O(log(n)) parallel time finite field inversion

  • Bruce E. Litow
  • George I. Davida
NC Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 319)


Let p be prime and assume that GF(p n ) is given via an irreducible nth degree GF(p) polynomial. We exhibit a boolean circuit of size n O(1) and depth O(log(n)) such that for any x ε GF(p n ) the circuit produces x −1. The circuit is based upon an interesting connection between finite field computations and the eigenvalues of certain matrices. The issue of circuit uniformity is also considered.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Bruce E. Litow
    • 1
  • George I. Davida
    • 1
  1. 1.Electrical Engineering and Computer Science DepartmentUniversity of Wisconsin-MilwaukeeUSA

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