Edwards curves and CM curves - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

Edwards curves and CM curves


Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their j-invariant, a problematic that arises from using curves with complex multiplication, for instance. We add to the catalogue the links with Kubert parameterizations of X0(2) and X0(4). We classify CM curves that admit an Edwards or Montgomery form over a finite field, and justify the use of isogenous curves when needed.
Fichier principal
Vignette du fichier
edwards.pdf (173.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00375427 , version 1 (14-04-2009)


  • HAL Id : inria-00375427 , version 1
  • ARXIV : 0904.2243


François Morain. Edwards curves and CM curves. 2009. ⟨inria-00375427⟩
599 View
529 Download



Gmail Facebook Twitter LinkedIn More