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DOI: 10.4230/LIPIcs.TQC.2017.3
URN: urn:nbn:de:0030-drops-85816
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8581/
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Belovs, Aleksandrs ; Brassard, Gilles ; H°yer, Peter ; Kaplan, Marc ; Laplante, Sophie ; Salvail, Louis

Provably Secure Key Establishment Against Quantum Adversaries

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LIPIcs-TQC-2017-3.pdf (0.6 MB)


Abstract

At Crypto 2011, some of us had proposed a family of cryptographic protocols for key establishment capable of protecting quantum and classical legitimate parties unconditionally against a quantum eavesdropper in the query complexity model. Unfortunately, our security proofs were unsatisfactory from a cryptographically meaningful perspective because they were sound only in a worst-case scenario. Here, we extend our results and prove that for any \eps > 0, there is a classical protocol that allows the legitimate parties to establish a common key after O(N) expected queries to a random oracle, yet any quantum eavesdropper will have a vanishing probability of learning their key after O(N^(1.5-\eps)) queries to the same oracle. The vanishing probability applies to a typical run of the protocol. If we allow the legitimate parties to use a quantum computer as well, their advantage over the quantum eavesdropper becomes arbitrarily close to the quadratic advantage that classical legitimate parties enjoyed over classical eavesdroppers in the seminal 1974 work of Ralph Merkle. Along the way, we develop new tools to give lower bounds on the number of quantum queries required to distinguish two probability distributions. This method in itself could have multiple applications in cryptography. We use it here to study average-case quantum query complexity, for which we develop a new composition theorem of independent interest.

BibTeX - Entry

@InProceedings{belovs_et_al:LIPIcs:2018:8581,
  author =	{Aleksandrs Belovs and Gilles Brassard and Peter H\oyer and Marc Kaplan and Sophie Laplante and Louis Salvail},
  title =	{{Provably Secure Key Establishment Against Quantum Adversaries}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Mark M. Wilde},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8581},
  URN =		{urn:nbn:de:0030-drops-85816},
  doi =		{10.4230/LIPIcs.TQC.2017.3},
  annote =	{Keywords: Merkle puzzles, Key establishment schemes, Quantum cryptography, Adversary method, Average-case analysis}
}

Keywords: Merkle puzzles, Key establishment schemes, Quantum cryptography, Adversary method, Average-case analysis
Seminar: 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)
Issue Date: 2018
Date of publication: 26.02.2018


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