Secret Sharing in the Rank Metric
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912815774695424 |
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| author | Dinesen, Johan Vester Byrne, Eimear Freij-Hollanti, Ragnar Hollanti, Camilla |
| author_facet | Dinesen, Johan Vester Byrne, Eimear Freij-Hollanti, Ragnar Hollanti, Camilla |
| contents | The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to $q$-polymatroids. Specifically, we introduce the notion of an access structure on a vector space, and consider properties related to duality, minors, and the relationship to $q$-polymatroids. Finally, we show how rank-metric codes give rise to secret sharing schemes within this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secret Sharing in the Rank Metric Dinesen, Johan Vester Byrne, Eimear Freij-Hollanti, Ragnar Hollanti, Camilla Information Theory The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to $q$-polymatroids. Specifically, we introduce the notion of an access structure on a vector space, and consider properties related to duality, minors, and the relationship to $q$-polymatroids. Finally, we show how rank-metric codes give rise to secret sharing schemes within this framework. |
| title | Secret Sharing in the Rank Metric |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.18294 |