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Construction of resilient S-boxes with higherdimensional vectorial outputs and strictly almost optimal non-linearity
Zhang, WeiGuo ; Li, LuYang ; Pašalić, Enes
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 ▫$m > \lfloor n/4 \rfloor$▫. Thus, resilient S-boxes with extremely high non-linearity and a larger output space compared with other design methods have been obtained.
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