构造具有好的密码学性质的布尔函数一直是布尔函数的研究热点.在构造具有好的密码学性质的布尔函数的方法中,级联构造方法是一种重要的研究方法,利用级联构造方法可以构造密码学性质好的布尔函数.本文利用级联构造了布尔函数f1‖f3‖f3‖f2,并且在文中详细讨论了这类级联布尔函数的密码学性质:相关免疫性、扩散性、线性结构、代数免疫阶等.通过我们的讨论发现,在布尔函数f1,f2,f3的密码学性质较好的前提下,级联布尔函数f1‖f3‖f3‖f2的密码学性质也较好.
It is always an important problem to construct Boolean functions with good cryptographic properties. Concatenation is an important method by which we can construct Boolean functions with good cryptographic properties. In this paper, we construct Boolean functions f1‖f3‖f3‖f2 by concatenation; moreover, we investigate their cryptographic properties:correlation immunity, propagation, linear structure and algebraic immunity and so on. By our investigation, we find their cryptographic properties of the Boolean functions f1‖f3‖f3‖f2 are good when the cryptographic properties of the Boolean functions f1,f2,f3 are good.