Distortion maps for genus two curves

Steven D.  Galbraith; Jordi Pujolàs; Christophe Ritzenthaler; Benjamin Smith

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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 curves pairings
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},
      note = {\url{https://eprint.iacr.org/2006/375}},
      url = {https://eprint.iacr.org/2006/375}
}