为提高密码系统抵抗线性逼近攻击、差分攻击、相关攻击、代数攻击等众多密码攻击的能力,提高密码系统的安全性,利用布尔函数导数部分和e-导数部分求非线性度中与函数距离最近的线性函数和求函数最低代数次数零化子的方法.分别给出了平衡H布尔函数、Bent函数、重量2n-1+2n-2的H布尔函数的与函数距离最近的线性函数、非线性度,最低代数次数零化子、代数免疫阶等结果,并给出了提高奇数元函数非线性度和代数免疫阶的方法和结果. In order to improve the cryptosystems’ ability of resisting linear approximation attacks, differential attacks, related attacks and algebraic attacks and many other cryptographic attacks, the security of the cryptosystem is improved. By using the derivative part of the Boolean function and the e-derivative part, Linear function of the function and the method of finding the lowest algebraic number of the function.We give the linear function which is closest to the function distance of the equilibrium H Boolean function, the Bent function and the H-Boolean function of the weight 2n-1 + 2n-2 respectively Linearity, the lowest number of algebras, algebraic immunity, and so on. The methods and results of improving the nonlinearity of algebraic functions and algebraic immunity order are given.