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. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.
Received: 2006-11-30
Revised: 2009-01-08
Published Online: 2009-06-10
Published in Print: 2009-May
© de Gruyter 2009
