Factoring polynomials over finite fields with Drinfeld modules

In the following, we describe a way of factoring polynomials in Fq[X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm. 1. Defining Fq[X ]-module structures with Drinfeld modules Throughout this paper we will denote A = Fq[X ], where q is a power of some prime p, and N ∈ A for the polynomial which is to be factored. Let B be an A-algebra coming from an Fq-linear ring homomorphism γ : A −→ B. (1) B{τ} is the skew-polynomial ring which consists as set of all finite expressions ∑ n≥0 bnτ , bi ∈ B, and B{τ} has addition and multiplication defined ∑