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DOI: 10.4230/LIPIcs.ITC.2022.15

Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW

Authors: Gilad Asharov, Ran Cohen, and Oren Shochat

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)

Abstract

Adaptive security is a highly desirable property in the design of secure protocols. It tolerates adversaries that corrupt parties as the protocol proceeds, as opposed to static security where the adversary corrupts the parties at the onset of the execution. The well-accepted folklore is that static and adaptive securities are equivalent for perfectly secure protocols. Indeed, this folklore is backed up with a transformation by Canetti et al. (EUROCRYPT'01), showing that any perfectly secure protocol that is statically secure and satisfies some basic requirements is also adaptively secure. Yet, the transformation results in an adaptively secure protocol with inefficient simulation (i.e., where the simulator might run in super-polynomial time even if the adversary runs just in polynomial time). Inefficient simulation is problematic when using the protocol as a sub-routine in the computational setting. Our main question is whether an alternative efficient transformation from static to adaptive security exists. We show an inherent difficulty in achieving this goal generically. In contrast to the folklore, we present a protocol that is perfectly secure with efficient static simulation (therefore also adaptively secure with inefficient simulation), but for which efficient adaptive simulation does not exist (assuming the existence of one-way permutations). In addition, we prove that the seminal protocol of Ben-Or, Goldwasser and Wigderson (STOC'88) is secure against adaptive, semi-honest corruptions with efficient simulation. Previously, adaptive security of the protocol, as is, was only known either for a restricted class of circuits, or for all circuits but with inefficient simulation.

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Gilad Asharov, Ran Cohen, and Oren Shochat. Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{asharov_et_al:LIPIcs.ITC.2022.15,
  author =	{Asharov, Gilad and Cohen, Ran and Shochat, Oren},
  title =	{{Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.15},
  URN =		{urn:nbn:de:0030-drops-164933},
  doi =		{10.4230/LIPIcs.ITC.2022.15},
  annote =	{Keywords: secure multiparty computation, perfect security, adaptive security, BGW protocol}
}

Document

DOI: 10.4230/LIPIcs.ITC.2020.11

Oblivious Parallel Tight Compaction

Authors: Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, and Elaine Shi

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

Abstract

In tight compaction one is given an array of balls some of which are marked 0 and the rest are marked 1. The output of the procedure is an array that contains all of the original balls except that now the 0-balls appear before the 1-balls. In other words, tight compaction is equivalent to sorting the array according to 1-bit keys (not necessarily maintaining order within same-key balls). Tight compaction is not only an important algorithmic task by itself, but its oblivious version has also played a key role in recent constructions of oblivious RAM compilers. We present an oblivious deterministic algorithm for tight compaction such that for input arrays of n balls requires O(n) total work and O(log n) depth. Our algorithm is in the Exclusive-Read-Exclusive-Write Parallel-RAM model (i.e., EREW PRAM, the most restrictive PRAM model), and importantly we achieve asymptotical optimality in both total work and depth. To the best of our knowledge no earlier work, even when allowing randomization, can achieve optimality in both total work and depth.

Cite as

Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, and Elaine Shi. Oblivious Parallel Tight Compaction. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{asharov_et_al:LIPIcs.ITC.2020.11,
  author =	{Asharov, Gilad and Komargodski, Ilan and Lin, Wei-Kai and Peserico, Enoch and Shi, Elaine},
  title =	{{Oblivious Parallel Tight Compaction}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{11:1--11:23},
  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.2020.11},
  URN =		{urn:nbn:de:0030-drops-121164},
  doi =		{10.4230/LIPIcs.ITC.2020.11},
  annote =	{Keywords: Oblivious tight compaction, parallel oblivious RAM, EREW PRAM}
}

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Documents authored by Asharov, Gilad

Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW

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Oblivious Parallel Tight Compaction

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