Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Chapitre D'ouvrage Année : 2016

Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations

Antoine Joux
Cécile Pierrot

Résumé

In this article, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. We modify Block Wiedemann algorithm and show that the contribution of these heavy columns can be made negligible compared to the one of the sparse part of the matrix. In particular, this eases the computation of discrete logarithms in medium and high characteristic finite fields, where nearly sparse matrices naturally appear.
Fichier principal
Vignette du fichier
Nearly Sparse Linear Algebra.pdf (380.75 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01154879 , version 1 (25-05-2015)
hal-01154879 , version 2 (25-08-2018)

Identifiants

Citer

Antoine Joux, Cécile Pierrot. Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations. Contemporary Developments in Finite Fields and Applications , 2016, 978-981-4719-27-8 ⟨10.1142/9789814719261_0008⟩. ⟨hal-01154879v1⟩
402 Consultations
592 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More