On quantum advantage in information theoretic single-server PIR

Dorit Aharonov*, Zvika Brakerski, Kai Min Chung, Ayal Green, Ching-Yi Lai, Or Sattath

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

In (single-server) Private Information Retrieval (PIR), a server holds a large database DB of size n, and a client holds an index i∈[n] and wishes to retrieve DB[i] without revealing i to the server. It is well known that information theoretic privacy even against an “honest but curious” server requires Ω(n) communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (“input purification attack”). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity O√n, and a protocol by Kerenidis et al. (QIC 2016) with communication complexity O(log(n)), and O(n) shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called anchored privacy, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsYuval Ishai, Vincent Rijmen
PublisherSpringer Verlag
Pages219-246
Number of pages28
ISBN (Print)9783030176587
DOIs
StatePublished - 1 Jan 2019
Event38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 - Darmstadt, Germany
Duration: 19 May 201923 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11478 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019
CountryGermany
CityDarmstadt
Period19/05/1923/05/19

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