Abstract:

Using the relationship between the sum of square and algebraic immunity by GAC, the divisibility properties concerning the autocorrelation coefficient of the Boolean functions with propagation criterion is derived by Walshspectrum and coefficient, and the inequality among variables, algebraic immunity, propagation criteria and algebraic degree is deduced by this divisibility, and by the computer search methods a compactly expression among these four parameters is given from 4 variables to 30 variables. Finally, the relationships between the propagation criterion and the liner structure and normality are discussed.

Key words: Boolean functions;Algebraic immunity;Propagation criteria;GAC