具有良好密码学性质的布尔函数的级联构造

Constructing Boolean Functions with Good Cryptographic Properties by Concatenation

通过对靳庆芳等学者构造的具有良好密码学性质的布尔函数进行改造,得到两类偶数变元的平衡布尔函数,它们在假设广义Tu-Deng猜想成立的条件下具有最优的代数免疫度.进而对这两类布尔函数进行级联,得到一类奇数变元的1-阶弹性布尔函数,它们在假设广义Tu-Deng猜想成立的条件下具有至少次优的代数免疫度,且具有最优的代数次数和较高的非线性度.特别地,当构造函数时的某些参数取特殊值时,在不需要假定任何猜想的前提下所构造的函数具有至少次优的代数免疫度.

By modifying the functions with good cryptographic properties constructed by Jin et al., we construct two classes of balanced Boolean functions which have optimal algebraic immunity assuming the correctness of the generalized Tu-Deng conjecture. Considering concatenations of functions from these two classes, we obtain a class of 1-resilient Boolean functions which have suboptimal algebraic immunity assuming the correctness of the generalized Tu-Deng conjecture, and have optimal algebraic degree and high nonlinearity. For some special instances of parameters, functions belonging to this class have suboptimal algebraic immunity without assumption of the correctness of any combinatorial conjectures.