T-D猜想上多输出布尔函数构造  

Construction of Vectorial Boolean Function Based on T-D Conjecture

作　　者：陈怡然 周梦[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,数学、信息与行为教育部重点实验室,北京

出　　处：《应用数学进展》2014年第2期62-69,共8页Advances in Applied Mathematics

基　　金：国家自然科学基金NSFC 11271040 资助项目。

摘　　要：本文针对基于涂自然等人提出的组合猜想上布尔函数的构造方法和有关结论,将组合猜想和构造方法一般化,并将其推广到多输出布尔函数上去,构造出具有最优代数免疫度的多输出bent函数F,同时通过修改F构造出具有好的非线性度、最优代数度和最优代数免疫度兼具的多输出平衡布尔函数函数。An improvement has been made on the construction method of Boolean Functions and the relevant conclusions of combinatorial conjecture proposed by Ziran Tu. We generalized their results and extended to the vectorial case. A class of bent Boolean functions F with the maximum algebraic immunity is presented by a more general construction method. Then by modifying F, we get new vectorial balanced functions with optimum algebraic degree, good nonlinearity and good algebraic immunity even maximum algebraic immunity for some cases.

关 键 词：多输出布尔函数 代数免疫度 BENT函数 平衡性 非线性度 

分 类 号：TN91[电子电信—通信与信息系统]