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应用数学进展  >> Vol. 3 No. 2 (May 2014)

T-D猜想上多输出布尔函数构造
Construction of Vectorial Boolean Function Based on T-D Conjecture

DOI: 10.12677/AAM.2014.32010, PDF, HTML, 下载: 2,303  浏览: 7,718  国家自然科学基金支持

作者: 陈怡然, 周 梦：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

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；Vectorial Boolean Functions； Algebraic Immunity； Bent Function； Balancedness； Nonlinearity

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。
Abstract: 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.

文章引用: 陈怡然, 周梦. T-D猜想上多输出布尔函数构造[J]. 应用数学进展, 2014, 3(2): 62-69. http://dx.doi.org/10.12677/AAM.2014.32010

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