A Unified Framework for Constructing Information-Theoretic Private Information Retrieval
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911294359076864 |
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| author | Zhang, Liang Feng |
| author_facet | Zhang, Liang Feng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_00480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Framework for Constructing Information-Theoretic Private Information Retrieval Zhang, Liang Feng Cryptography and Security Information Theory 11T71 E.4 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. |
| title | A Unified Framework for Constructing Information-Theoretic Private Information Retrieval |
| topic | Cryptography and Security Information Theory 11T71 E.4 |
| url | https://arxiv.org/abs/2512.00480 |