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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05738 |
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| _version_ | 1866915330657353728 |
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| author | Cui, Yuehui Luo, Jinquan |
| author_facet | Cui, Yuehui Luo, Jinquan |
| contents | Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\mathbb{F}_{p^n}$, where $n=2m$ and $\gcd(s,p^m+1)=t$. In \cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what happens if $t\geq1$? In this paper, we extend the result of \cite{kpm-1} from $t=1$ to general case. We use a different method than in \cite{kpm-1} to determine the differential spectrum and boomerang spectrum of $f$ by studying the number of rational points on some curves. This method may be helpful for calculating the differential spectrum and boomerang spectrum of some Niho type power functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Spectrum and Boomerang Spectrum of Some Power Mapping Cui, Yuehui Luo, Jinquan Information Theory Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\mathbb{F}_{p^n}$, where $n=2m$ and $\gcd(s,p^m+1)=t$. In \cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what happens if $t\geq1$? In this paper, we extend the result of \cite{kpm-1} from $t=1$ to general case. We use a different method than in \cite{kpm-1} to determine the differential spectrum and boomerang spectrum of $f$ by studying the number of rational points on some curves. This method may be helpful for calculating the differential spectrum and boomerang spectrum of some Niho type power functions. |
| title | Differential Spectrum and Boomerang Spectrum of Some Power Mapping |
| topic | Information Theory |
| url | https://arxiv.org/abs/2506.05738 |