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 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. Next, we show that the disentropy of autocorrelation is able to detect small patterns injected in PUFs responses and then we applied it to photonic PUFs simulations.

翻译：信号规律性的研究具有重要意义，典型应用包括医学领域的心电图（ECG）或肌电图（EMG）信号分析，以及气候研究、金融或安全领域。本文重点研究物理不可克隆函数（PUF）和伪随机数发生器（PRNG）等安全基元。这些基元必须在其响应中具有高复杂度或高熵值，才能为实际应用提供足够的安全性。目前已存在多种评估其响应复杂度的方法，尤其是在二进制域中。随着光学（光子）PUF等模拟PUF的发展，在信号转换（如将模拟信号转化为二进制信号）之前，能够评估其在模拟域的复杂度将十分有用。在本数值研究中，我们探索了自相关去熵作为模拟输出/响应式PUF或PRNG等安全基元复杂度度量的潜力。我们将该度量与用于评估模拟信号规律性的近似熵（ApEn）和模糊熵（FuzEn）等其他度量进行了比较。结果表明，在模拟域和二进制域中，自相关去熵能够更好地区分已知的PRNG与未经优化的或劣质PRNG，其对比度优于ApEn和FuzEn。此外，我们还展示了自相关去熵能够检测注入PUF响应中的微小模式，并将其应用于光子PUF的仿真。