Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with $(\ell,\ell,\ell)$-isogenies
This addresses cryptographic security for users of hyperelliptic curve cryptosystems by potentially weakening them through isogeny-based attacks.
The paper tackles the problem of computing (ℓ,ℓ,ℓ)-isogenies from Jacobians of genus 3 hyperelliptic curves to non-hyperelliptic curves, resulting in an algorithm that reduces the discrete logarithm problem in hyperelliptic Jacobians to non-hyperelliptic ones.
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.