不重复齐次函数的性质及其应用

Properties and Applications of Non-repeated Homogeneous Functions

不重复齐次函数是一类特殊的布尔函数 ,它在构造密码安全非线性组合函数中有着重要的应用 ,因此 ,文中研究了这类函数的密码性质 ,作为结果 ,得知不重复齐次一次函数有良好的平衡性和相关免疫性 ,不重复齐次二次函数是一类Bent函数 ,有着最高的非线性度和最高的扩散次数等。并以此为基础 ,深入研究了不重复齐次函数在构造非线性组合函数中的应用 ,从而得到了具有高非线性度且平衡相关免疫的函数和具有较高非线性度且代数次数达到最高的函数的结构。

Non-repeated homogeneous functions are a class of special Boolean functions They are very important in constructing cryptographic security nonlinear combining functions So,their cryptographic properties are studied in this paper As a result,we know that non-repeated homogeneous functions of one degree are possessed of good equilibrium and correlation-immunity,and those of two degrees are one class of Bent functions with the highest non-linearity,the largest order number of diffusion,etc On the basis of the above,the applications of non-repeated homogeneous functions to constructing non-linear combining functions are studied in detail Therefore,the constructions of balanced correlation-immune functions with higher non-linearity as well as of functions with the highest non-linearity and the highest algebra degree are obtained