Abstract: Selecting the combinations of two appropriate monomial functions, the authors construct several functions with low differential uniformity, find some quadratic highly nonlinear differentially 4-uniform and cubic differentially 6-uniform binomial functions, and give a bound of nonlinearity of cubic functions by second order nonlinearity. These new functions have higher nonlinearity and lower uniformity.

Key words: differential uniformity, almost perfect nonlinear functions, perfect nonlinear functions, Walsh spectrum, second order nonlinearity

摘要： 通过选取两个单项式的组合，给出几种低差分一致的函数的构造, 得到一些二次差分4一致性和三次差分6一致性的二项式函数, 并利用二阶非线性度等给出了三次函数的非线性度的一个下界。新构造的函数具有低差分一致性和较高的非线性度。

关键词: 差分一致性, 几乎完全非线性函数, 完全非线性函数, Walsh谱, 二阶非线性度