Construction of secure random curves of genus 2 over prime fields

Abstract : For counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof's algorithm. We present several improvements on the algorithms described by Gaudry and Harley in 2000. In particular we rebuild the symmetry that had been broken by the use of Cantor's division polynomials and design a faster division by 2 and a division by 3. Combined with the algorithm by Matsuo, Chao and Tsujii, our implementation can count the points on a Jacobian of size 164 bits within about one week on a PC.
Type de document :
Communication dans un congrès
Christian Cachin and Jan Camenisch. Eurocrypt, 2004, Interlaken, Switzerland. Springer Verlag, 3027, pp.239-256, 2004, LNCS. 〈10.1007/978-3-540-24676-3_15〉
Liste complète des métadonnées

https://hal.inria.fr/inria-00514121
Contributeur : Pierrick Gaudry <>
Soumis le : mercredi 1 septembre 2010 - 12:03:16
Dernière modification le : jeudi 10 mai 2018 - 02:06:54
Document(s) archivé(s) le : jeudi 2 décembre 2010 - 02:44:37

Fichier

secureg2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Pierrick Gaudry, Eric Schost. Construction of secure random curves of genus 2 over prime fields. Christian Cachin and Jan Camenisch. Eurocrypt, 2004, Interlaken, Switzerland. Springer Verlag, 3027, pp.239-256, 2004, LNCS. 〈10.1007/978-3-540-24676-3_15〉. 〈inria-00514121〉

Partager

Métriques

Consultations de la notice

177

Téléchargements de fichiers

80