When does a bent concatenation not belong to the completed Maiorana-McFarland class?
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910422878126080 |
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| author | Kudin, Sadmir Pasalic, Enes Polujan, Alexandr Zhang, Fengrong |
| author_facet | Kudin, Sadmir Pasalic, Enes Polujan, Alexandr Zhang, Fengrong |
| contents | Every Boolean bent function $f$ can be written either as a concatenation $f=f_1||f_2$ of two complementary semi-bent functions $f_1,f_2$; or as a concatenation $f=f_1||f_2||f_3||f_4$ of four Boolean functions $f_1,f_2,f_3,f_4$, all of which are simultaneously bent, semi-bent, or 5-valued spectra-functions. In this context, it is essential to ask: When does a bent concatenation $f$ (not) belong to the completed Maiorana-McFarland class $\mathcal{M}^\#$? In this article, we answer this question completely by providing a full characterization of the structure of $\mathcal{M}$-subspaces for the concatenation of the form $f=f_1||f_2$ and $f=f_1||f_2||f_3||f_4$, which allows us to specify the necessary and sufficient conditions so that $f$ is outside $\mathcal{M}^\#$. Based on these conditions, we propose several explicit design methods of specifying bent functions outside $\mathcal{M}^\#$ in the special case when $f=g||h||g||(h+1)$, where $g$ and $h$ are bent functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When does a bent concatenation not belong to the completed Maiorana-McFarland class? Kudin, Sadmir Pasalic, Enes Polujan, Alexandr Zhang, Fengrong Information Theory Cryptography and Security Discrete Mathematics Combinatorics Every Boolean bent function $f$ can be written either as a concatenation $f=f_1||f_2$ of two complementary semi-bent functions $f_1,f_2$; or as a concatenation $f=f_1||f_2||f_3||f_4$ of four Boolean functions $f_1,f_2,f_3,f_4$, all of which are simultaneously bent, semi-bent, or 5-valued spectra-functions. In this context, it is essential to ask: When does a bent concatenation $f$ (not) belong to the completed Maiorana-McFarland class $\mathcal{M}^\#$? In this article, we answer this question completely by providing a full characterization of the structure of $\mathcal{M}$-subspaces for the concatenation of the form $f=f_1||f_2$ and $f=f_1||f_2||f_3||f_4$, which allows us to specify the necessary and sufficient conditions so that $f$ is outside $\mathcal{M}^\#$. Based on these conditions, we propose several explicit design methods of specifying bent functions outside $\mathcal{M}^\#$ in the special case when $f=g||h||g||(h+1)$, where $g$ and $h$ are bent functions. |
| title | When does a bent concatenation not belong to the completed Maiorana-McFarland class? |
| topic | Information Theory Cryptography and Security Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2404.16220 |