Distortion maps for genus two curves

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

Paper 2006/375 Original: eprint.iacr.org/2006/375 ↗

Distortion maps for genus two curves

Steven D. Galbraith

Jordi Pujolàs

Christophe Ritzenthaler

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 $2$.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2006-11-05: last updated; 2006-11-03: published
Short URL: https://ia.cr/2006/375
License: https://creativecommons.org/licenses/by/4.0/

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}
}