New secondary constructions of Bent functions

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• 作者：Fengrong Zhang ; Claude Carlet ; Yupu Hu…
• 关键词：Boolean function ; Bent function ; High nonlinearity ; Algebraic degree
• 刊名：Applicable Algebra in Engineering, Communication and Computing
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：27
• 期：5
• 页码：413-434
• 全文大小：556 KB
• 刊物类别：Computer Science
• 刊物主题：Symbolic and Algebraic Manipulation
  Computer Hardware
  Theory of Computation
  Artificial Intelligence and Robotics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0622
• 卷排序：27

文摘

In this paper, we first present a novel secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, the algebraic degree and algebraic immunity of the constructed functions are analysed. Finally, we apply the construction using as initial functions some specific bent functions and then specify sufficient conditions for the resulting bent functions not to be contained in the completed Maiorana–McFarland class. In the second part of the paper, we present a corrigendum of “Constructions of bent–negabent functions and their relation to the completed Maiorana–McFarland Class” (IEEE Trans Inf Theory 61(3):1496–1506, 2015).