Decision trees of cryptographic Boolean functions

In this paper, we investigate the use of decision trees as a measure of the cryptographic strength of Boolean functions. In particular, we consider the univariate decision trees and the multivariate linear decision trees. Trees with bounded errors are also considered. We also introduce the concept of the entropy profile of Boolean functions. Experimental upper bounds are evaluated for several tree complexity measures of cryptographic Boolean functions of interest such as the coordinate functions of the DES and Rijndael (AES) s-boxes.