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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.01190 |
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| _version_ | 1866909718643998720 |
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| author | Xie, Xi Li, Nian Wang, Qiang Zeng, Xiangyong Du, Yinglong |
| author_facet | Xie, Xi Li, Nian Wang, Qiang Zeng, Xiangyong Du, Yinglong |
| contents | The differential-linear connectivity table (DLCT), introduced by Bar-On et al. at EUROCRYPT'19, is a novel tool that captures the dependency between the two subciphers involved in differential-linear attacks. This paper is devoted to exploring the differential-linear properties of $(n,n)$-functions. First, by refining specific exponential sums, we propose two classes of power functions over $\mathbb{F}_{2^n}$ with low differential-linear uniformity (DLU). Next, we further investigate the differential-linear properties of $(n,n)$-functions that are polynomials by utilizing power functions with known DLU. Specifically, by combining a cubic function with quadratic functions, and employing generalized cyclotomic mappings, we construct several classes of $(n,n)$-functions with low DLU, including some that achieve optimal or near-optimal DLU compared to existing results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01190 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of $(n,n)$-functions with low differential-linear uniformity Xie, Xi Li, Nian Wang, Qiang Zeng, Xiangyong Du, Yinglong Information Theory The differential-linear connectivity table (DLCT), introduced by Bar-On et al. at EUROCRYPT'19, is a novel tool that captures the dependency between the two subciphers involved in differential-linear attacks. This paper is devoted to exploring the differential-linear properties of $(n,n)$-functions. First, by refining specific exponential sums, we propose two classes of power functions over $\mathbb{F}_{2^n}$ with low differential-linear uniformity (DLU). Next, we further investigate the differential-linear properties of $(n,n)$-functions that are polynomials by utilizing power functions with known DLU. Specifically, by combining a cubic function with quadratic functions, and employing generalized cyclotomic mappings, we construct several classes of $(n,n)$-functions with low DLU, including some that achieve optimal or near-optimal DLU compared to existing results. |
| title | Construction of $(n,n)$-functions with low differential-linear uniformity |
| topic | Information Theory |
| url | https://arxiv.org/abs/2508.01190 |