High-order harmonic generation due to the interaction of a short ultrarelativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultrarelativistic similarity theory we show that the high-order harmonic spectrum is universal, i.e., it does not depend on the interaction details. The spectrum includes the power-law part In proportional variantion for n(-8/3) for n < sqrt of 8 alpha gammamax3, followed by exponential decay. Here gammamax is the largest relativistic gamma factor of the plasma surface and alpha is the second derivative of the surface velocity at this moment. The high-order harmonic cutoff at proportional variantion gammamax3 is parametrically larger than the 4gammamax2 predicted by the simple "oscillating mirror" model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic gamma factor of the plasma surface. These spikes define the high-order harmonic spectrum and lead to attosecond pulses in the reflected radiation.