具有K阶代数免疫的布尔函数  

Boolean Functions with K Algebraic Immune Degree

作　　者：张毛优[1] 常祖领[1] 

机构地区：[1]郑州大学数学系,河南郑州450001

出　　处：《计算机技术与发展》2011年第3期158-160,共3页Computer Technology and Development

摘　　要：代数免疫度是衡量布尔函数抵抗代数攻击的重要性能指标,具有低代数免疫度的布尔函数是不能抵抗代数攻击的。根据1型线性结构布尔函数的代数免疫阶完全取决于其零化子代数次数的结论,文中从线性结构的角度构造了具有K代数免疫阶的布尔函数,并且给出了此类函数循环谱特征、自相关特征及非线性度值。一系列的结论揭示了布尔函数的线性结构对其代数免疫阶的制约作用。并且通过特殊"分配"A和S\A中点的取值可重新调整循环谱值及自相关值。Algebraic immunity is an important index to measure the ability to resist algebraic attack. If a Boolean function has a low algebraic immunity, it cannot resist the algebraic attack. According to the algebraic immune degree of a Boolean function with 1 -form linear structure is completely determined by the lowest degree of the annihilator forf. From the perspective of linear structure, this paper is giv- en Boolean functions with K algebraic immunity and the characters of walsh transform and the nonlinearity of the functions. A series of conclusions reveals a linear structure of Boolean function restricts algebraic immunity. Meanwhile, special allocation of points of Sand S／Awhich can be re-adjusted value of cyclic spectrum and autocorrelation values.

关 键 词：代数免疫度 循环谱 非线性度 

分 类 号：O153.2[理学—数学]