关于Bent函数的一些研究

利用布尔置换 ,构造了一种新的Bent函数 ,并对这类布尔函数的构造进行了研究 ,发现利用Bent函数的满足扩散准则的特性和布尔函数非线性度的中间结果可以构造出两类函数形式简单的 ,满足高次扩散准则的、具有较高非线性度的平衡布尔函数 ,从而拓宽了Bent函数的应用领域

THE RESEARCH ON BENT FUNCTION

Because of its the nonlinearity and stability,bent function have high value in the cryptogram theory.Because of its poor quantity and nonbalance, how to construct new bent function and how to apply bent function in new fields became a very significant problems.Some research on the construction and application of bent function was made.First, on the basis of literature 8 and 10,a new construction method of bent function by using boolean permutation that was the content of theorem 4 was put forward.In addition,according to the wide use of balance boolean functions with high nonlinearity in cryptogram theory,some research on this kind of functions was made.Two kinds of boolean functions satisfying the balancedness,the nonlinearity and the propagation criterion by using the characteristic of bent function and the conclusion of literature 8 about the nonlinearity of boolean function,which was the content of theorem 8 and 9 was put forward.So some new fields in the application of bent function were devoleped.