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

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Mathematical Cryptology
Volume	3
Issue number	1
DOIs	https://doi.org/10.1515/JMC.2009.001
Publication status	Published - 1 May 2009

Keywords

Distortion maps
Hyperelliptic curve cryptography
Pairings
Supersingular curves

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10.1515/JMC.2009.001

Cite this

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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.",

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KW - Distortion maps

KW - Hyperelliptic curve cryptography

KW - Pairings

KW - Supersingular curves

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Distortion maps for supersingular genus two curves

Abstract

Keywords

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