Differential uniformity for arrays

The susceptibility of iterated block ciphers to differential cryptanalysis is minimised by using S-box functions with low differential uniformity. We extend the idea of differential uniformity to S-boxes with array inputs, giving a unified perspective from which to approach existence and construction problems for highly nonlinear functions. Properties of 2D differentially m-uniform functions are derived, two constructions are given and relationships with known 1D PN and APN functions are demonstrated.