computational complexity

, Volume 2, Issue 3, pp 187–224

Computing Frobenius maps and factoring polynomials

  • Joachim von zur Gathen
  • Victor Shoup

DOI: 10.1007/BF01272074

Cite this article as:
von zur Gathen, J. & Shoup, V. Comput Complexity (1992) 2: 187. doi:10.1007/BF01272074


A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degreen overFq, the number of arithmetic operations inFq isO((n2+nlogq). (logn)2 loglogn). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.

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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Victor Shoup
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada