A note on two classes of Boolean functions with optimal algebraic immunity

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• 作者：Baofeng Wu (1) (2)
  Zhuojun Liu (2)
  Qingfang Jin (2)
  Xiaoming Zhang (2)
  
• 关键词：Algebraic immunity ; bent function ; Boolean function ; Kloosterman sums ; Walsh transform
• 刊名：Journal of Systems Science and Complexity
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：27
• 期：4
• 页码：785-794
• 全文大小：189 KB
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• 作者单位：Baofeng Wu (1) (2)
  Zhuojun Liu (2)
  Qingfang Jin (2)
  Xiaoming Zhang (2)
  
  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China
  2. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  
• ISSN：1559-7067

文摘

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.