  We report on a recent implementation of Giesbrecht's algorithm for factoring
polynomials in a skew-polynomial ring. We also discuss the equivalence between
factoring polynomials in a skew-polynomial ring and decomposing
$p^s$-polynomials over a finite field, and how Giesbrecht's algorithm is
outlined in some detail by Ore in the 1930's. We end with some observations on
the security of the Hidden Field Equation (HFE) cryptosystem, where
$p$-polynomials play a central role.
