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International Colloquium on Automata, Languages, and Programming

ICALP 2006: Automata, Languages and Programming pp 216–227Cite as

Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4052))

Abstract

We present three new quantum hardcore functions for any quantum one-way function. We also give a “quantum” solution to Damgård’s question (CRYPTO’88) on his pseudorandom generator by proving the quantum hardcore property of his generator, which has been unknown to have the classical hardcore property. Our technical tool is quantum list-decoding of “classical” error-correcting codes (rather than “quantum” error-correcting codes), which is defined on the platform of computational complexity theory and cryptography (rather than information theory). In particular, we give a simple but powerful criterion that makes a polynomial-time computable code (seen as a function) a quantum hardcore for any quantum one-way function. On their own interest, we also give quantum list-decoding algorithms for codes whose associated quantum states (called codeword states) are “nearly” orthogonal using the technique of pretty good measurement.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Akinori Kawachi

  2. ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Tomoyuki Yamakami

Authors
  1. Akinori Kawachi
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  2. Tomoyuki Yamakami
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice,  

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, LS2, Univ. Dortmund, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Kawachi, A., Yamakami, T. (2006). Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_19

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  • DOI: https://doi.org/10.1007/11787006_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35907-4

  • Online ISBN: 978-3-540-35908-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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