  We study relativistic particles undergoing surfing acceleration at
perpendicular shocks. We assume that particles undergo diffusion in the
component of momentum perpendicular to the shock plane due to moderate
fluctuations in the shock electric and magnetic fields. We show that dN/dE, the
number of surfing-accelerated particles per unit energy, attains a power-law
form, dN/dE \propto E^{-b}. We calculate b analytically in the limit of weak
momentum diffusion, and use Monte Carlo test-particle calculations to evaluate
b in the weak, moderate, and strong momentum-diffusion limits.
