Complexity analysis of challenges and speckle patterns in an Optical Physical Unclonable Function

Speckle patterns, arising from the interference of coherent wave fronts scattered by disordered materials, serve as the basis for Optical Physical Unclonable Functions (Optical PUF), offering inherent randomness crucial for generating secure cryptographic keys. This paper investigates the universal properties of speckle images through an analysis of their complexity using a multiscale entropy-based methodology. Utilizing an experimental setup simulating Optical PUFs, eight sets of uncorrelated challenges produce speckle patterns meeting contemporary literature specifications. The Pearson’s Cross-Correlation Coefficient and the cross-correlation function are used to assess the similarity between the speckle patterns within each individual set, by calculating these measures for all possible pairs of corresponding patterns. The entropy-based complexity analysis of these patterns is found to be sensitive to their grain size while elucidating in a multiscale fashion the entropy footprint of their short and long-range correlations. Finally, it is shown that the presence of grains in the speckle patterns determines their complexity, while a kind of duality between the challenges and the produced speckle patterns is highlighted.