Analysis of Rabin's polynomial irreducibility test

  • Daniel Panario
  • Alfredo Viola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)


We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We provide upper and lower bounds for this probability. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case behavior of Rabin's variants presented by von zur Gathen & Shoup and by Gao & Panario.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Daniel Panario
    • 1
  • Alfredo Viola
    • 2
  1. 1.Department of Computer ScienceUniv. of TorontoTorontoCanada
  2. 2.Pedeciba InformáticaMontevideoUruguay

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