research-article

The Hardness of Being Private

Authors:

Arkadev Chattopadhyay,

Stephen A. Cook,

Michal Koucký,

Toniann PitassiAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 6, Issue 1

Article No.: 1, Pages 1 - 24

https://doi.org/10.1145/2567671

Published: 01 March 2014 Publication History

Abstract

Kushilevitz [1989] initiated the study of information-theoretic privacy within the context of communication complexity. Unfortunately, it has been shown that most interesting functions are not privately computable [Kushilevitz 1989, Brandt and Sandholm 2008]. The unattainability of perfect privacy for many functions motivated the study of approximate privacy. Feigenbaum et al. [2010a, 2010b] define notions of worst-case as well as average-case approximate privacy and present several interesting upper bounds as well as some open problems for further study. In this article, we obtain asymptotically tight bounds on the trade-offs between both the worst-case and average-case approximate privacy of protocols and their communication cost for Vickrey auctions.

Further, we relate the notion of average-case approximate privacy to other measures based on information cost of protocols. This enables us to prove exponential lower bounds on the subjective approximate privacy of protocols for computing the Intersection function, independent of its communication cost. This proves a conjecture of Feigenbaum et al. [2010a].

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Joan Feigenbaum, Aaron D. Jaggard, and Michael Schapira. 2010a. Approximate privacy: Foundations and quantification. In Proceedings of the 11th Conference on Electronic Commerce. 167--178.

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Joan Feigenbaum, Aaron D. Jaggard, and Michael Schapira. 2010b. Approximate privacy: PARs for set problems. DIMACS Tech. rep. 2010-01, 1--34. http://dimacs.rutgers.edu/~adj/Research/type.html.

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Cited By

Gay RKerenidis IWee H(2022)Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based EncryptionAdvances in Cryptology -- CRYPTO 201510.1007/978-3-662-48000-7_24(485-502)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1007/978-3-662-48000-7_24
Liu TVaikuntanathan VWee H(2017)Conditional Disclosure of Secrets via Non-linear ReconstructionAdvances in Cryptology – CRYPTO 201710.1007/978-3-319-63688-7_25(758-790)Online publication date: 29-Jul-2017
https://doi.org/10.1007/978-3-319-63688-7_25
Brody JChakrabarti AKondapally RWoodruff DYaroslavtsev G(2016)Certifying Equality With Limited InteractionAlgorithmica10.1007/s00453-016-0163-676:3(796-845)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s00453-016-0163-6
Show More Cited By

Index Terms

The Hardness of Being Private
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes

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cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 6, Issue 1

March 2014

92 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/2600088

Editor:
Eric Allender
Rutgers University, USA

Issue’s Table of Contents

Copyright © 2014 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 March 2014

Accepted: 01 December 2013

Revised: 01 December 2013

Received: 01 September 2012

Published in TOCT Volume 6, Issue 1

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RVO
GA ČR
Natural Sciences and Engineering Research Council of Canada
Center of Excellence CE-ITI
GA AV ČR
Ontario Ministry of Research and Innovation

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Cited By

Gay RKerenidis IWee H(2022)Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based EncryptionAdvances in Cryptology -- CRYPTO 201510.1007/978-3-662-48000-7_24(485-502)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1007/978-3-662-48000-7_24
Liu TVaikuntanathan VWee H(2017)Conditional Disclosure of Secrets via Non-linear ReconstructionAdvances in Cryptology – CRYPTO 201710.1007/978-3-319-63688-7_25(758-790)Online publication date: 29-Jul-2017
https://doi.org/10.1007/978-3-319-63688-7_25
Brody JChakrabarti AKondapally RWoodruff DYaroslavtsev G(2016)Certifying Equality With Limited InteractionAlgorithmica10.1007/s00453-016-0163-676:3(796-845)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s00453-016-0163-6
Göös MPitassi TWatson T(2016)Zero-Information Protocols and Unambiguity in Arthur---Merlin CommunicationAlgorithmica10.1007/s00453-015-0104-976:3(684-719)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s00453-015-0104-9
Göös MPitassi TWatson TRoughgarden T(2015)Zero-Information Protocols and Unambiguity in Arthur-Merlin CommunicationProceedings of the 2015 Conference on Innovations in Theoretical Computer Science10.1145/2688073.2688074(113-122)Online publication date: 11-Jan-2015
https://dl.acm.org/doi/10.1145/2688073.2688074
Kerenidis ILaplante SLerays VRoland JXiao D(2015)Lower Bounds on Information Complexity via Zero-Communication Protocols and ApplicationsSIAM Journal on Computing10.1137/13092827344:5(1550-1572)Online publication date: 27-Oct-2015
https://dl.acm.org/doi/10.1137/130928273

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