Evolutionary Design of S-Box with Cryptographic Properties

Based on a theorem on the construction of a permutation, we propose an evolutionary algorithm that can efficiently design S-boxes with good cryptographic properties like high nonlinearity, low autocorrelation, low difference and high algebraic immunity. Furthermore, we observe that the polynomial representing a concrete designed S-box over a small field can be generalized to that over a large field. That is, we not only can design many concrete S-boxes, but also may find many types of affinely in equivalent S-boxes.