# Challenging Assumptions of Normality in AES s-Box Configurations under Side-Channel Analysis
## 1 Introduction  
Computational systems all share at least one component, the consumption of electricity to facilitate computational tasks. When observed, this power consumption can be leveraged to exfiltrate information, leading to a violation of the confidentiality of the victimized system. Two distinct variants, leakage exploitation and leakage detection, serve as pillars of this subfield, referenced as power-based Side-Channel Analysis (SCA). In the twenty-four years since the first presentation by [PERSON] et al. [1], SCA has experienced a renaissance of development. Novel strategies for power-based cryptanalysis have continued to develop over the years, with targets focusing on both symmetric encryption [1; 2; 3] and asymmetric encryption [4] algorithms. Through power usage, it has readily been demonstrated that valid attack vectors may be leveraged against properly instrumented low-power embedded systems running cryptographic algorithms. While the world ushers in the age of quantum-resistant cryptography, low-power embedded systems, such as Internet of Things (IoT) devices, remain an attractive and lucrative target for adversaries to potentially exploit. In general, SCA seeks to obtain the secret key used for cryptographic operations. For example, the Advanced Encryption Standard (AES) [5] is still widely used in the embeddedsystems space. One common method for exploring SCA is to replicate known attacks on AES, which traditionally focus on examining what changes occur during the _SubBytes_ step of encryption [5, 6]. This step applies a nonlinear substitution to replace the input byte with an output byte corresponding to a set lookup table, commonly referred to as a substitution-box (s-box). It is important to note that this style of attack vector formation is typical when working within the realm of SCA. Valid cryptanalysis often targets a critical component of an algorithm, otherwise known as a subprocess. While both Differential Power Analysis (DPA) [1] and Correlation Power Analysis (CPA) [7] facilitate strong attack vectors, modern tooling has sought to bring more powerful analytics to fruition. Currently, the state-of-the-art techniques focus on Test Vector Leakage Assessment (TVLA), a versatile method used to evaluate whether there is information leakage under SCA; it has been invaluable for researchers in assessing whether power-based leakage constitutes a viable attack vector. TVLA utilizes [PERSON]'s \(t\)-test to determine whether there are meaningful differences in the means between two groups of collected data. When leakage of information has been detected, traditional side-channel attacks can then be leveraged to recover a key from the collected power usage data associated with a cryptographic operation. This collected data is often referred to as a power trace. Focusing on key recovery has largely relied on statistical tests that assume power trace data is derived from a normal distribution. This assumption is wide-spread, affecting any work utilizing or building upon CPA or TVLA. Such an assumption not only limits the utility of classical SCA, but to a large extent, it may also be inappropriate. This body of work focuses on challenging the assumption of normality in power trace data by using TVLA on nine unique s-box configurations as the guiding framework. Each of these configurations introduce unique nonlinearity in their associated power trace data, giving a reliable, varied dataset. Using this collected data, the assumption of normality is assessed using the Shapiro-Wilk and Kolmogorov-Smirnov tests. From a statistical standpoint, the Wilcoxon Signed-Rank and Kruskal-Wallis tests are presented as potentially statistical alternatives to [PERSON]'s \(t\)-test.