Giesbrecht's algorithm, the HFE cryptosystem and Ore's p^s-polynomials [article]

Robert S. Coulter, George Havas, Marie Henderson
<span title="2016-11-14">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.04479v1">arXiv:1611.04479v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3c23gi6vsbhhxbhoxu5dxzfg4a">fatcat:3c23gi6vsbhhxbhoxu5dxzfg4a</a> </span>
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