Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with $(\ell ,\ell ,\ell )$-isogenies

Abstract

We give an algorithm to compute $(\ell ,\ell ,\ell )$-isogenies from the Jacobians of genus three hyperelliptic curves to the Jacobians of non-hyperelliptic curves. An important application is to reduce the discrete logarithm problem in the Jacobian of a hyperelliptic curve to the corresponding problem in the Jacobian of a non-hyperelliptic curve.

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• Cover attacks for elliptic curves with prime order