Analysis and synthesis of cryptographic Boolean functions in Haar domain: Initial results

Boolean functions play a central role in the design of information protection systems. The strength of cryptographic systems against any potential attack is determined by several criteria which the cryptographic functions should meet. These criteria can be analyzed and measured through the aid of specific tools or methods of approach. In this paper, we explore and address issues related to these methods of approach. We first present an overview of the important cryptographic criteria including the existing tools used to analyze and measure these properties. Then we introduce the Haar spectral transform as an alternative tool that can as well be used for the analysis of the cryptographic Boolean functions, and present the initial simple results on its direct implications to cryptographic functions.