  The low flux of the ultra-high energy cosmic rays (UHECR) at the highest
energies provides a challenge to answer the long standing question about their
origin and nature. A significant increase in the number of detected UHECR is
expected to be achieved by employing Earth's moon as detector, and search for
short radio pulses that are emitted when a particle interacts in the lunar
rock. Observation of these short pulses with current and future radio
telescopes also allows to search for the even lower fluxes of neutrinos with
energies above $10^{22}$ eV, that are predicted in certain
Grand-Unifying-Theories (GUTs), and e.g. models for super-heavy dark matter
(SHDM). In this contribution we present the initial design for such a search
with the LOFAR radio telescope.
