Orders of Gauss Periods in Finite Fields

  • Joachim von zur Gathen
  • Igor Shparlinski


It is shown that Gauss periods of a special type give an explicit polynomial-time computation of elements of exponentially large multiplicative order in some finite fields. This can be considered as a step towards solving the celebrated problem of finding primitive roots in finite fields in polynomial time.

Key words Finite fields, Algorithms, Primitive roots, Normal bases, Artin's conjecture 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Igor Shparlinski
    • 2
  1. 1.FB Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany (e-mail:
  2. 2.School of MPCE Macquarie University Sydney, NSW 2109, Australia (e-mail:

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