Heuristic Approach for Nonlinear n × n (3 ≤ n ≤ 7) Substitution-Boxes

Substitution boxes are meant to enact nonlinear transformations of n-bit input streams to n-bit output streams. A highly nonlinear essence of them is imperative to induce obligatory confusion of data and to mitigate the potential linear cryptanalysis as well. It has been known that cryptographically potent S-boxes are creditworthy for the success of modern block encryption systems. This paper proposes to suggest an approach to frame a generic design that has the efficacy of synthesizing highly nonlinear balanced n × n S-boxes for 3 ≤ n ≤ 7. The proposed approach is based on the heuristic optimization that seeks for local and global best S-box candidates on each iteration. The resultant optimized S-boxes are provided and tested for nonlinearity soundness. The performance outcomes and assessment analysis justify that the generic approach is consistent for contriving highly nonlinear key-dependent S-boxes.

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