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.