Constructing 8×8 S-Boxes with Optimal Boolean Function Nonlinearity

Substitution boxes (S-Boxes) are the core components of modern block ciphers, responsible for introducing the essential nonlinearity that protects against attacks like linear and differential cryptanalysis. For an 8-bit S-Box, the highest possible nonlinearity for a balanced Boolean function is 116. The best results previously reported in the literature were only able to achieve a nonlinearity of 114.5. Our new method surpasses this prior record, generating 8×8 S-Boxes with a nonlinearity of 116. This is a significant achievement as it reaches the highest known bound for balanced functions and sets the new standard for this criterion. The approach is also highly effective, capable of producing a large number of S-Boxes, all with these optimal cryptographic properties. This ensures they are exceptionally resistant to cryptanalysis. Our S-Box construction is not only superior in nonlinearity but also performs well when evaluated against other standard cryptographic metrics, making it a leading solution for secure cipher design.