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Paper 2006/375

Distortion maps for genus two curves

Steven D. Galbraith and Jordi Pujolàs 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 $2$.

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.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
hyperelliptic curvespairings
Contact author(s)
Steven Galbraith @ rhul ac uk
History
2006-11-05: revised
2006-11-03: received
See all versions
Short URL
https://ia.cr/2006/375
License
Creative Commons Attribution
CC BY
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