LAUTER, Kristin; ROBERT, Damien

doi:10.2140/obs.2013.1.437

Metadatos

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Licencia de uso del documento

LAUTER, Kristin
Cryptography group

ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]

Idioma

Communication dans un congrès

Este ítem está publicado en

ANTS X - Algorithmic Number Theory 2012, 2012-07-09, San Diego. 2013-11-14, vol. 1, p. 437-461

Mathematical Sciences Publisher

Resumen en inglés

We present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Br{ö}ker-Gruenewald-Lauter algorithm for the genus~2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for ''going up'' to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right isogeny class. Then we use the structure of the Shimura class group and the computation of $(\ell,\ell)$-isogenies to compute all isogenous maximal curves from an initial one. This is an extended version of the article published at ANTS~X.< Leer menos

Palabras clave en inglés

Class polynomials

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189638

DOI

http://dx.doi.org/10.2140/obs.2013.1.437

Proyecto europeo

Algorithmic Number Theory in Computer Science

Proyecto ANR

Espaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes - ANR-12-BS01-0010

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251