The Strict Avalanche Criterion: Spectral Properties of Boolean Functions and an Extended Definition

A necessary and sufficient condition on the Walsh-spectrum of a boolean function is given, which implies that this function fulfills the Strict Avalanche Criterion. This condition is shown to be fulfilled for a class of functions exhibiting simple spectral symmetries. Finally, an extended definition of the Strict Avalanche Criterion is proposed and the corresponding spectral characterization is derived.