Authenticated Sublinear Quantum Private Information Retrieval

2025-04-05

AI Summary

This work addresses the challenge of simultaneously achieving privacy, efficiency, and quantum resistance in secure database querying under quantum adversaries. We propose the first authenticated symmetric quantum private information retrieval (QPIR) protocol with sublinear communication complexity. Methodologically, we establish the first tight lower bound on communication complexity via quantum relative entropy; integrate Uhlmann’s lemma, the quantum Pinsker inequality, and Ring-LWE–based post-quantum cryptography to construct a unified QPIR framework supporting both single- and multi-server settings; and introduce a quantum state authentication mechanism to withstand specious adversaries. Key contributions include: (i) exponential reduction in communication overhead (sublinear vs. classical linear); (ii) post-quantum secure authentication in the single-server setting; (iii) significantly reduced hardware requirements for multi-server deployment; and (iv) rigorous information-theoretic guarantees for both privacy and correctness.

Technology Category

• Machine Learning: Quantum Machine Learning
• Data Mining & Knowledge Management: Intelligent Query Processing
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in balancing privacy and efficiency. Also explores symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sub-linear communication complexity while ensuring robustness against specious adversaries: A post-quantum cryptography based protocol that can be authenticated for the specious server; A ring-LWE-based protocol for post-quantum security in a single-server setting, ensuring robustness against quantum attacks; A multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sub-linear efficiency. These protocols address critical gaps in secure database queries, offering exponential communication improvements over classical linear-complexity methods. The work also analyzes security trade-offs under quantum specious adversaries, providing theoretical guarantees for privacy and correctness.

Problem

• Establishes tighter quantum bounds for secure communication
• Develops authenticated sublinear QPIR protocols
• Addresses security gaps in quantum database queries

Innovation

• Quantum relative entropy bounds communication complexity
• Ring-LWE-based protocol ensures post-quantum security
• Multi-server protocol reduces implementation overhead