Distortion maps for supersingular genus two curves
Galbraith Steven D., Pujolàs Jordi, Ritzenthaler Christophe and 1 more
Journal of Mathematical Cryptology · 2009
doi:10.1515/jmc.2009.001 (opens in a new tab)
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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.
Abstract licence: CC BY
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