International Association
for Cryptologic Research

Side-channel analysis recovers a secret by exploiting the key-dependent characteristics of the leakages. Practical techniques, such as Distance-of-Means analysis (DoM), Kolmogorov-Smirnov analysis (KSA) and Cramér-von Mises analysis (CvMA), provide valuable insights about the secret from the indirect perspectives of statistical moment and cumulative distribution function (CDF) respectively, circumventing the direct and costly estimation of leakage probability densities and therefore enabling wider applicability in practice. Though both the perspectives are informative, their relationships in the context of side-channel analysis remain unclear. In other words, the fundamental questions of "which one is better?'' and ``why and under what circumstances?" leave as open problems. In this paper, we introduce the probability-probability (PP) plot in statistics as a common framework for explaining the mathematical foundations of CDF-based techniques, which facilitates an intuitive understanding of different variant strategies. Then, inspired by the growth pattern of the PP curve, we propose a novel distinguisher based on the famous Mann-Kendall test, where measurements are managed with ordinality and nominality. This goodness-of-fit test checks whether a key-dependent binary sequence originates from a random binomial distribution, by efficiently searching potential label clusters. Finally, we explore the symmetry and dual counterpart of CDF in mathematics, introducing the quantile-quantile (QQ) plot and develop an interesting technique based on the inverse cumulative distribution function (ICDF). We present a general discussion of its bridging role, regarding detail capture as well as signal-to-noise ratio (SNR). On this basis, we establish the relationships among moment-based, ICDF-based, and CDF-based techniques, which additionally allows for bounding the security level of the CDF-based techniques using well-established metrics that are originally proposed for evaluating the traditional moment-based family. Experiments across various settings validate our theoretical findings and demonstrate the effectiveness of the two proposed distinguishers.