Distortion maps for genus two curves

Details Distortion maps for genus two curves Distortion maps for genus two curves

2006-11-15

arxiv.org/abs/math/0611471v1

Mathematics

Number Theory

16 pages

Scientific paper

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).

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