Strict avalanche criterion in Boolean functions-a spectral approach

Abstract

For the first time, the Strict Avalanche Criterion (SAC) in Boolean functions is identified through the Walsh spectral symmetries. In order to reduce the processing time, a filtering procedure to eliminate the Boolean functions that do not satisfy the SAC is proposed. New types of spectral symmetries are introduced and used in the proposed technique together with the known symmetries. In the case that a given function fulfils SAC, the proposed algorithm needs up to 3/4 of the spectral coefficients at any stage to identify the SAC. In a case of functions that do not fulfil SAC the algorithm can eliminate them from further checking by using smaller number of coefficients. It is a big advantage over previous methods of SAC identification that required the calculation of the full Walsh spectrum for all the functions.