通过扩展集构造Bent函数支撑的一种算法

Joseph Nelson, Chungath Srinivasan, K. V. Lakshmy
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引用次数: 0

摘要

布尔函数构成对称密码系统的基本组成部分,充当构建块。修改bent函数使得设计具有表现出高度非线性的期望性质的布尔函数变得可行。目前的研究通过其支持对bent函数进行了全面的分析,最终引入了一种用于系统构建四变量bent函数的算法。该算法能够完全生成所有896个四变量bent函数。此外,我们介绍了一种构造n变量bent函数(其中n>4)的方法,利用该算法和已建立的bent函数构造辅助技术。最后,我们通过利用与bent函数的支持相关的某些性质来检验bent函数计数的估计。
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An Algorithm for Constructing Support of Bent Functions by Extending a Set
Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 four-variable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions.
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来源期刊
CiteScore
3.80
自引率
6.20%
发文量
57
审稿时长
20 weeks
期刊介绍: IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.
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