Deterministic Encoding and Hashing to Odd Hyperelliptic Curves

Pierre-Alain Fouque 1, 2, 3 Mehdi Tibouchi 3
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : In this paper we propose a very simple and efficient encoding function from Fq to points of a hyperelliptic curve over Fq of the form H : y2 = f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of Fq -rational points on H . This makes it easy to construct well-behaved hash functions to the Jacobian J of H , as well as injective maps to J (Fq ) which can be used to encode scalars for such applications as ElGamal encryption. The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux?s supersingular elliptic curves.
Type de document :
Communication dans un congrès
Marc Joye and Atsuko Miyaji and Akira Otsuka. Pairing-Based Cryptography - Pairing 2010 - 4th International Conference, 2010, Yamanaka Hot Spring, Japan. Springer, 6487, pp.265-277, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-17455-1_17〉
Liste complète des métadonnées

Littérature citée [26 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00556678
Contributeur : Pierre-Alain Fouque <>
Soumis le : lundi 17 janvier 2011 - 15:36:47
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : lundi 18 avril 2011 - 02:58:50

Fichier

pairing10.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Pierre-Alain Fouque, Mehdi Tibouchi. Deterministic Encoding and Hashing to Odd Hyperelliptic Curves. Marc Joye and Atsuko Miyaji and Akira Otsuka. Pairing-Based Cryptography - Pairing 2010 - 4th International Conference, 2010, Yamanaka Hot Spring, Japan. Springer, 6487, pp.265-277, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-17455-1_17〉. 〈inria-00556678〉

Partager

Métriques

Consultations de la notice

195

Téléchargements de fichiers

461