  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.
