eng
Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-06-30
1:1
1:20
10.4230/LIPIcs.ITC.2022.1
article
Multi-Server PIR with Full Error Detection and Limited Error Correction
Eriguchi, Reo
1
2
https://orcid.org/0000-0002-0019-6934
Kurosawa, Kaoru
3
2
Nuida, Koji
4
2
Graduate School of Information Science and Technology, The University of Tokyo, Japan
National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Research and Development Initiative, Chuo University, Tokyo, Japan
Institute of Mathematics for Industry, Kyushu University, Japan
An π-server Private Information Retrieval (PIR) scheme allows a client to retrieve the Ο-th element a_Ο from a database a = (aβ,β¦,a_n) which is replicated among π servers. It is called t-private if any coalition of t servers learns no information on Ο, and b-error correcting if a client can correctly compute a_Ο from π answers containing b errors. This paper concerns the following problems: Is there a t-private π-server PIR scheme with communication complexity o(n) such that a client can detect errors with probability 1-Ξ΅ even if π-1 servers return false answers? Is it possible to add error correction capability to it? We first formalize a notion of (1-Ξ΅)-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., Ξ΅ = 0) PIR scheme with o(n) communication. Next, for Ξ΅ > 0, we construct 1-private (1-Ξ΅)-fully error detecting and (π/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 β₯ 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol230-itc2022/LIPIcs.ITC.2022.1/LIPIcs.ITC.2022.1.pdf
Private Information Retrieval
Error Detection
Error Correction