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A Unified Framework for Constructing Information-Theoretic Private Information Retrieval

  • Liangfeng Zhang

Received: 12 Aug 2025 | Revised: 07 Nov 2025 | Accepted: 07 Nov 2025 | Published: 18 Nov 2025

Abstract

Retrieving up-to-date information from a publicly accessible database poses significant threats to the user’s privacy. Private information retrieval (PIR) protocols allow a user to retrieve any entry from a database, without revealing the identity of the entry being retrieved to the server(s). Such protocols have found numerous applications in both theoretical studies and real-life scenarios. The existing PIR constructions mainly give multi-server information-theoretic PIR (IT-PIR) protocols or single-server computational PIR (CPIR) protocols. Compared with CPIR, IT-PIR protocols are computationally more efficient and secure in the presence of unbounded servers. The most classical and challenging problem in the realm of IT-PIR is constructing protocols with lower communication complexity. In this review, we introduce a new discrete structure called families of orthogonal arrays with span capability (FOASC) and propose a unified framework for constructing IT-PIR protocols. We show how the most influential IT-PIR protocols in the literature can be captured by the framework. We also put forward several interesting open problems concerning FOASC, whose solutions may result in innovative IT-PIR protocols.

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Zhang, L. A Unified Framework for Constructing Information-Theoretic Private Information Retrieval. Pragmatic Cybersecurity 2025, 1 (1), 3.
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