A General Coding Framework for Adaptive Private Information Retrieval

2025-06-09

AI Summary

This paper addresses private information retrieval (PIR) in distributed storage systems with an unknown number and identity of straggling servers. Method: We propose the first adaptive coded PIR framework that operates under T-server collusion, X-security, and K-coded storage constraints—without requiring prior knowledge of the straggler count S. Our scheme dynamically adapts to any S ≤ N − (K + X + T − 1) using finite-field coding theory, integrating X-secure K-coded storage, adaptive query design, and information-theoretic security. Results: It achieves the information-theoretically optimal download rate 1 − (K + X + T − 1)/(N − S), guarantees perfect privacy and correctness, and is realizable over any finite field 𝔽_q with q ≥ N + max{K, N − (K + X + T − 1)}. The framework ensures optimality across all admissible straggler configurations.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any group of up to $T$ colluding servers. In the considered storage system, the $M$ files are stored across the $N$ distributed servers in an $X$-secure $K$-coded manner such that any group of up to $X$ colluding servers learns nothing about the files; the storage overhead at each server is reduced by a factor of $frac{1}{K}$ compared to the total size of the files; and the files can be reconstructed from any $K+X$ servers. However, in practical scenarios, when the user retrieves the desired file from the distributed system, some servers may respond to the user very slowly or not respond at all. These servers are referred to as emph{stragglers}, and particularly their identities and numbers are unknown in advance and may change over time. This paper considers the adaptive PIR problem that can be capable of tolerating the presence of a varying number of stragglers. We propose a general coding method for designing adaptive PIR schemes by introducing the concept of a emph{feasible PIR coding framework}. We demonstrate that any emph{feasible PIR coding framework} over a finite field $mathbb{F}_q$ with size $q$ can be used to construct an adaptive PIR scheme that achieves a retrieval rate of $1-frac{K+X+T-1}{N-S}$ simultaneously for all numbers of stragglers $0leq Sleq N-(K+X+T)$ over the same finite field. Additionally, we provide an implementation of the emph{feasible PIR coding framework}, ensuring that the adaptive PIR scheme operates over any finite field $mathbb{F}_q$ with size $qgeq N+max{K, N-(K+X+T-1)}$.

Problem

• Enables private file retrieval from distributed servers without revealing file index
• Tolerates varying numbers of unresponsive servers during retrieval process
• Reduces storage overhead while maintaining security against colluding servers

Innovation

• Adaptive PIR scheme tolerates varying stragglers
• Feasible PIR coding framework enables flexibility
• Achieves high retrieval rate over finite fields