Spatial Correlation Analysis on Physical Unclonable Functions

The evaluation of the quality of physical unclonable functions (PUFs) is still under research. Most state-of-the-art metrics are found to measure only bias, while correlations, e.g., within the PUF response of a single device, remain unnoticed. In this paper, we introduce spatial autocorrelation analysis (SPACA), which is used in other fields of research, as a method to reveal correlations in the response of single-challenge PUFs. The presented statistics-Moran's I, Geary's c, and Join Count statistic-can be used to test the quality of an implementation using a set of sample devices as well as monitor ongoing production. Their results are also important for selecting an appropriate post-processing of the raw PUF response. Experiments on data sets from three different PUF implementations on field-programmable gate array and application-specific integrated circuit using SPACA show the capabilities of the introduced statistics. An efficient implementation of SPACA in MATLAB was developed to conduct the experiments. We discuss how SPACA can be used in practical testing and suggest to consider SPACA for a future test suite for PUFs.