Multi-Server PIR with Full Error Detection and Limited Error Correction
An 𝓁-server Private Information Retrieval (PIR) scheme allows a client to retrieve the τ-th element a_τ from a database a = (a₁,…,a_n) which is replicated among 𝓁 servers. It is called t-private if any coalition of t servers learns no information on τ, and b-error correcting if a client can correctly compute a_τ from 𝓁 answers containing b errors. This paper concerns the following problems: Is there a t-private 𝓁-server PIR scheme with communication complexity o(n) such that a client can detect errors with probability 1-ε even if 𝓁-1 servers return false answers? Is it possible to add error correction capability to it? We first formalize a notion of (1-ε)-fully error detecting PIR in such a way that an answer returned by any malicious server depends on at most t queries, which reflects t-privacy. We then prove an impossibility result that there exists no 1-fully error detecting (i.e., ε = 0) PIR scheme with o(n) communication. Next, for ε > 0, we construct 1-private (1-ε)-fully error detecting and (𝓁/2-O(1))-error correcting PIR schemes which have n^{o(1)} communication, and a t-private one which has O(n^{c}) communication for any t ≥ 2 and some constant c < 1. Technically, we show generic transformation methods to add error correction capability to a basic fully error detecting PIR scheme. We also construct such basic schemes by modifying certain existing PIR schemes which have no error detection capability.
Private Information Retrieval
Error Detection
Error Correction
Security and privacy~Information-theoretic techniques
1:1-1:20
Regular Paper
This research was partially supported by JSPS KAKENHI Grant Numbers JP20J20797 and 19H01109, Japan and JST CREST Grant Numbers JPMJCR19F6 and JPMJCR2113, Japan.
https://eprint.iacr.org/2022/500
Reo
Eriguchi
Reo Eriguchi
Graduate School of Information Science and Technology, The University of Tokyo, Japan
National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
https://orcid.org/0000-0002-0019-6934
Kaoru
Kurosawa
Kaoru Kurosawa
Research and Development Initiative, Chuo University, Tokyo, Japan
National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Koji
Nuida
Koji Nuida
Institute of Mathematics for Industry, Kyushu University, Japan
National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
10.4230/LIPIcs.ITC.2022.1
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Reo Eriguchi, Kaoru Kurosawa, and Koji Nuida
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