一类Bent函数的再证明和新构造

New Proof of a Class of Bent Functions and New Construction

Bent函数作为非线性最优的布尔函数在对称密码系统的设计中有着诸多应用。利用组合布尔函数方法给出了一类间接构造的Bent函数的新证明,所给方法证明过程较为简便、计算量小。其次,利用新的构造方法得到了具有n+m+2个变元的Bent函数,并在特殊取值下分析了所得构造与已有间接构造之间的关系。

As a nonlinear optimal Boolean functions,Bent function has many applications in the design of symmetric cryptography systems.In this paper,a new proof of a class of indirectly constructed Bent functions is presented by using the method of combined Boolean function.The method is simple and the calculation is small.In addition,The Bent function with n+m+2 variables is obtained by using new method,and the relationship between the obtained structure and the existing indirect structure is analyzed under the special value.