Estimating the secrecy-rate of Physical Unclonable Functions with the context-tree weighting method

We propose methods to estimate the secrecy-rate of fuzzy sources (e.g. biometrics and Physical Unclonable Functions (PUFs)) using context-tree weighting (CTW, Willems et al. [1995]). In this paper we focus on PUFs. In order to show that our estimates are realistic we first generalize Maurer's [1993] result to the ergodic case. Then we focus on the fact that the entropy of a stationary two-dimensional structure is a limit of a series of conditional entropies, a result by Anastassiou and Sakrison (1982). We extend this result to the conditional entropy of one two-dimensional structure given another one. Finally we show that the general CTW-method approaches the source entropy also in the two-dimensional stationary case. We further extend this result to the two-dimensional conditional entropy. Based on the obtained results we do several measurements on (our) optical PUFs. These measurements allow us to conclude that a secrecy-rate of 0.3 bit/location is possible.