Bent函数与高度非线性弹性函数的二级构造
Secondary Constructions of Bent Functions and Highly Nonlinear Resilient Functions
摘要：
在本文中，我们首先提出了一个新的二级结构的bent函数（建立新的bent函数从两个已经定义的）。此外，我们还应用了以某些特定的bent函数为初始函数的构造，并给出了bent函数的几种具体构造。本文的第二部分致力于弹性函数的构造。给出了构造高非线性弹性函数的间接和构造的一个推广。此外，我们修改了广义结构，以确保高非线性的构造函数。
英文摘要：
In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and then provide several concrete constructions of bent functions. The second part of the paper is devoted to the constructions of resilient functions. We give a generalization of the indirect sum construction for constructing resilient functions with high nonlinearity. In addition, we modify the generalized construction to ensure a high nonlinearity of the constructed function.
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