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Distortion maps for supersingular genus two curves

Steven Galbraith 1 Christophe Ritzenthaler 2 Jordi Pujolas 3 Benjamin Smith 4 
1 Department of Mathematics [Auckland]
2 IML - Institut de mathématiques de Luminy
3 Departament d'Informatica i Enginyeria Industrial
4 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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 and we give several examples in genus 2.
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https://hal.inria.fr/inria-00537877
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Submitted on : Friday, November 19, 2010 - 3:45:14 PM
Last modification on : Friday, February 4, 2022 - 3:23:29 AM

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Steven Galbraith, Christophe Ritzenthaler, Jordi Pujolas, Benjamin Smith. Distortion maps for supersingular genus two curves. Journal of Mathematical Cryptology, De Gruyter, 2009, 3 (1), pp.1-18. ⟨10.1515/JMC.2009.001⟩. ⟨inria-00537877⟩

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