LUBICZ, David; ROBERT, Damien

doi:10.1016/j.jsc.2014.08.001

Metadatos

Licencia de uso del documento

LUBICZ, David
Institut de Recherche Mathématique de Rennes [IRMAR]

ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]

Idioma

Article de revue

Este ítem está publicado en

Journal of Symbolic Computation. 2015, vol. 67, p. 68-92

Elsevier

Resumen en inglés

In this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten the loop of the Weil and Tate pairings algorithms. This extend preceding results about ate and twisted ate pairings to all abelian varieties. Then building upon the two preceding ingredients, we obtain a variant of optimal pairings on abelian varieties. Finally, by introducing new addition formulas, we explain how to compute optimal pairings on Kummer varieties. We compare in term of performance the resulting algorithms to the algorithms already known in the genus one and two case.< Leer menos

Palabras clave en inglés

Pairings

Abelian varieties

Cryptography

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189644

DOI

http://dx.doi.org/10.1016/j.jsc.2014.08.001

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
SIM et théorie des couplages pour la sécurité de l'information et des communications - ANR-12-INSE-0014
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251