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将布尔函数的导数和与导数一起便可直接明确刻画布尔函数的重量而定义的e-导数一起作研究工具,深入到布尔函数取值的内部结构中去,同时通过级联计算和组合分析的方法,讨论满足一次扩散准则,重量为2n 1+2n 2的H布尔函数的扩散性、代数免疫、相关免疫等性质之间的关系及相容性问题。得出布尔函数的扩散次数与相关免疫阶和代数免疫阶的关系等结果。这些结果对提高密码系统抵抗相关攻击的能力,提供了理论依据。
The derivative of the Boolean function and the derivative together with the e-derivative defined directly by the weight of the Boolean function can be used as a research tool to go deep into the internal structure of the Boolean function, and at the same time, through the cascade calculation and the combination analysis Method to discuss the relationship and compatibility between the properties of diffusivity, algebraic immunity and related immunity which satisfy the first diffusion rule and the weight of 2n 1 + 2n 2 H-Boolean functions. Obtained the Boolean function of the proliferation of the number of immune-related and immune algebraic grade and other results. These results provide a theoretical basis for improving the ability of the cryptosystem to resist attacks.