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Information-Theoretic Random-Index PIR

Authors Sebastian Kolby , Lawrence Roy , Jure Sternad , Sophia Yakoubov

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Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Private information retrieval
  • Multi-server
  • Lower bounds

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Abstract

A Private Information Retrieval (PIR) protocol allows a client to learn the ith row of a database held by one or more servers, without revealing i to the servers. A Random-Index PIR (RPIR) protocol, introduced by Gentry et al. (TCC 2021), is a PIR protocol where, instead of being chosen by the client, i is random. This has applications in e.g. anonymous committee selection. Both PIR and RPIR protocols are interesting only if the communication complexity is smaller than the database size; otherwise, the trivial solution where the servers send the entire database suffices.
Unlike PIR, where the client must send at least one message (to encode information about i), RPIR can be executed in a single round of server-to-client communication. In this paper, we study such one-round, information-theoretic RPIR protocols. The only known construction in this setting is SimpleMSRPIR (Gentry et al.), which requires the servers to communicate approximately N/2 bits, N being the database size. We show an Ω(√N) lower bound on communication complexity for one-round two-server information-theoretic RPIR, and a sublinear upper bound. Finally, we show how to use a sublinear amount of database-independent correlated randomness among multiple servers to get near-optimal online communication complexity (the size of one row plus the size of one index description per server).

Cite As Get BibTex

Sebastian Kolby, Lawrence Roy, Jure Sternad, and Sophia Yakoubov. Information-Theoretic Random-Index PIR. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITC.2025.5

Author Details

Sebastian Kolby
  • Aarhus University, Denmark
Lawrence Roy
  • Aarhus University, Denmark
Jure Sternad
  • Aarhus University, Denmark
Sophia Yakoubov
  • Aarhus University, Denmark

Funding

Danish Independent Research Council under Grant-ID DFF-2032-00122B and DFF-2064-00016B (YOSO)

Acknowledgements

Supported by the Danish Independent Research Council under Grant-ID DFF-2032-00122B and DFF-2064-00016B (YOSO).

References

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