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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.29
URN: urn:nbn:de:0030-drops-63080
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6308/
Goyal, Vipul ;
Khurana, Dakshita ;
Mironov, Ilya ;
Pandey, Omkant ;
Sahai, Amit
Do Distributed Differentially-Private Protocols Require Oblivious Transfer?
Abstract
We study the cryptographic complexity of two-party differentially-private protocols for a large natural class of boolean functionalities. Information theoretically, McGregor et al. [FOCS 2010] and Goyal et al. [Crypto 2013] demonstrated several functionalities for which the maximal possible accuracy in the distributed setting is significantly lower than that in the client-server setting. Goyal et al. [Crypto 2013] further showed that "highly accurate" protocols in the distributed setting for any non-trivial functionality in fact imply the existence of one-way functions. However, it has remained an open problem to characterize the exact cryptographic complexity of this class. In particular, we know that semi-honest oblivious transfer helps obtain optimally accurate distributed differential privacy. But we do not know whether the reverse is true. We study the following question: Does the existence of optimally accurate distributed differentially private protocols for any class of functionalities imply the existence of oblivious transfer (or equivalently secure multi-party computation)? We resolve this question in the affirmative for the class of boolean functionalities that contain an XOR embedded on adjacent inputs. We give a reduction from oblivious transfer to:
- Any distributed optimally accurate epsilon-differentially private protocol with epsilon > 0 computing a functionality with a boolean XOR embedded on adjacent inputs.
- Any distributed non-optimally accurate epsilon-differentially private protocol with epsilon > 0, for a constant range of non-optimal accuracies and constant range of values of epsilon, computing a functionality with a boolean XOR embedded on adjacent inputs.
Enroute to proving these results, we demonstrate a connection between optimally-accurate twoparty differentially-private protocols for functions with a boolean XOR embedded on adjacent inputs, and noisy channels, which were shown by Crépeau and Kilian [FOCS 1988] to be sufficient for oblivious transfer.
BibTeX - Entry
@InProceedings{goyal_et_al:LIPIcs:2016:6308,
author = {Vipul Goyal and Dakshita Khurana and Ilya Mironov and Omkant Pandey and Amit Sahai},
title = {{Do Distributed Differentially-Private Protocols Require Oblivious Transferl}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {29:1--29:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6308},
URN = {urn:nbn:de:0030-drops-63080},
doi = {10.4230/LIPIcs.ICALP.2016.29},
annote = {Keywords: Oblivious Transfer, Distributed Differential Privacy, Noisy Channels, Weak Noisy Channels}
}
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Keywords: |
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Oblivious Transfer, Distributed Differential Privacy, Noisy Channels, Weak Noisy Channels |
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Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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23.08.2016 |
