Construction of resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal non-linearity

Resilient substitution boxes (S-boxes) with high non-linearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimisation is regarded as a difficult task. In this study, the authors provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal non-linearity for a larger number of output bits m than previously known. This is the first time that the non-linearity bound 2 n−1 − 2 n/2 of resilient (n,m) S-boxes, where n and m denote the number of the input and output bits, respectively, has been exceeded for m>⌊n/4⌋. Thus, resilient S-boxes with extremely high non-linearity and a larger output space compared with other design methods have been obtained.