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The Cantor-Zassenhaus Method for Factoring Polynomials over Finite Fields

Wade Combs

Wade Combs / Eastern Kentucky University

Various strategies exist for factoring polynomials whose coefficients come from finite fields.  In this presentation, we will describe the Cantor-Zassenhaus factoring method, which is broken up into two stages: 1) Distinct Degree Factorization (DDF) and 2) Equal Degree Factorization (EDF). We will give a deterministic algorithm for DDF and a probabilistic algorithm for EDF.  We will then conclude by considering a few specialized mathematical applications of our factoring tools. in particular, we will present a root finding process for polynomials over finite fields and a test for irreducibility.

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