Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Kaplan, Marc; Kerenidis, Iordanis; Laplante, Sophie; Roland, Jérémie http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-23226
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Non-Local Box Complexity and Secure Function Evaluation

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Abstract

A non-local box is an abstract device into which Alice and Bob input bits $x$ and $y$ respectively and receive outputs $a$ and $b$ respectively, where $a,b$ are uniformly distributed and $a \oplus b = x \wedge y$. Such boxes have been central to the study of quantum or generalized non-locality as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in order to compute a Boolean function $f$. We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We show that non-local box complexity has interesting applications to classical cryptography, in particular to secure function evaluation, and study the question posed by Beimel and Malkin \cite{BM} of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function $f$. We show that this question is related to the non-local box complexity of the function and conclude by greatly improving their bounds. Finally, another consequence of our results is that traceless two-outcome measurements on maximally entangled states can be simulated with 3 \nlbs, while no finite bound was previously known.

BibTeX - Entry

@InProceedings{kaplan_et_al:LIPIcs:2009:2322,
  author =	{Marc Kaplan and Iordanis Kerenidis and Sophie Laplante and J{\'e}r{\'e}mie Roland},
  title =	{{Non-Local Box Complexity and Secure Function Evaluation}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{239--250},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Ravi Kannan and K. Narayan Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2322},
  URN =		{urn:nbn:de:0030-drops-23226},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2009.2322},
  annote =	{Keywords: Communication complexity, non-locality, non-local boxes, secure function evaluation}
}

Keywords: Communication complexity, non-locality, non-local boxes, secure function evaluation
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue date: 2009
Date of publication: 2009


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