Paper 2006/375
Distortion maps for genus two curves
Steven D. Galbraith, Jordi Pujolàs, 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
-
CC BY
BibTeX
@misc{cryptoeprint:2006/375,
author = {Steven D. Galbraith and Jordi Pujolàs and Christophe Ritzenthaler and Benjamin Smith},
title = {Distortion maps for genus two curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2006/375},
year = {2006},
url = {https://eprint.iacr.org/2006/375}
}