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A Note on Two Classes of Boolean Functions With Optimal Algebraic Immunity
  • ISSN号：1009-6124
  • 期刊名称：Journal of Systems Science and Complexity
  • 时间：2014
  • 页码：785-794
  • 分类：O153.2[理学—数学;理学—基础数学] S858.315.3[农业科学—临床兽医学;农业科学—兽医学;农业科学—畜牧兽医]
  • 作者机构：[1]State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences, [2]Key Laboratory of Mathematics Mechanization.Academy of Mathematics and Systems Science,Chinese Academy of Sciences
  • 相关基金：supported by National Basic Research Program of China under Grant No.2011CB302400
  • 相关项目：数学机械化方法及其在信息技术中的应用
作者： Baofeng Wu|Zhuojun Liu|Qingfang Jin|Xiaoming Zhang|
关键词： 布尔函数, 免疫, 代数, KLOOSTERMAN和, 邓小平, 类似形, 二进制, 猜想, Algebraic immunity, bent function, Boolean function, Kloosterman sums, Walsh trans-form.
中文摘要：

Tu 和邓建议了具有在假设下面的最佳的代数学的免疫的弄弯的函数的一个类一组合推测。在这份报纸，作者计算他们仍然具有在一样的假设下面的最佳的代数学的免疫的功能然后表演推测的 Tu-Deng 双。为唐构造的布尔功能的另一个班，等。它具有有到 Tu-Deng 函数的类似的形式的最佳的代数学的免疫，他们用二进制完全的 Kloosterman 的一些基本性质是没弄弯的函数由的作者表演加。

英文摘要：

Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125