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. 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