Factoring in Skew-polynomial Rings over Finite Fields

Efficient algorithms are presented for factoring polynomials in the skew-polynomial ringF[x;σ], a non-commutative generalization of the usual ring of polynomialsF[x], whereFis a finite field and σ:F → Fis an automorphism (iterated Frobenius map). Applications include fast functional decomposition algorithms for a class of polynomials inF[x] whose decompositions are “wild” and previously thought to be difficult to compute.