Distortion maps for supersingular genus two curves

Steven D. Galbraith; Jordi Pujolàs; Christophe Ritzenthaler; Benjamin Smith

doi:10.1515/JMC.2009.001

Distortion maps for supersingular genus two curves

Steven D. Galbraith
, Jordi Pujolàs
, Christophe Ritzenthaler
, Benjamin Smith

Royal Holloway University of London
IRBLleida-University of Lleida
Université de Provence

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

10 Citations (Scopus)

Résumé

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

langue originale	Anglais
Pages (de - à)	1-18
Nombre de pages	18
journal	Journal of Mathematical Cryptology
Volume	3
Numéro de publication	1
Les DOIs	https://doi.org/10.1515/JMC.2009.001
état	Publié - 1 mai 2009

Accès au document

10.1515/JMC.2009.001

Contient cette citation

@article{c74a97e7e63b4a5daa3f08ca3d0213ec,

title = "Distortion maps for supersingular genus two curves",

abstract = "Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.",

keywords = "Distortion maps, Hyperelliptic curve cryptography, Pairings, Supersingular curves",

author = "Galbraith, \{Steven D.\} and Jordi Pujol{\`a}s and Christophe Ritzenthaler and Benjamin Smith",

year = "2009",

month = may,

day = "1",

doi = "10.1515/JMC.2009.001",

language = "English",

volume = "3",

pages = "1--18",

journal = "Journal of Mathematical Cryptology",

issn = "1862-2976",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Distortion maps for supersingular genus two curves

AU - Galbraith, Steven D.

AU - Pujolàs, Jordi

AU - Ritzenthaler, Christophe

AU - Smith, Benjamin

PY - 2009/5/1

Y1 - 2009/5/1

N2 - Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

AB - Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

KW - Distortion maps

KW - Hyperelliptic curve cryptography

KW - Pairings

KW - Supersingular curves

U2 - 10.1515/JMC.2009.001

DO - 10.1515/JMC.2009.001

M3 - Article

AN - SCOPUS:84863393814

SN - 1862-2976

VL - 3

SP - 1

EP - 18

JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

IS - 1

ER -

Distortion maps for supersingular genus two curves

Résumé

Accès au document

Empreinte digitale

Contient cette citation