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