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Documents authored by Nissim, Kobbi

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.129
The Complexity of Verifying Loop-Free Programs as Differentially Private

Authors: Marco Gaboardi, Kobbi Nissim, and David Purser

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We study the problem of verifying differential privacy for loop-free programs with probabilistic choice. Programs in this class can be seen as randomized Boolean circuits, which we will use as a formal model to answer two different questions: first, deciding whether a program satisfies a prescribed level of privacy; second, approximating the privacy parameters a program realizes. We show that the problem of deciding whether a program satisfies ε-differential privacy is coNP^#P-complete. In fact, this is the case when either the input domain or the output range of the program is large. Further, we show that deciding whether a program is (ε,δ)-differentially private is coNP^#P-hard, and in coNP^#P for small output domains, but always in coNP^{#P^#P}. Finally, we show that the problem of approximating the level of differential privacy is both NP-hard and coNP-hard. These results complement previous results by Murtagh and Vadhan [Jack Murtagh and Salil P. Vadhan, 2016] showing that deciding the optimal composition of differentially private components is #P-complete, and that approximating the optimal composition of differentially private components is in P.
Cite as

Marco Gaboardi, Kobbi Nissim, and David Purser. The Complexity of Verifying Loop-Free Programs as Differentially Private. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 129:1-129:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gaboardi_et_al:LIPIcs.ICALP.2020.129,
  author =	{Gaboardi, Marco and Nissim, Kobbi and Purser, David},
  title =	{{The Complexity of Verifying Loop-Free Programs as Differentially Private}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{129:1--129:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.129},
  URN =		{urn:nbn:de:0030-drops-125362},
  doi =		{10.4230/LIPIcs.ICALP.2020.129},
  annote =	{Keywords: differential privacy, program verification, probabilistic programs}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.14
The Power of Synergy in Differential Privacy: Combining a Small Curator with Local Randomizers

Authors: Amos Beimel, Aleksandra Korolova, Kobbi Nissim, Or Sheffet, and Uri Stemmer

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Motivated by the desire to bridge the utility gap between local and trusted curator models of differential privacy for practical applications, we initiate the theoretical study of a hybrid model introduced by "Blender" [Avent et al., USENIX Security '17], in which differentially private protocols of n agents that work in the local-model are assisted by a differentially private curator that has access to the data of m additional users. We focus on the regime where m ≪ n and study the new capabilities of this (m,n)-hybrid model. We show that, despite the fact that the hybrid model adds no significant new capabilities for the basic task of simple hypothesis-testing, there are many other tasks (under a wide range of parameters) that can be solved in the hybrid model yet cannot be solved either by the curator or by the local-users separately. Moreover, we exhibit additional tasks where at least one round of interaction between the curator and the local-users is necessary - namely, no hybrid model protocol without such interaction can solve these tasks. Taken together, our results show that the combination of the local model with a small curator can become part of a promising toolkit for designing and implementing differential privacy.
Cite as

Amos Beimel, Aleksandra Korolova, Kobbi Nissim, Or Sheffet, and Uri Stemmer. The Power of Synergy in Differential Privacy: Combining a Small Curator with Local Randomizers. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{beimel_et_al:LIPIcs.ITC.2020.14,
  author =	{Beimel, Amos and Korolova, Aleksandra and Nissim, Kobbi and Sheffet, Or and Stemmer, Uri},
  title =	{{The Power of Synergy in Differential Privacy: Combining a Small Curator with Local Randomizers}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.14},
  URN =		{urn:nbn:de:0030-drops-121195},
  doi =		{10.4230/LIPIcs.ITC.2020.14},
  annote =	{Keywords: differential privacy, hybrid model, private learning, local model}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.65
Exploring Differential Obliviousness

Authors: Amos Beimel, Kobbi Nissim, and Mohammad Zaheri

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
In a recent paper, Chan et al. [SODA '19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM '96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.
Cite as

Amos Beimel, Kobbi Nissim, and Mohammad Zaheri. Exploring Differential Obliviousness. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{beimel_et_al:LIPIcs.APPROX-RANDOM.2019.65,
  author =	{Beimel, Amos and Nissim, Kobbi and Zaheri, Mohammad},
  title =	{{Exploring Differential Obliviousness}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.65},
  URN =		{urn:nbn:de:0030-drops-112803},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.65},
  annote =	{Keywords: Differential Obliviousness, Differential Privacy, Oblivious RAM, Graph Property Testing}
}
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