Improved Rijndael-like S-box and its transform domain analysis

In this paper, we propose a simple scheme which produces a new S-box from a given S-box. We use the well-known conversion technique between the polynomial functions over F-2n and the boolean functions from F-2(n) to F-2. We have applied the scheme to Rijndael S-box and obtained 29 new S-boxes, of which only one is a bijection with better algebraic expression than the original Rijndael S-box and has the same spectral properties as the original Rijndael S-box. All others turned out to be non-bijective, and have different spectral properties, and hence, they all are inequivalent to the original as boolean functions.