New bounds on the sum-of-squares indicator

The two indicators the sum-of-squares indicator and the absoluate indicator between two different Boolean functions f and g are introduced by Yu Zhou, Min Xie, Guozhen Xiao, On the global avalanche characteristics of two Boolean functions and the higher order nonlinearity. Information Sciences. 180(2010) 256-265, to measure of cryptographic behavior in a global manner. In this paper, we derive a new bound on the sum-of-squares indicator. Moreover, we obtain some bounds on the sum-of-squares indicator of a Boolean function f by using two decomposition functions f₁, f₂. Finally, we give a method to construct balanced Boolean functions with n(n >;= 6) variables by the disjoint spectra functions, where n is an even integer, satisfying strict avalanche criterion, high nonlinearity and lower GAC.