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Improved Zero-Knowledge Identification with Lattices

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Provable Security (ProvSec 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6402))

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Abstract

Zero-knowledge identification schemes solve the problem of authenticating one party to another via an insecure channel without disclosing any additional information that might be used by an impersonator. In this paper we propose a scheme whose security relies on the existence of a commitment scheme and on the hardness of worst-case lattice problems. We adapt a code-based identification scheme devised by Cayrel and Véron, which constitutes an improvement of Stern’s construction. Our solution sports analogous improvements over the lattice adaption of Stern’s scheme which Kawachi et al. presented at ASIACRYPT 2008. Specifically, due to a smaller cheating probability close to 1/2 and a similar communication cost, any desired level of security will be achieved in fewer rounds. Compared to Lyubashevsky’s scheme presented at ASIACRYPT 2009, our proposal, like Kawachi’s, offers a much milder security assumption: namely, the hardness of SIS for trinary solutions. The same assumption was used for the SWIFFT hash function, which is secure for much smaller parameters than those proposed by Lyubashevsky.

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Author information

Authors and Affiliations

  1. CASED – Center for Advanced Security Research Darmstadt, Mornewegstrasse, 32, 64293, Darmstadt, Germany

    Pierre-Louis Cayrel

  2. Fachbereich Informatik, Kryptographie und Computeralgebra, Technische Universität Darmstadt, Hochschulstraße 10, 64289, Darmstadt, Germany

    Richard Lindner & Markus Rückert

  3. Institute of Computing, State University of Campinas (UNICAMP), P.O. Box 6176, 13084-971, Campinas, Brazil

    Rosemberg Silva

Authors
  1. Pierre-Louis Cayrel
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  2. Richard Lindner
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  3. Markus Rückert
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  4. Rosemberg Silva
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Editor information

Editors and Affiliations

  1. Faculty of Information Science and Technology, Jalan Ayer Keroh Lama, Multimedia University, 75450, Malacca, Malaysia

    Swee-Huay Heng

  2. Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Kaoru Kurosawa

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Cayrel, PL., Lindner, R., Rückert, M., Silva, R. (2010). Improved Zero-Knowledge Identification with Lattices. In: Heng, SH., Kurosawa, K. (eds) Provable Security. ProvSec 2010. Lecture Notes in Computer Science, vol 6402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16280-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-16280-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16279-4

  • Online ISBN: 978-3-642-16280-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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