Converse Bounds for Sun-Jafar-type Weak Private Information Retrieval

2026-01-15

AI Summary

This work investigates the optimality of Sun–Jafar-type schemes in weak private information retrieval (WPIR) under non-colluding replicated storage, MDS-coded storage, and T-collusion settings, focusing on the trade-off between retrieval rate and privacy leakage. Employing information-theoretic tools—specifically mutual information and maximal leakage—the authors derive a converse bound and identify a threshold condition on system parameters. They establish, for the first time, that under this threshold, existing Sun–Jafar-type and Banawan–Ulukus-type WPIR schemes are optimal within their respective classes in terms of the rate–privacy trade-off. When the condition is violated, they construct explicit counterexamples demonstrating the existence of feasible schemes with strictly superior performance, thereby expanding the known theoretical limits of WPIR.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Non-convex Optimization
• Machine Learning: Privacy

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

Building on the well-established capacity-achieving schemes of Sun-Jafar (for replicated storage) and the closely related scheme of Banawan-Ulukus (for MDS-coded setting), a recent work by Chandan et al. proposed new classes of weak private information retrieval (WPIR) schemes for the collusion-free (replication and MDS-coded) setting, as well as for the $T$-colluding scenario. In their work, Chandan et al. characterized the expressions for the rate-privacy trade-offs for these classes of WPIR schemes, under the mutual information leakage and maximal leakage metrics. Explicit achievable trade-offs for the same were also presented, which were shown to be competitive or better than prior WPIR schemes. However, the class-wise optimality of the reported trade-offs were unknown. In this work, we show that the explicit rate-privacy trade-offs reported for the Sun-Jafar-type schemes by Chandan et al. are optimal for the non-colluding and replicated setting. Furthermore, we prove the class-wise optimality for Banawan-Ulukus-type MDS-WPIR and Sun-Jafar-type $T$-colluding WPIR schemes, under threshold-constraints on the system parameters. When these threshold-constraints do not hold, we present counter-examples which show that even higher rates than those reported before can be achieved.

Problem

• Weak Private Information Retrieval
• Rate-Privacy Trade-off
• Sun-Jafar Scheme
• MDS-coded Storage
• Collusion

Innovation

• weak private information retrieval
• rate-privacy trade-off
• class-wise optimality
• Sun-Jafar scheme
• MDS-coded storage