一类平衡的最优代数免疫度布尔函数的构造

摘要

自从代数攻击思想被提出以后,关于布尔函数代数免疫度的研究一度成为比较热门的研究内容.布尔函数学者致力于构造各类密码学性质较好的高代数免疫度布尔函数.这些密码学性质主要包括函数的平衡性、代数次数、非线性度、相关免疫阶数等.构造了一类偶数阶的最优代数免疫度布尔函数,这类函数在具有最优代数免疫度的条件之下,还被证明具有较高的代数次数以及非线性度.最后还对这类函数的相关免疫阶数做出简单的分析.%The algebraic immunity for Boolean function once become a hot research since algebraic attack had been proposed.The Boolean function scholar dedicated to construct optimal algebraic immunity Boolean function with good cryptographic properties,which includes the function balance,algebraic degree,nonlinearity,and correlation immunity order.In this paper,author have constructed a family of balanced even-variable Boolean function with optimal algebraic immunity.Also,it is proved that under the condition of having the optimal algebraic immunity,this function has higher algebraic degree and nonlinearity.Finally,the correlation immunity order of this function is also analyzed simply.