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Computer Science > Information Theory

arXiv:2209.08712 (cs)
[Submitted on 19 Sep 2022]

Title:Systematic Constructions of Bent-Negabent Functions, 2-Rotation Symmetric Bent-Negabent Functions and Their Duals

Authors:Fei Guo, Zilong Wang, Guang Gong
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Abstract:Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new systematic constructions of bent-negabent functions on $4k, 8k, 4k+2$ and $8k+2$ variables, respectively, by modifying the truth tables of two classes of quadratic bent-negabent functions with simple form. The algebraic normal forms and duals of these constructed functions are also determined. We further identify necessary and sufficient conditions for those bent-negabent functions which have the maximum algebraic degree. At last, by modifying the truth tables of a class of quadratic 2-rotation symmetric bent-negabent functions, we present a construction of 2-rotation symmetric bent-negabent functions with any possible algebraic degrees. Considering that there are probably no bent-negabent functions in the rotation symmetric class, it is the first significant attempt to construct bent-negabent functions in the generalized rotation symmetric class.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2209.08712 [cs.IT]
  (or arXiv:2209.08712v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2209.08712

Submission history

From: Zilong Wang [view email]
[v1] Mon, 19 Sep 2022 02:03:53 UTC (30 KB)
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