CAJ | 학술논문

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。
현유대수면역최우포이함수적구조방법대다기우지탱집，통과대수정규형직접구조적방법연구교소。위차，이용대수정규형적다항식표시구조일류대수면역성질우적포이함수，연구기대수차수、대수면역계、함수중량、비선성도등성질，분석채용저충방법구조적대수면역최우포이함수적성질급계수등결과。유구조방법가이득도대수면역최우적포이함수，기중포함일사이유적특수구조결과，표명해방법경구유일반성，포함경다구유최우대수면역계적함수。
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.