Cryptology ePrint Archive: Report 2006/375
Distortion maps for genus two curves
Steven D. Galbraith and Jordi Pujol\`as and Christophe Ritzenthaler and Benjamin Smith
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 $2$.
Category / Keywords: public-key cryptography / hyperelliptic curves, pairings
Date: received 29 Oct 2006, last revised 5 Nov 2006
Contact author: Steven Galbraith at rhul ac uk
Available formats: PDF | BibTeX Citation
Note: This paper is the improved and extended version of the paper with the same title by Galbraith and Pujolas which appeared in:
R. Cramer and T. Okamoto (eds.), Proceedings of a workshop on Mathematical Problems and Techniques in Cryptology, CRM Barcelona (2005) 46--58.
Version: 20061105:113524 (All versions of this report)
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