Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field
Combinatorics
2020-01-13 v1
Abstract
We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field F_q of q elements when the highest-degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f which are relatively prime with g and for the average degree of gcd(g,f). The accuracy of our estimates is confirmed by practical experiments. We also exhibit asymptotically optimal bounds for the average-case complexity of the Euclidean algorithm applied to pairs (g,f) as above.
Cite
@article{arxiv.2001.03222,
title = {Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field},
author = {Nardo Giménez and Guillermo Matera and Mariana Pérez and Melina Privitelli},
journal= {arXiv preprint arXiv:2001.03222},
year = {2020}
}
Comments
20 pages