S₈ affine-power-affine S-boxes and their applications

The encryption process relies on the use of nonlinear mapping subsystems to create confusion in the ciphertext. The design of these nonlinear components is a challenging task and requires complex algebraic expression for their descriptions. In an effort to increase the complexity of nonlinear mappings, several implementations exhibiting interesting properties are proposed in the literature. In particular, affine-power-affine structure is designed for advanced encryption standard, which improves the complexity of its algebraic expression by increasing the number of terms. Based on the characteristics of affine-power-affine structure, we propose a new nonlinear component that uses the symmetric group permutation S₈ on the Galois field GF(2⁸) elements and provides the possibility to incorporate 40320 unique instances. A rigorous analysis is presented to evaluate the properties of these new nonlinear components by applying nonlinearity analysis, linear approximation analysis, differential approximation analysis, bit independence criterion and strict avalanche criterion. In order to determine the suitability to various encryption applications, the S-boxes are tested with generalized majority logic criterion.