### On Quantum Advantage in Information Theoretic Single-Server PIR

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

##### Abstract

In (single-server) Private Information Retrieval (PIR), a server holds a large database $DB$ of size $n$, and a client holds an index $i \in [n]$ 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 $\Omega(n)$ 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 $O(\sqrt{n})$, 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 \emph{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).

Available format(s)
Publication info
Preprint. MINOR revision.
Keywords
quantum complexityprivate information retrievalspecious security
Contact author(s)
zvika brakerski @ weizmann ac il
History
2019-03-01: revised
See all versions
Short URL
https://ia.cr/2019/232

CC BY

BibTeX

@misc{cryptoeprint:2019/232,
author = {Dorit Aharonov and Zvika Brakerski and Kai-Min Chung and Ayal Green and Ching-Yi Lai and Or Sattath},
title = {On Quantum Advantage in Information Theoretic Single-Server PIR},
howpublished = {Cryptology ePrint Archive, Paper 2019/232},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/232}},
url = {https://eprint.iacr.org/2019/232}
}

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