Abstract
Substitution boxes (S-boxes) are the basis of symmetric cryptosystems. They bring nonlinearity and strength to the cipher. If we generate dynamic strong S-boxes, the strength of cryptosystem would be increased. In this paper, we use Brownian motion to generate strong 8 × 8 S-box generated from Brownian motion using a secret key, which will increase the complexity for cryptanalysis attacks. The generated S-boxes showed near similar results in security analysis compared to well-knowns S-boxes. Our proposed method is analyzed through algebraic immunity, correlation-immunity, strict avalanche criterion, differential uniformity, algebraic degree, autocorrelation, nonlinearity and key sensitivity.
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