License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2021.56
URN: urn:nbn:de:0030-drops-135953
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13595/
Chen, Lijie ;
Ghazi, Badih ;
Kumar, Ravi ;
Manurangsi, Pasin
On Distributed Differential Privacy and Counting Distinct Elements
Abstract
We study the setup where each of n users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of (ε,δ)-differentially privacy:
- In the non-interactive local setting, we prove that the additive error of any protocol is Ω(n) for any constant ε and for any δ inverse polynomial in n.
- In the single-message shuffle setting, we prove a lower bound of Ω̃(n) on the error for any constant ε and for some δ inverse quasi-polynomial in n. We do so by building on the moment-matching method from the literature on distribution estimation.
- In the multi-message shuffle setting, we give a protocol with at most one message per user in expectation and with an error of Õ(√n) for any constant ε and for any δ inverse polynomial in n. Our protocol is also robustly shuffle private, and our error of √n matches a known lower bound for such protocols. Our proof technique relies on a new notion, that we call dominated protocols, and which can also be used to obtain the first non-trivial lower bounds against multi-message shuffle protocols for the well-studied problems of selection and learning parity.
Our first lower bound for estimating the number of distinct elements provides the first ω(√n) separation between global sensitivity and error in local differential privacy, thus answering an open question of Vadhan (2017). We also provide a simple construction that gives Ω̃(n) separation between global sensitivity and error in two-party differential privacy, thereby answering an open question of McGregor et al. (2011).
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs.ITCS.2021.56,
author = {Lijie Chen and Badih Ghazi and Ravi Kumar and Pasin Manurangsi},
title = {{On Distributed Differential Privacy and Counting Distinct Elements}},
booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
pages = {56:1--56:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-177-1},
ISSN = {1868-8969},
year = {2021},
volume = {185},
editor = {James R. Lee},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13595},
URN = {urn:nbn:de:0030-drops-135953},
doi = {10.4230/LIPIcs.ITCS.2021.56},
annote = {Keywords: Differential Privacy, Shuffle Model}
}
Keywords: |
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Differential Privacy, Shuffle Model |
Collection: |
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12th Innovations in Theoretical Computer Science Conference (ITCS 2021) |
Issue Date: |
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2021 |
Date of publication: |
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04.02.2021 |