ENGE, Andreas; MORAIN, François

doi:10.4064/aa164-4-1

Métadonnées

Licence d’utilisation du document

ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

MORAIN, François
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]

Langue

Article de revue

Ce document a été publié dans

Acta Arithmetica. 2014, vol. 164, n° 4, p. 309-341

Instytut Matematyczny PAN

Résumé en anglais

A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power $\w_N^e$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $\w_N(z)$ and $j(z)$. Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use.< Réduire

Mots clés en anglais

Weber function

complex multiplication

class invariant

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189502

DOI

http://dx.doi.org/10.4064/aa164-4-1

Projet Européen

Algorithmic Number Theory in Computer Science

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251