A New Approach to the Definition of Information Diffusion and Confusion of Boolean Transformation

Mass, energy and information are the three important quantities in the physical world. The diffusion and confusion of information is the guiding ideology of cipher algorithm coding. Linear transformation is generally used to realize the diffusion of information and S-box is used to realize the confusion. This paper presents the concept of the information diffusion and confusion degree in Boolean transformation and proves that the biggest information diffusion and confusion degrees are both 1 n in the n tuples Boolean linear invertible transform. Furthermore, we give the method to construct the maximum degree of diffusion and confusion degree for the structure of the reversible Boolean nonlinear transform. That is to say, the diffusion of information technology through reversible linear transformation in AES and SMS4, CAST is not optimal. The results presented in this paper, combined with the algebraic immune degree, balance, correlation immune, linear deviation and difference deviation, and other security cryptography parameters, can be used to design cryptographic algorithm with better properties.