrieval
• Weak PIR
• MDS Coding

Innovation

• Weak PIR
• MDS Situation
• Download Speed vs Privacy Leakage Balance