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中国科学院大学学报 ›› 2010, Vol. 27 ›› Issue (2): 257-262.DOI: 10.7523/j.issn.2095-6134.2010.2.017

• 论文 • 上一篇    下一篇

Gold 型Bent函数的两个注记

孙光洪1,2, 武传坤2   

  1. 1. 河海大学理学院,南京 210098;;
    2. 中国科学院软件研究所信息安全国家重点实验室,北京 100190
  • 收稿日期:2009-06-13 修回日期:2009-11-06 发布日期:2010-03-15
  • 通讯作者: 孙光洪
  • 基金资助:

    国家自然科学基金(60673068)和河海大学理科基金(2084/409270)资助 

Two notes on Bent functions of Gold case SUN Guang-Hong1,2, WU Chuan-Kun2   

  1. 1. College of Sciences, Hohai University, Nanjing 210098,China;
    2. State Key Lab of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2009-06-13 Revised:2009-11-06 Published:2010-03-15

摘要:

Bent 函数一直是密码学研究中的重要课题,如何判断给出的布尔函数是否为bent函数是必须要解决的问题.通过对Gold型函数中指数的分析,得到了Gold型函数成为bent函数的充要条件,此充要条件是Leander文献中定理的部分推广,用该结论判断bent函数更加简便.同时还讨论了多个迹函数之和成为bent函数的一个充要条件.

关键词: 布尔函数, bent 函数, 迹函数, Walsh谱

Abstract:

Bent functions are important in cryptography, and one must know how to judge whether a Boolean function is bent. We obtain a sufficient and necessary condition by analyzing the power in functions of Gold case. This sufficient and necessary condition is a partial generalization of the theorem in Leanders reference. Our result makes the judgement of bentness of Gold case much easier. We also discuss a sufficient and necessary condition for that the sum of a few trace functions is bent.

Key words: Boolean function, bent function, trace function, Walsh spectrum

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