Complexity Assessment of Analog and Digital Security Primitives Signals Using the Disentropy of Autocorrelation

The study of regularity in signals can be of great importance, typically in medicine to analyse electrocardiogram (ECG) or electromyography (EMG) signals, but also in climate studies, finance or security. In this work we focus on security primitives such as Physical Unclonable Functions (PUFs) or Pseudo-Random Number Generators (PRNGs). Such primitives must have a high level of complexity or entropy in their responses to guarantee enough security for their applications. There are several ways of assessing the complexity of their responses, especially in the binary domain. With the development of analog PUFs such as optical (photonic) PUFs, it would be useful to be able to assess their complexity in the analog domain when designing them, for example, before converting analog signals into binary. In this numerical study, we decided to explore the potential of the disentropy of autocorrelation as a measure of complexity for security primitives as PUFs, TRNGs or PRNGs with analog output or responses. We compare this metric to others used to assess regularities in analog signals such as Approximate Entropy (ApEn) and Fuzzy Entropy (FuzEn). We show that the disentropy of autocorrelation is able to differentiate between well-known PRNGs and non-optimised or bad PRNGs in the analog and binary domain with a better contrast than ApEn and FuzEn. Then, we show that the disentropy of autocorrelation is able to detect small patterns injected in PUFs responses.