Several proteins have been shown to undergo 'one-dimensional' diffusion along the surface of microtubules. Diffusion is thought to enhance the rate of targeting of proteins to the microtubule end for the depolymerizing kinesin-13 and the polymerase XMAP215, or to increase the processivity of kinesin-1 and dynein. According to the Einstein-Smolukowski relation, the diffusion coefficient, D, is related to the friction coefficient, gamma, according to D = kT/gamma. This relation, however, has not been experimentally tested for individual bio-molecules. We measured both the diffusional and frictional properties of single yeast kinesin-8 motor proteins, Kip3p, interacting with microtubule filaments in the ADP state. Using single molecule fluorescence we found that that the diffusion coefficient was 5400±1400 nm2/s with an average lifetime on the microtubule lattice of 8 s. Using an optical trap to drag a microsphere coated with Kip3p along microtubules, we measured a single molecule drag coefficient of 790±230 nNs/m at low speeds. Thus we verified the Einstein-Smolukowski relation. For larger speeds and drag forces, we measured a non-linear force-velocity relation which was well fit by a model in which Kip3p is diffusing in a periodic potential with an 8-nm periodicity and a barrier height between binding sites of 14±2 kT. This finding of an 8-nm periodicity is supported by an analysis of the positional fluctuations. Our measurements are a step towards resolving the molecular mechanism underlying protein friction an important parameter for active protein locomotion limiting the efficiency.