Spectral properties and information leakage of multi-output Boolean functions

In this paper, we extend the concept of information leakage in Forre (1990) and Zhang et al. (1994) to the case of multi-output Boolean functions. A spectral characterization of multi-output boolean function is given. This result is used to express different forms of information leakage of multi-output Boolean function in terms of the Walsh transform of every linear combination of its output coordinates. Conditions on the Walsh transform of the multi-output Boolean function are given, which imply that the function satisfies certain cryptographic properties of interest such as balance, correlation immunity, strict avalanche criterion (SAG), higher order SAG, propagation criterion (PC), higher order PC, and perfect non-linearity