Distortion maps for genus two curves

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

Distortion maps for genus two curves

Authors

Galbraith, Steven D.

Pujolàs, Jordi

Ritzenthaler, Christophe

Smith, Benjamin

Description

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 construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).
16 pages