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On the Autocorrelation of Cyclotomic Generators

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

We extend a result of Ding and Helleseth on the autocorrelation of a cyclotomic generator in several ways. We define and analyze cyclotomic generators of arbitrary orders and over arbitrary finite fields, and we consider two, in general, different definitions of autocorrelation. Cyclotomic generators are closely related to the discrete logarithm. Hence, the results of this paper do not only describe interesting cryptographic properties of cyclotomic generators and their generalizations but also desirable features of the discrete logarithm.

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Author information

Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, 10 Kent Ridge, Crescent, Singapore, 119260

    Wilfried Meidl & Arne Winterhof

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, c/o Johannes Kepler University Linz, Altenbergerstraße 69, 4040, Linz, Austria

    Arne Winterhof

Authors
  1. Wilfried Meidl
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  2. Arne Winterhof
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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© 2004 Springer-Verlag Berlin Heidelberg

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Meidl, W., Winterhof, A. (2004). On the Autocorrelation of Cyclotomic Generators. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_1

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

  • eBook Packages: Springer Book Archive

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