Laser surface authentication (LSA) is a technique for authenticating optically rough surfaces based on the intensity of diffusely scattered light. The degradation in the LSA signature over linear and rotational displacement is examined. Randomly roughened glass surfaces with roughness amplitudes ranging from $0.4\mu \mathrm{m}\text{to}3\mu \mathrm{m}$ and correlation lengths from $16\mu \mathrm{m}\text{to}45\mu \mathrm{m}$ are examined experimentally, showing that the average size of the surface feature has a negligible impact on the rate of LSA signature degradation. The average size of the surface features is shown to have a greater effect on the fractional intensity of the variations in diffuse light and on the quality of LSA signature match.