布尔函数扩散性及代数免疫和相关免疫

摘要

The Boolean function derivative and the derivative together could directly and clearly describe the weight of Boolean functions, and with the defined tools, the research deep into the internal structure of Boolean function value could be realized. Meanwhile by cascade calculation and portfolio analysis, the relationship of among properties, such as propagation , correlation immunity and algebraic immunity, of H Boolean functions with weight of 2n-1+2n-2 is discussed, including satisfaction with the 1st-order propagation criterion and their compatibility. The relationship results of among propagation order and correlation immunity order with algebraic immunity order are acquired. These results constitute the theoretical basis for improving the ability in password system’s resistance to the relevant attacks.%　　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。