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/
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Chen, Lijie ; Ghazi, Badih ; Kumar, Ravi ; Manurangsi, Pasin

On Distributed Differential Privacy and Counting Distinct Elements

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LIPIcs-ITCS-2021-56.pdf (0.6 MB)

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: Differential Privacy, Shuffle Model
Collection: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue Date: 2021
Date of publication: 04.02.2021

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