Giesbrecht's algorithm, the HFE cryptosystem and Ore's $p^s$-polynomials
Commutative Algebra
2016-11-15 v1
Abstract
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 -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 -polynomials play a central role.
Cite
@article{arxiv.1611.04479,
title = {Giesbrecht's algorithm, the HFE cryptosystem and Ore's $p^s$-polynomials},
author = {Robert S. Coulter and George Havas and Marie Henderson},
journal= {arXiv preprint arXiv:1611.04479},
year = {2016}
}