一种构造高阶弹性函数的新方法

本文基于GF(2)^n上(n，m，t)弹性函数，运用向量单位分化定义及多输出函数的广义互补分布性质，给出了(n k，m，t k)弹性函数的一种非线性构造方法。这种方法使得自变量的维数与弹性阶同步增长，且弹性函数的代数次数也相应增加，从而避免了线性构造的缺陷。此外，本文还引入了局部非线性度的定义，并对这些(n k，m，t k)弹性函数的非线性度进行研究，由此得到了其非线性度下界的一个关系。

A New Method for Constructing High Order Resilient Functions

This paper proposes a new method for constructing (n+k,m,t+k) resilient functions by basing on (n,m,t) resilient functions over the field GF(2)n, and using both the definition of unit differentiation in vectors and generalized inmutex distributing properties of multitude output functions. This method is nonlinear, which leads to the fact that both the dimension of input vectors and the order of resiliency are increasing together, and algebraic degree is also enhancing. As a result, the method avoids the defect from linear construction. Moreover, the nonlinearity of (n+k,m,t+k) resilient functions is deeply researched by introducing a new definition of local nonlinearity. Furthermore, a lower boundary of its nonlinearity is obtained.