Improving the time complexity of the computation of irreducible and primitive polynomials in finite fields

  • Josep Rifà
  • Joan Borrell
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)


In this paper, we present a method to compute all the irreducible and primitive polynomials of degree m over a finite field. We also describe two concrete implementations of our method with respective time complexities O(m2 + m log m) and O(m2 + log m). These implementations, using in parallel different devices introduced to operate in these fields [1], [7], allows us to reduce the time complexity of our method below that of the best previously known methods [3]. Our algorithm is especially well-suited for applications using large finite fields.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Josep Rifà
    • 1
  • Joan Borrell
    • 1
  1. 1.Dept. d'InformàticaUniversitat Autònoma de BarcelonaBellaterraSpain

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