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计算机工程 ›› 2012, Vol. 38 ›› Issue (11): 124-125,129. doi: 10.3969/j.issn.1000-3428.2012.11.038

• 安全技术 • 上一篇    下一篇

基于布尔函数正规性的广义Bent函数构造

许广魁1,李远华1,马凤丽2   

  1. (1. 淮南师范学院数学与计算科学系,安徽 淮南 232001;2. 中国人民解放军理工大学理学院,南京 211101)
  • 收稿日期:2011-10-15 出版日期:2012-06-05 发布日期:2012-06-05
  • 作者简介:许广魁(1981-),男,助教、硕士,主研方向:密码学,信息安全;李远华,副教授;马凤丽,讲师、硕士
  • 基金资助:
    安徽高校省级自然科学研究基金资助项目(KJ2011Z356)

Construction of Generalized Bent Function Based on Boolean Function Normality

XU Guang-kui 1, LI Yuan-hua 1, MA Feng-li 2   

  1. (1. Department of Mathematics and Computational Science, Huainan Normal University, Huainan 232001, China; 2. School of Science, PLA University of Science and Technology, Nanjing 211101, China)
  • Received:2011-10-15 Online:2012-06-05 Published:2012-06-05

摘要: 基于广义Bent函数的正规性,结合子空间上的特征函数,分析广义正规Bent函数的Chrestenson谱特征。利用间接构造Bent函数的方法,在整数模m的剩余类环Zm以及 元域Zp上,给出2类新的 元广义Bent函数。理论分析结果表明,与传统构造方法相比,该方法可构造出更多的 元广义Bent函数。

关键词: 广义布尔函数, 广义Bent函数, 正规性, 正则Bent函数, Chrestenson谱, 仿射子空间

Abstract: This paper is based on the normality of generalized Bent functions, combines the characteristic functions of linear subspace. The Chrestenson spectral characteristics of generalized normal Bent functions are studied. According to the indirect construction method, two new classes of generalized Bent functions of n variables over integers module m residue class Zm and p meta-field Zp are presented. Theory analysis result shows that more generalized Bent functions can be constructed by using the proposed construction method compared with the traditional construction method.

Key words: generalized Boolean function, generalized Bent function, normality, regular Bent function, Chrestenson spectrum, affine subspace

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