Multi-Server PIR with Full Error Detection and Limited Error Correction

Reo Eriguchi, Kaoru Kurosawa, Koji Nuida

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An ℓ-server Private Information Retrieval (PIR) scheme allows a client to retrieve the τ-th element aτ from a database a = (a1,..., an) 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 aτ 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 no(1) communication, and a t-private one which has O(nc) 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.

Original languageEnglish
Title of host publication3rd Conference on Information-Theoretic Cryptography, ITC 2022
EditorsDana Dachman-Soled
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772389
DOIs
Publication statusPublished - Jul 1 2022
Event3rd Conference on Information-Theoretic Cryptography, ITC 2022 - Cambridge, United States
Duration: Jul 5 2022Jul 7 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume230
ISSN (Print)1868-8969

Conference

Conference3rd Conference on Information-Theoretic Cryptography, ITC 2022
Country/TerritoryUnited States
CityCambridge
Period7/5/227/7/22

All Science Journal Classification (ASJC) codes

  • Software

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