Construction of statistically optimal dynamic S-boxes for secure image encryption

Abstract

Introducing innovative ways to generate dynamic substitution boxes (S-boxes) is essential in achieving the desired diffusion and confusion. One kind of algebraic S-box generators attain these two properties either by fixed degree irreducible polynomials or by an algebraic map, which limits the randomness and security in the resultant output. The other type use total orders to avoid these limitations, making the time complexity nonlinear. In this study, we present an S-box generator that integrates dynamic polynomial with its induced map to generate highly secure and dynamic outputs, and keep the time complexity flexible. The current scheme incorporates a polynomial as an injective mapping to increase its algebraic strength. We present two highly nonlinear S-boxes by the proposed method. To validate the effectiveness of our scheme, we conduct comprehensive comparative analyses regarding construction mechanism and standard cryptographic metrics, confirming the robustness of the proposed method. Statistical analyses are also performed to assess key sensitivity, correlation, fixed points, time and space complexity, ensuring that the scheme meets practical security requirements. Furthermore, we propose an image encryption by employing the generated S-boxes, and the rigorous analysis confirms their applicability in secure multimedia transmissions.