Composition of Boolean functions: An application to the secondary constructions of bent functions
Composition of Boolean functions: An application to the secondary constructions of bent functions
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布尔函数的复合：弯曲函数二次构造的应用
DOI：
10.1016/j.disc.2019.111711
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发表时间：
2020-03
影响因子：
0.8
通讯作者：
Wang Yongjuan
中科院分区：
文献类型：
--
作者：
Gao Guangpu;Lin Dongdai;Liu Wenfen;Wang Yongjuan
Bent函数是最优组合对象，四十年来一直受到人们的关注。二级结构在构造Bent函数中起着核心作用，因为这类函数的完整分类似乎是难以捉摸的。本文致力于建立二次结构与布尔函数合成之间的关系。我们首先证明了Bent函数的一些著名的二次构造可以用一个平台型布尔函数和一些Bent函数的组合来描述。然后利用拉格朗日插值公式计算出它们的对偶函数。在此基础上，给出了Bent函数的两个二级结构。我们证明了它们与已有的不等价，并且可以在主类M和PS之外产生Bent函数。这些结果表明，本文提出的方法是遗传的和统一的，因此可以应用于具有其他密码准则的布尔函数的构造。
Bent functions are optimal combinatorial objects and have been attracted their research for four decades. Secondary constructions play a central role in constructing bent functions since a complete classification of this class of functions seems to be elusive. This paper is devoted to establishing a relationship between the secondary constructions and the composition of Boolean functions. We firstly prove that some well-known secondary constructions of bent functions, can be described by the composition of a plateaued Boolean function and some bent functions. Then their dual functions can be calculated by the Lagrange interpolation formula. By following this observation, two secondary constructions of bent functions are presented. We show that they are inequivalent to the known ones, and may generate bent functions outside the primary classes M and PS. These results show that the method we present in this paper is genetic and unified and therefore can be applied to the constructions of Boolean functions with other cryptographical criteria.
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DOI：
10.1017/cbo9780511780448.011
发表时间：
2010-06
期刊：
--
影响因子：
--
作者：
C. Carlet;Y. Crama;Peter L. Hammer
通讯作者：
C. Carlet;Y. Crama;Peter L. Hammer
影响因子：
2.5
作者：
Sihem Mesnager
通讯作者：
Sihem Mesnager
DOI：
10.3934/amc.2017026
发表时间：
2017-05
期刊：
Adv. Math. Commun.
影响因子：
--
作者：
Sihem Mesnager;Fengrong Zhang
通讯作者：
Sihem Mesnager;Fengrong Zhang
影响因子：
2.5
作者：
K. Gupta;P. Sarkar
通讯作者：
K. Gupta;P. Sarkar
影响因子：
0.9
作者：
Mesnager Sihem;Zhang Fengrong;Yong Zhou
通讯作者：
Yong Zhou