Efficient method for simplifying and approximating the s-boxes based on power functions

In recently proposed cipher algorithms, power functions over finite fields and specially inversion functions play an important role in the S-box design structure. In this study, a new systematic efficient method is introduced to cryptanalyse (to simplify and approximate) such S-boxes. This method is very simple and does not need any heuristic attempt and can be considered as a quick criterion to find some simple approximations. Using this new method, some approximations can be obtained for advanced encryption standard (AES) like S-boxes, such as AES, Camellia, Shark and so on. Finally as an application of this method, a simple linear approximation for AES S-box is presented.