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DOI: 10.4230/LIPIcs.TQC.2015.73
URN: urn:nbn:de:0030-drops-55507
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5550/
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Berta, Mario ; Fawzi, Omar ; Scholz, Volkher B.

Semidefinite Programs for Randomness Extractors

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Abstract

Randomness extractors are an important building block for classical and quantum cryptography. However, for many applications it is crucial that the extractors are quantum-proof, i.e., that they work even in the presence of quantum adversaries. In general, quantum-proof extractors are poorly understood and we would like to argue that in the same way as Bell inequalities (multiprover games) and communication complexity, the setting of randomness extractors provides a operationally useful framework for studying the power and limitations of a quantum memory compared to a classical one. We start by recalling how to phrase the extractor property as a quadratic program with linear constraints. We then construct a semidefinite programming (SDP) relaxation for this program that is tight for some extractor constructions. Moreover, we show that this SDP relaxation is even sufficient to certify quantum-proof extractors. This gives a unifying approach to understand the stability properties of extractors against quantum adversaries. Finally, we analyze the limitations of this SDP relaxation.

BibTeX - Entry

@InProceedings{berta_et_al:LIPIcs:2015:5550,
  author =	{Mario Berta and Omar Fawzi and Volkher B. Scholz},
  title =	{{Semidefinite Programs for Randomness Extractors}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{73--91},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Salman Beigi and Robert Koenig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5550},
  URN =		{urn:nbn:de:0030-drops-55507},
  doi =		{10.4230/LIPIcs.TQC.2015.73},
  annote =	{Keywords: Randomness Extractors, Quantum adversaries, Semidefinite programs}
}

Keywords: Randomness Extractors, Quantum adversaries, Semidefinite programs
Seminar: 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)
Issue Date: 2015
Date of publication: 28.10.2015


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