Generating dynamical S-boxes using 1D Chebyshev chaotic maps

Abstract

This paper considers the construction of chaotic dynamic substitution boxes (S-boxes) using chaotic Chebyshev polynomials of the first kind. The proposed algorithm provides dynamic S-boxes with acceptable security performance compared to twenty-one recent schemes. This algorithm is used to generate 80 random 8 × 8 S-boxes and analyzed their security performance. Their average performance shows acceptable security. The security of the generated S-boxes is measured against several mandatory security requirements for S-box designs including bijective property, strict avalanche criterion (SAC), linear approximation probability (LAP), differential approximation probability, bit independence criterion, correlation immunity, algebraic immunity, auto-correlation, and propagation criterion. Moreover, the set of majority logic criterion measures is used to measure the quality and robustness of the generated S-boxes in image encryption. Because obtaining a chaotic sequence with one dimensional Chebyshev polynomials of the first kind is very simpler and efficient than the hyper-chaotic mappings, the proposed algorithm is of lower computational costs compared with recent chaotic S-box generation algorithms.