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A Quantum Goldreich-Levin Theorem with Cryptographic Applications

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We investigate the Goldreich-Levin Theorem in the context of quantum information. This result is a reduction from the problem of inverting a one-way function to the problem of predicting a particular bit associated with that function. We show that the quantum version of the reduction is quantitatively more efficient than the known classical version. If the one-way function acts on n-bit strings then the overhead in the reduction is by a factor of O(n/ε2) in the classical case but only by a factor of O(1/ε) in the quantum case, where 1/2 +ε is the probability of predicting the hard-predicate. We also show that, using the Goldreich- Levin Theorem, a quantum bit (or qubit) commitment scheme that is perfectly binding and computationally concealing can be obtained from any quantum one-way permutation.

Partially supported by Canada’s NSERC and the Killam Trust.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Mark Adcock & Richard Cleve

Authors
  1. Mark Adcock
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  2. Richard Cleve
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Adcock, M., Cleve, R. (2002). A Quantum Goldreich-Levin Theorem with Cryptographic Applications. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_26

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  • DOI: https://doi.org/10.1007/3-540-45841-7_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

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