Construction of New S-boxes via Permuting the Inverse Mapping on Special Subsets

S-boxes are crucial components of symmetric ciphers. In this article, firstly we examine the nonlinearity and differential uniformity of mappings obtained via switching given mappings over 􀥲􀫛􀢔, on arbitrary subsets. Then, using this investigation, we construct new families of S-boxes with good cryptographic properties, through permuting the inverse mapping over 􀥲􀫛􀢔 on some special subsets. We provide the polynomial representation of the proposed S-boxes. In other words, we present new permutation polynomials over 􀥲􀫛􀢔 which are strong S-boxes from cryptographic aspect.