Constructions of correlation immnue S-boxes with high nonlinearity
Yanhan Ji, Zhuo Ma, Luyang Li, Yujuan Sun · Journal of Information and Intelligence · 2024
S-boxes play a central role role in the design of symmetric cipher schemes. For stream cipher applications, a S-box should satisfy several criteria such as high nonlinearity, balanceness, correlation immunity, and so on. In this paper, by using disjoint linear codes, a class of S-boxes possessing high nonlinearity and 1st-order correlation immunity is given. It is shown that the constructed correlation immune S-boxes can possess currently best known nonlinearity, which is confirmed by the example 1st-order correlation immune (12, 3) S-box with nonlinearity 2000. In addition, two other frameworks concerning the criteria of balanced and resiliency are obtained respectively.