基于代数正规型构造的代数免疫最优布尔函数

摘要

现有代数免疫最优布尔函数的构造方法大多基于支撑集,通过代数正规型直接构造的方法研究较少.为此,利用代数正规型的多项式表示构造一类代数免疫性质优的布尔函数,研究其代数次数、代数免疫阶、函数重量、非线性度等性质,分析采用这种方法构造的代数免疫最优布尔函数的性质及计数等结果.由构造方法可以得到代数免疫最优的布尔函数,其中包含一些已有的特殊构造结果,表明该方法更具有一般性,包含更多具有最优代数免疫阶的函数.%The present methods of constructing optimal algebraic immune Boolean functions are mostly based on the support set.The methods by algebraic normal form are few.This paper gives a method of constructing optimal algebraic immune Boolean functions by algebraic normal form,and studies the primarily cryptographic properties of these functions.Such as algebraic degree,the algebraic immunity,the hamming weight,the nonlinearity etc.The number of the constructed optimal algebraic immune functions is given.By using the construction method,a large class of Boolean functions can be obtained with optimal algebraic immunity,which contains some special known results,and shows this method is more general,contains more functions with maximum algebraic immunity order.