A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic

Razvan Barbulescu 1 Pierrick Gaudry 1 Antoine Joux 2, 3 Emmanuel Thomé 1
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 Chaire de cryptologie
UPMC - Université Pierre et Marie Curie - Paris 6
3 CryptoExperts
Abstract : In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main result gives a quasi-polynomial heuristic complexity for the discrete logarithm problem in finite field of small characteristic. By quasi-polynomial, we mean a complexity of type $n^{O(\log n)}$ where $n$ is the bit-size of the cardinality of the finite field. Such a complexity is smaller than any $L(\varepsilon)$ for $\epsilon>0$. It remains super-polynomial in the size of the input, but offers a major asymptotic improvement compared to $L(1/4+o(1))$.
Type de document :
Communication dans un congrès
Phong Q. Nguyen and Elisabeth Oswald. Eurocrypt 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.1-16, 2014, Advances in Cryptology - EUROCRYPT 2014. 〈10.1007/978-3-642-55220-5_1〉
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-00835446
Contributeur : Emmanuel Thomé <>
Soumis le : lundi 25 novembre 2013 - 21:36:59
Dernière modification le : mercredi 21 mars 2018 - 18:57:57
Document(s) archivé(s) le : mercredi 26 février 2014 - 08:35:09

Fichiers

article.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INRIA | INSMI | UPMC | UNIV-LORRAINE | LORIA-ALGO | LORIA

Citation

Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé. A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. Phong Q. Nguyen and Elisabeth Oswald. Eurocrypt 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.1-16, 2014, Advances in Cryptology - EUROCRYPT 2014. 〈10.1007/978-3-642-55220-5_1〉. 〈hal-00835446v2〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

4219

Téléchargements de fichiers

937

Contact


archive-ouverte@inria.fr