Abstract
The construction of substitution boxes (s-boxes) is an important research area in cryptography. S-box is an important mathematical object. The aim of this study is to construct s-box designs with the best performance criteria for all chaotic system classes. The proposed method achieves the best s-box designs for all chaotic systems classes. The method is independent of the chosen chaotic system. The analyses show that maximum value of nonlinearity criterion is 106.75 and minimum value of equiprobable input/output XOR distribution table is 10. The importance of the best generated s-boxes based on chaotic systems is that cryptologic properties of the best generated s-box structures are the upper bound for chaos-based s-box literature.
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