Next Articles

Several Binomial Functions with Low Differential Uniformity

GUO Feiwang, ZHANG Xiyong, HAN Wenbao   

  1. Department of Applied Mathematics, School of Institute of Information Engineering, Information Engineering University, Zhengzhou 450002;
  • Received:2010-11-30 Online:2011-11-20 Published:2011-11-20



  1. 信息工程大学信息工程学院应用数学系,郑州 450002;

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

CLC Number: