A Unified Framework for Constructing Information-Theoretic Private Information Retrieval

• URL: http://arxiv.org/abs/2512.00480v1
• Date: Sat, 29 Nov 2025 13:24:09 GMT
• Title: A Unified Framework for Constructing Information-Theoretic Private Information Retrieval
• Authors: Liang Feng Zhang,
• Abstract summary: em 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)<n>We introduce a new discrete structure called em families of unbounded arrays with span capability (FOASC) and propose a unified framework for constructing IT-PIR protocols.
• Score: 5.025654873456755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Retrieving up-to-date information from a publicly accessible database poses significant threats to the user's privacy. {\em 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 {\em 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 {\em communication complexity}. In this review, we introduce a new discrete structure called {\em 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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