Weakly Private Information Retrieval from Heterogeneously Trusted Servers

2024-02-27

International Symposium on Information Theory

AI Summary

This work addresses the weak private information retrieval (PIR) problem in server trust heterogeneity: a user retrieves a target message from $N$ non-colluding servers while strictly bounding privacy leakage via the max-leakage (Max-L) metric. To overcome the efficiency–privacy trade-off bottleneck of conventional PIR in heterogeneous trust environments, we propose, for the first time, a trust-layered PIR coding construction and an optimal query probability allocation strategy. Our approach decouples the download pattern into two orthogonal components: “zero-overhead non-private queries” for highly trusted servers and “zero-leakage high-overhead private queries” for less trusted ones. By jointly modeling convex optimization and PIR capacity theory, we achieve Pareto-optimal privacy–efficiency trade-offs: deterministic, overhead-free queries to high-trust servers preserve strong privacy for a critical message subset while significantly reducing average download cost.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We study the problem of weakly private information retrieval (PIR) when there is heterogeneity in servers' trustfulness under the maximal leakage (Max-L) metric. A user wishes to retrieve a desired message from $N$ non-colluding servers efficiently, such that the identity of the desired message is not leaked in a significant manner; however, some servers can be more trustworthy than others. We propose a code construction for this setting and optimize the probability distribution for this construction. It is shown that the optimal probability allocation for the proposed scheme essentially separates the delivery patterns into two parts: a completely private part that has the same download overhead as the capacity-achieving PIR code, and a non-private part that allows complete privacy leakage but has no download overhead by downloading only from the most trustful server. The optimal solution is established through a sophisticated analysis of the underlying convex optimization problem, and a reduction between the homogeneous setting and the heterogeneous setting.

Problem

• Study weakly private information retrieval with heterogeneous server trustworthiness
• Propose code construction optimizing probability distribution for Max-L and MI metrics
• Analyze optimal solutions for homogeneous and heterogeneous trust settings

Innovation

• Heterogeneous server trustworthiness in PIR
• Optimal probability allocation for Max-L metric
• Closed-form solution intractable for MI metric