Gauss periods and fast exponentiation in finite fields

Extended abstract
  • Shuhong Gao
  • Joachim von zur Gathen
  • Daniel Panario
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 911)


Gauss periods can be used to implement finite field arithmetic efficiently. For a small prime p and infinitely many integers n, exponentiation of an arbitrary element in F p n can be done with O(n2 loglog n) operations in F p , and exponentiation of a Gauss period with O(n2) operations in F p . Comparing to the previous estimate O(n2 log nloglog n), using polynomial bases, this shows that normal bases generated by Gauss periods offer some asymptotic computational advantage. Experimental results indicate that Gauss periods are often primitive elements in finite fields.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Shuhong Gao
    • 1
  • Joachim von zur Gathen
    • 1
  • Daniel Panario
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

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