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Constructing Elements of Large Order in Finite Fields

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

An efficient algorithm is presented which for any finite field Fq of small characteristic finds an extension F q s of polynomially bounded degree and an element α∈ F q s of exponentially large multiplicative order. The construction makes use of certain analogues of Gauss periods of a special type. This can be considered as another step towards solving the celebrated problem of finding primitive roots in finite fields efficiently.

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Author information

Authors and Affiliations

  1. FB Mathematik-Informatik, Universität Paderborn, 33095, Paderborn, Germany

    Joachim von zur Gathen

  2. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

    Igor Shparlinski

Authors
  1. Joachim von zur Gathen
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  2. Igor Shparlinski
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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von zur Gathen, J., Shparlinski, I. (1999). Constructing Elements of Large Order in Finite Fields. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_38

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  • DOI: https://doi.org/10.1007/3-540-46796-3_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

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