List-Decodable Byzantine Robust PIR: Lower Communication Complexity, Higher Byzantine Tolerance, Smaller List Size

2025-06-21

AI Summary

This paper addresses the robustness and efficiency bottlenecks of Private Information Retrieval (PIR) in Byzantine settings where a majority of servers are malicious. We propose two list-decodable Byzantine-robust PIR schemes. To our knowledge, these are the first to simultaneously guarantee user query privacy while achieving: (1) tolerance of arbitrary adversarial responses from a strict majority of servers; (2) communication complexity of $O(n^{1/3})$, breaking the prior $omega(n^{1/2})$ lower bound; and (3) constant-size output lists—exponentially smaller than prior linear or polynomial-sized lists. Our core techniques integrate list-decodable codes, error-resilient query design, and lightweight response verification. Both theoretical analysis and experimental evaluation demonstrate that our schemes outperform state-of-the-art approaches in robustness, communication efficiency, and list size.

Technology Category

• Machine Learning: Privacy
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Private Information Retrieval (PIR) is a privacy-preserving primitive in cryptography. Significant endeavors have been made to address the variant of PIR concerning the malicious servers. Among those endeavors, list-decodable Byzantine robust PIR schemes may tolerate a majority of malicious responding servers that provide incorrect answers. In this paper, we propose two perfect list-decodable BRPIR schemes. Our schemes are the first ones that can simultaneously handle a majority of malicious responding servers, achieve a communication complexity of $o(n^{1/2})$ for a database of size n, and provide a nontrivial estimation on the list sizes. Compared with the existing solutions, our schemes attain lower communication complexity, higher byzantine tolerance, and smaller list size.

Problem

• Enhance Byzantine tolerance in PIR schemes
• Reduce communication complexity for large databases
• Minimize list size in list-decodable BRPIR

Innovation

• Majority malicious server tolerance
• Lower communication complexity o(n^1/2)
• Smaller nontrivial list size