We propose a method to calculate the ideal shear strength tau of two surfaces in contact by ab initio calculations. This quantity and the work of adhesion gamma are the interfacial parameters usually derived from tip-based friction force measurements. We consider diamond interfaces and quantitatively evaluate the effects of surface orientation and passivation. We find that in the case of fully passivated interfaces, gamma is not affected by the orientation and the alignment of the surfaces in contact. On the contrary, tau does show a dependence on the atomic-scale roughness of the interface. The surface termination has a major impact on the tribological properties of diamond. The presence of dangling bonds, even at concentrations low enough to prevent the formation of interfacial C-C bonds, causes an increase in the resistance to sliding by 2 orders of magnitude with respect to the fully hydrogenated case. We discuss our findings in relation to experimental observations.