The characterization of hyper-bent function with multiple trace terms in the extension field

2024/07/02 by Peng Han, Han, Peng, Keli Pu +1
Computer Science · Mathematics · Medicine · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Lung Cancer Treatments and Mutations #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2407.01946

openalex publication_date 2024/07/02 · openalex created_date 2024/07/06 · openalex updated_date 2026/07/28

Abstract

Bent functions are maximally nonlinear Boolean functions with an even number of variables, which include a subclass of functions, the so-called hyper-bent functions whose properties are stronger than bent functions and a complete classification of hyper-bent functions is elusive and inavailable.~In this paper,~we solve an open problem of Mesnager that describes hyper-bentness of hyper-bent functions with multiple trace terms via Dillon-like exponents with coefficients in the extension field~\mathbbF_2^2m~of this field~\mathbbF_2^m. By applying Möbius transformation and the theorems of hyperelliptic curves, hyper-bentness of these functions are successfully characterized in this field~\mathbbF_2^2m with~m~odd integer.

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