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International Workshop on Post-Quantum Cryptography

PQCrypto 2010: Post-Quantum Cryptography pp 81–94Cite as

Information-Set Decoding for Linear Codes over F q

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6061))

Abstract

The best known non-structural attacks against code-based cryptosystems are based on information-set decoding. Stern’s algorithm and its improvements are well optimized and the complexity is reasonably well understood. However, these algorithms only handle codes over F 2.

This paper presents a generalization of Stern’s information-set- decoding algorithm for decoding linear codes over arbitrary finite fields F q and analyzes the complexity. This result makes it possible to compute the security of recently proposed code-based systems over non-binary fields.

As an illustration, ranges of parameters for generalized McEliece cryptosystems using classical Goppa codes over F 31 are suggested for which the new information-set-decoding algorithm needs 2128 bit operations.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600, MB, Eindhoven, Netherlands

    Christiane Peters

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  1. Christiane Peters
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Editors and Affiliations

  1. Projet Team SECRET, Centre de Recherche INRIA Paris-Rocquencourt,, B.P. 105, 78153, Le Chesnay Cedex, France

    Nicolas Sendrier

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Peters, C. (2010). Information-Set Decoding for Linear Codes over F q . In: Sendrier, N. (eds) Post-Quantum Cryptography. PQCrypto 2010. Lecture Notes in Computer Science, vol 6061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12929-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-12929-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12928-5

  • Online ISBN: 978-3-642-12929-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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