The kth order nonhomomorphicity of S-boxes

S-boxes are a core component of a cryptographically strong (secret-key) cipher. Mathematically, an n/spl times/m S-box is a nonlinear mapping from V/sub n/ to V/sub m/, where V/sub n/ and V/sub m/ represent the vector spaces of n and m tuples of elements from GF(2) respectively. The significance of research into S-boxes is indicated by the large number of papers published by researchers from around the world over the past decade.