Bent函数估计的可计算达到上界

A Best Possible Computable Upper Bound on Bent Functions

Bent函数的计数和数目估计问题与依据其设计的流密码的安全性有密切联系。通过将Bent函数表示为定序特征矩阵,引入Bent矩阵的概念;根据Bent函数的定义,得到Bent矩阵的一些性质;利用解决一阶相关免疫布尔函数计数问题的方法,给出Bent函数个数估计的一个基于整数分拆表示的可计算上界,计算实例说明该上界是可达到的上界。

Enumeration and estimation of bent functions are closely related to the security of stream ciphers designed by them. In this paper, bent matrix is introduced when bent function is denoted by the ordered characteristic matrix. With help of the definition of bent function, some properties of bent matrix are obtained. On the basis of the author抯 approach to solving the enumeration of the first order correlation-immune Boolean functions, a computable upper bound on the number of bent functions, which is represented by the summation over the integer partition, is given. Examples show that the upper bound is a best possible upper bound.