A Disguise-and-Squeeze PIR Scheme for the MDS-TPIR Setting and Beyond

2026-03-11

AI Summary

This work addresses the problem of collusion-resistant private information retrieval from MDS-coded databases (MDS-TPIR) by proposing a novel scheme based on a “masking-compression” framework, applicable to arbitrary $(N,K)$-MDS systems and extensible to multi-file retrieval and cyclically adjacent collusion patterns. Leveraging generalized Reed–Solomon codes and linear coding theory, the scheme achieves an efficient construction over finite fields: it attains the linear MDS-TPIR capacity when $K=2$ while significantly reducing the required field size, and for parameters $(2,N,2,K)$, it achieves a rate of $(N^2 - N)/(N^2 + KN - 2K)$, surpassing existing results. Furthermore, this work refutes the conjectured MDS-TPIR capacity proposed by Freij-Hollanti et al. and extends the scheme to the $\varepsilon$-error setting for $T \geq 3$.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Multiagent Systems: Mechanism Design
• Machine Learning: Multi-instance/Multi-view Learning

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

We consider the problem of private information retrieval (PIR) from MDS coded databases with colluding servers, i.e., MDS-TPIR. In the MDS-TPIR setting, $M$ files are stored across $N$ servers, where each file is stored independently using an $(N,K)$-MDS code. A user wants to retrieve one file without disclosing the index of the desired file to any set of up to $T$ colluding servers. The general problem in studying PIR schemes is to maximize the PIR rate, defined as the ratio of the size of the desired file to the size of the total download. Freij-Hollanti et al. proposed a conjecture of the MDS-TPIR capacity (the maximum achievable PIR rate), which was later disproved by Sun and Jafar by a counterexample with $(M,N,T,K)=(2,4,2,2)$. In this paper, we propose a new MDS-TPIR scheme based on a disguise-and-squeeze approach. The features of our scheme include the following. Our scheme generalizes the Sun-Jafar counterexample to $(M,N,T,K)=(2,N,2,K)$ with $N\geq K+2$ for an arbitrary $(N,K)$-MDS coded system, providing more counterexamples to the conjecture by Freij-Hollanti et al. For $(M,N,T,K)=(2,N,2,K)$ and a GRS (generalized Reed-Solomon codes) coded system, our scheme has rate $\frac{N^2-N}{N^2+KN-2K}$, beating the state-of-the-art results. We further show that this rate achieves the linear MDS-TPIR capacity when $K=2$. Our scheme features a significantly smaller field size for implementation and the adaptiveness to generalized PIR models such as multi-file MDS-TPIR and MDS-PIR against cyclically adjacent colluding servers. Lastly, we provide an $ε$-error MDS-TPIR scheme for $T\geq 3$ based on the disguise-and-squeeze framework.

Problem

• Private Information Retrieval
• MDS-TPIR
• Colluding Servers
• PIR Capacity
• MDS Coded Databases

Innovation

• Disguise-and-Squeeze
• MDS-TPIR
• PIR Rate
• GRS Codes
• Colluding Servers