1Department of Mathematics [Auckland] (Department of Mathematics University of Auckland Private Bag 92019 Auckland Mail Centre Auckland 1142 NEW ZEALAND - New Zealand)
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.
Steven Galbraith, Christophe Ritzenthaler, Jordi Pujolas, Benjamin Smith. Distortion maps for supersingular genus two curves. Journal of Mathematical Cryptology, De Gruyter, 2009, 3 (1), pp.1-18. ⟨10.1515/JMC.2009.001⟩. ⟨inria-00537877⟩