Cryptology ePrint Archive: Report 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 $2$.

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 format(s): 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.

Short URL: ia.cr/2006/375

[ Cryptology ePrint archive ]