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Distortion maps for genus two curves

Steven D. Galbraith·Jordi Pujolàs·Christophe Ritzenthaler·Benjamin Smith
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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 and we construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).

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Steven D. Galbraith, Jordi Pujolàs, Christophe Ritzenthaler, Benjamin Smith. 2006-11-15. Distortion maps for genus two curves. https://arxiv.org/abs/math/0611471

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