Entropy Estimation for Optical PUFs Based on Context-Tree Weighting Methods

In this chapter we discuss estimation of the secrecy rate of fuzzy sources- more specifically of optical physical unclonable functions (PUFs)-using context-tree weighting (CTW) methods [291]. We show that the entropy of a stationary 2-D source is a limit of a series of conditional entropies [6] and extend this result to the conditional entropy of one 2-D source given another one. Furthermore, we show that the general CTW-method approaches the source entropy also in the 2-D stationary case. Moreover, we generalize Maurer's result [196] to the ergodic case, thus showing that we get realistic estimates of the achievable secrecy rate. Finally, we use these results to estimate the secrecy rate of speckle patterns from optical PUFs.