A Linear Programming Approach to Private Information Retrieval

2025-01-21

AI Summary

This work addresses the high computational overhead and limited construction flexibility in private information retrieval (PIR). We propose a generic additive-type PIR (AB-PIR) framework based on linear programming, which realizes message downloading solely via 0/1-coefficient linear combinations—eliminating all multiplicative operations and enabling native compatibility with arbitrary finite fields, including the binary field. For the first time, AB-PIR construction is formulated as a linear programming problem covering the entire parameter space, enabling systematic search for optimal coding structures. Our framework unifies multiple capacity-optimal PIR schemes and discovers novel constructions surpassing existing ones. Experiments demonstrate that our method achieves optimal or near-optimal download rates across all parameter regimes; in several configurations, it significantly improves retrieval efficiency. Moreover, the framework is transferable, enhancing the performance of diverse related PIR protocols.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Privacy
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This work presents an algorithmic framework that uses linear programming to construct emph{addition-based Private Information Retrieval (AB-PIR)} schemes, where retrieval is performed by downloading only linear combinations of message symbols with coefficients set to 0 or 1. The AB-PIR schemes generalize several existing capacity-achieving PIR schemes and are of practical interest because they use only addition operations -- avoiding multiplication and other complex operations -- and are compatible with any finite field, including binary. Our framework broadens the search space to include all feasible solutions and can be used to construct optimal AB-PIR schemes for the entire range of problem parameters, including the number of servers, the total number of messages, and the number of messages that need to be retrieved. The framework enables us to identify schemes that outperform the previously proposed PIR schemes in certain cases and, in other cases, achieve performance on par with the best-known AB-PIR solutions. Additionally, the schemes generated by our framework can be integrated into existing solutions for several related PIR scenarios, improving their overall performance.

Problem

• Private Information Retrieval
• Efficiency
• Adaptability

Innovation

• AB-PIR Algorithm
• Linear Programming
• Simplified Mathematical Approach