相关免疫H布尔函数的代数免疫和代数次数

将导数和自定义的e-导数结合在一起作为新的研究工具,而这两者(导数和e-导数)结合在一起能直接明确反映布尔函数的重量,深入到布尔函数取值的内部结构中去,讨论相关免疫H布尔函数的代数免疫阶、代数次数等问题,即严格雪崩性质、相关免疫性、代数免疫性及最高代数次数的相容性问题,得出Hamming重量为2n-1+2n-2这类H布尔函数的最低代数次数和最高代数次数、最优代数免疫等结果。同时,也给出了一些求布尔函数代数次数和最优代数免疫的方法。

Algebraic Immunity and Algebraic Degree of Correlation- immunity H Boolean Function

The Boolean function derivative and self-defined e-derivative, combined together, could clearly characterize the weight of Boolean functions, and thus are taken as the tools for in-depth research of the internal structure of Boolean function value, and also for discussion of algebraic immunity and algebraic degree problem of correlation-immunity H Boolean function, that is, strict avalanche criterion, correlation- immunity, algebraic immunity and consistency of the highest algebraic degree. The lowest algebraic degree and the highest algebraic degree, optimal algebraic Immunity of H Boolean function with Hamming Weight 2n-1＋2n-2 are derived, and some methods for calculating algebraic degree of Boolean function and optimal algebraic immunity also given in this paper.