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International Conference on Cryptology in India

INDOCRYPT 2004: Progress in Cryptology - INDOCRYPT 2004 pp 84–91Cite as

Algebraic Attacks over GF(q)

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3348))

Abstract

Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f q − − 1 – 1. In this case, many such low degree multiples exist.

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References

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Author information

Authors and Affiliations

  1. Deakin University, 221 Burwood Highway, Vic 3125, Australia

    Lynn Margaret Batten

Authors
  1. Lynn Margaret Batten
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Editor information

Editors and Affiliations

  1. INRIA Rocquencourt, France

    Anne Canteaut

  2. SETS, 21 Mangadu Swamy Street, Nungambakkam, 600 034, Chennai, India

    Kapaleeswaran Viswanathan

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© 2004 Springer-Verlag Berlin Heidelberg

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Batten, L.M. (2004). Algebraic Attacks over GF(q). In: Canteaut, A., Viswanathan, K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30556-9_8

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  • DOI: https://doi.org/10.1007/978-3-540-30556-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24130-0

  • Online ISBN: 978-3-540-30556-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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