Spatial Correlation in Weak Physical Unclonable Functions: A Comprehensive Overview

Physical Unclonable Functions (PUFs) are increasingly used in the process of securing applications. For this purpose, it is crucial that the PUF satisfies all the required properties adequately, including Unpredictability. An important aspect of Unpredictability is Randomness, which includes being free of spatial correlation effects. However, most methods for assessing randomness are not capable of detecting correlation, such that this aspect is often ignored. This work summarises the current literature to shed more light on the topic of analysing spatial correlation in weak PUFs, and evaluates the various methods proposed in the literature for detecting such effects. Additionally, the spatial correlation of a Dynamic Random Access Memory (DRAM) decay-based PUF implemented on the DRAM of a Raspberry Pi board, as well as that of a Carbon-NanoTube-based PUF (CNT-PUF), are examined, using, for the first time in the context of PUFs, not only other well-known metrics proposed in the relevant literature, but also the Getis-Ord G metric. Finally, a mitigation technique against attacks based on spatial auto-correlation is proposed and its effective application to PUF responses is discussed.