Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes

A Substitution box (S-box) is an important component used in symmetric key cryptosystems to satisfy Shannon’s property on confusion. As the only nonlinear operation, S-box must be cryptographically strong thwart any cryptanalysis tools cryptosystems. Generally, S-boxes can constructed using of following approaches: random search approach, heuristic/evolutionary approach or mathematical approach. However, current construction has some drawbacks, such as low cryptographic properties for and fact that it hard develop functions construct a S-box. In this paper, we explore non-permutation function was generated from binomial operation power By adopting method called Redundancy Removal Algorithm, propose enhancement algorithm desired result obtained. The analytical results our experiment indicate all criteria bijective, nonlinearity, differential uniformity, algebraic degree linear approximation are found hold obtained S-boxes. Our proposed also surpassed several bijective available literature terms properties.