Global Avalanche Characteristics of Boolean Functions by Concatenation

TP918.1; In order to measure the correlation propeties of two Boolean functions, the global avalanche characteristics of Boolean functions constructed by concatenation are discussed, i.e., f1‖f2 and f1‖f2‖f3‖f4. Firstly, for the function f = f1‖f2 , the cross?correlation function of f1 , f2 in the special condition are studied. In this case, f, f1 , f2 must be in desired form. By computing their sum?of?squares indicators, the cross?correlation function between f1 , f2 is obtained. Secondly, for the function g = f1‖f2‖f3‖f4 , by analyzing the relation among their auto?correlation functions, their sum?of?squares indicators are investigated. Based on them, the sum?of?squares indicators of functions obtained by Canteaut et al. are investigated. The results show that the correlation property of g is good when the correlation properties of Boolean functions f1 , f2 , f3 , f4 are good.