The characterization of hyper-bent function with multiple trace terms in the extension field
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929405970874368 |
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| author | Han, Peng Pu, Keli |
| author_facet | Han, Peng Pu, Keli |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The characterization of hyper-bent function with multiple trace terms in the extension field Han, Peng Pu, Keli Information Theory 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. |
| title | The characterization of hyper-bent function with multiple trace terms in the extension field |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.01946 |