Tr(x^(2^(n/2)+2^(n/2-1)+1))的二阶非线性度下界

The lower bound of the second order nonlinearity of Tr(x^(2^(n/2)+2^(n/2-1)+1))

作为影响系统安全的重要因素,对称密码中的密码函数应具有较高的r阶非线性度。对于r>1,目前对r阶非线性度的研究主要根据布尔函数微商的非线性度与其二阶非线性度之间的关系来进行。对于正整数n≡2(mod 4),确定了一类布尔函数Tr(x^(2^(n/2)+2^(n/2-1)+1))的二阶非线性度下界。与相同变元数的两类已知布尔函数相比,研究的函数具有更紧的二阶非线性度下界。

The Boolean functions used in symmetric ciphers should have high r-th order nonlinearity,which was one of the most important factors in system security.Making use of the relationship between the nonlinearity of derivative and the second order nonlinearity of a Boolean function,the lower bound of the second order nonlinearity could be deter-mined.For a positive integer n≡2（mod 4）,the lower bound of the second order nonlinearity of the Boolean function Tr（x^（2^（n/2）＋2^（n/2-1）＋1）） was given.Compared with two classes of Boolean functions with the same number of variables,the functions discussed had a tighter lower bound on the second order nonlinearity.