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Constructing Elements of Large Order in Finite Fields

  • Joachim von zur Gathen
  • Igor Shparlinski
Conference paper
Part of the Lecture Notes in Computer Science book series (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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Igor Shparlinski
    • 2
  1. 1.FB Mathematik-InformatikUniversität PaderbornPaderbornGermany
  2. 2.Department of ComputingMacquarie UniversitySydneyAustralia

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