减小平衡H布尔函数相关度的算法和相关问题研究

以布尔函数的导数和e-导数为工具,深入到平衡H布尔函数的内部结构中去分析,明确得出了不存在二阶相关免疫平衡H布尔函数的结论,解决了是否存在二阶相关免疫的平衡H布尔函数这一尚无正确实际结果的问题.从逻辑和理论的合理性上,明确了讨论平衡H布尔函数的广义相关免疫性对密码体制安全的必要性,并通过对平衡H布尔函数的广义相关免疫性和相关度的分析,导出了减小平衡H布尔函数相关度并同时提高较小相关度阶数的算法.

Algorithm of reducing the balanced H-Boolean function correlation-measure and research on correlative issue

Took the derivative and e-derivative of Boolean function as a tool,analyzed the inner structure of balanced H-Boolean functions,clearly obtained the conclusion that the second-order correlation-immune balanced H-Boolean function is not existent,solved the problem that whether there was a second-order correlation-immune balanced H-Boolean function which has not yet proper result.From the rationality of logic and theory,defined the necessity of discussing the generalized correlation-immune of balanced H-Boole...