Propagation characteristics and correlation-immunity of highly nonlinear Boolean functions

Abstract

We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics.We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with respect to a linear subspace of codimension 1 or 2 has a high nonlinearity. We also point out that most highly nonlinear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.