The geometry of flex tangents to a cubic curve and its parameterizations

Jean-Marc Couveignes (1, 2, 3, 4) , Jean-Gabriel Kammerer (5, 6)

1 LFANT - Lithe and fast algorithmic number theory
2 IMB - Institut de Mathématiques de Bordeaux
3 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 IRMAR - Institut de Recherche Mathématique de Rennes
6 DGA.MI - DGA Maîtrise de l'information

We show how the study of the geometry of the nine flex tangents to a cubic produces many pseudo-parameterizations, including the ones given by Icart, Kammerer, Lercier, Renault and Farashahi.

Mots clés: hashing into elliptic curves; encoding; cubic curves; parameterizations

Domaines: Géométrie algébrique [math.AG]; Cryptographie et sécurité [cs.CR]; Bibliothèque électronique [cs.DL]

Jean-Marc Couveignes, Jean-Gabriel Kammerer. The geometry of flex tangents to a cubic curve and its parameterizations. Journal of Symbolic Computation, 2012, 47 (3), pp.266 - 281. ⟨10.1016/j.jsc.2011.11.003⟩. ⟨hal-01104612⟩