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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.01946 |
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Table of Contents:
- 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~$\mathbb{F}_{2^{2m}}$~of this field~$\mathbb{F}_{2^{m}}$. By applying Möbius transformation and the theorems of hyperelliptic curves, hyper-bentness of these functions are successfully characterized in this field~$\mathbb{F}_{2^{2m}}$ with~$m$~odd integer.