Addition law structure of elliptic curves - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Number Theory Année : 2011

Addition law structure of elliptic curves

David Kohel

Résumé

The study of alternative models for elliptic curves has found recent interest from cryptographic applications, once it was recognized that such models provide more efficiently computable algorithms for the group law than the standard Weierstrass model. Examples of such models arise via symmetries induced by a rational torsion structure. We analyze the module structure of the space of sections of the addition morphisms, determine explicit dimension formulas for the spaces of sections and their eigenspaces under the action of torsion groups, and apply this to specific models of elliptic curves with parametrized torsion subgroups.
Fichier principal
Vignette du fichier
ec_group_law.pdf (219.47 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01257328 , version 1 (16-01-2016)

Identifiants

Citer

David Kohel. Addition law structure of elliptic curves. Journal of Number Theory, 2011, 131 (5), pp.894-919. ⟨10.1016/j.jnt.2010.12.001⟩. ⟨hal-01257328⟩
65 Consultations
241 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More