ENGE, Andreas; THOMÉ, Emmanuel

doi:10.1080/10586458.2013.878675

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

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

THOMÉ, Emmanuel
Cryptology, Arithmetic: Hardware and Software [CARAMEL]

Idioma

Article de revue

Este ítem está publicado en

Experimental Mathematics. 2014, vol. 23, n° 2, p. 129-145

Taylor & Francis

Resumen en inglés

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 20016.< Leer menos

Palabras clave en inglés

Number theory

Complex Multiplication

Theta functions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189518

DOI

http://dx.doi.org/10.1080/10586458.2013.878675

Proyecto europeo

Algorithmic Number Theory in Computer Science

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251