S-box是密码理论与实践中十分重要的一种装置 ,它的密码性能由其分量函数所决定 .于是 ,选择适当的分量函数来构造 S-box就成了一个重要的研究课题 .在一定意义上 ,Bent函数是最优良的密码函数 .本文通过函数序列半群和置换群来构造其任何非零线性组合为 Bent函数与线性函数之和的函数组 ,从而可由 Bent函数构造出具有高度非线性度和其他良好性状的 S-box S-box is a very important device in the theory and practice of cryptography, and its cryptographic performance is determined by its component function. Therefore, it is an important research topic to choose the appropriate component function to construct S-box. In the sense, Bent function is the best cryptographic function.This paper constructs a function group whose any non-zero linear combination is the sum of Bent function and linear function through function sequence semigroups and permutation groups, Linearity and other good traits of the S-box