摘要
文章研究旋转对称布尔函数的最高扩散次数、最高非线性度和代数免疫性等问题.利用导数和e-导数证明了元数为偶数的完全2次齐次旋转对称布尔函数的非线性度达到布尔函数的最大非线性度.又利用导数从n次扩散性角度,证明了旋转对称Bent函数的存在性,即验证了最大非线性度旋转对称布尔函数的存在性.另外,利用导数证明了最优代数免疫旋转对称布尔函数的存在性,并给出了用Bent函数构造最优代数免疫旋转对称布尔函数的方法.利用导数还得出了一类旋转对称布尔函数的相关免疫性.
The problems of RSBFs including the highest degree of propagation,the highest nonlinearity and algebraic immunity were studied in this article.Using the derivative and the e-derivative of the Boolean functions,the nonlinearity of quadratic homogeneous RSBFs was proved with even variables reaches the highest one of Boolean functions.Additionally,the existence of rotation symmetric Bent functions was verified using the derivative from n-degree propagation.That indicated that the existence of RSBFs with the highest nonlinearity had been proved.Moreover the paper proved that the existence of RSBFs with the optimal algebraic immunity,and provided the method of constructing RSBFs with the optimal algebraic immunity using Bent functions.The correlation immunity of a class of RSBFs using the derivative was also obtained.
出处
《西北民族大学学报（自然科学版）》
2015年第2期1-7,35,共8页
Journal of Northwest Minzu University(Natural Science)
