Fast construction of irreducible polynomials over finite fields - Archive ouverte HAL Access content directly
Journal Articles Israel Journal of Mathematics Year : 2013

Fast construction of irreducible polynomials over finite fields

Abstract

We present a randomized algorithm that on input a finite field $K$ with $q$ elements and a positive integer $d$ outputs a degree $d$ irreducible polynomial in $K[x]$. The running time is $d^{1+o(1)} \times (\log q)^{5+o(1)}$ elementary operations. The $o(1)$ in $d^{1+o(1)}$ is a function of $d$ that tends to zero when $d$ tends to infinity. And the $o(1)$ in $(\log q)^{5+o(1)}$ is a function of $q$ that tends to zero when $q$ tends to infinity. In particular, the complexity is quasi-linear in the degree $d$.
Fichier principal
Vignette du fichier
0905.1642v3.pdf (288.98 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00456456 , version 1 (09-10-2015)

Identifiers

Cite

Jean-Marc Couveignes, Reynald Lercier. Fast construction of irreducible polynomials over finite fields. Israel Journal of Mathematics, 2013, 194 (1), pp.77-105. ⟨10.1007/s11856-012-0070-8⟩. ⟨hal-00456456⟩
468 View
1175 Download

Altmetric

Share

Gmail Facebook X LinkedIn More