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arXiv · 2504.18294

Secret Sharing in the Rank Metric

Johan Vester Dinesen·Eimear Byrne·Ragnar Freij-Hollanti·Camilla Hollanti
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Abstract

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.

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Johan Vester Dinesen, Eimear Byrne, Ragnar Freij-Hollanti, Camilla Hollanti. 2025-04-25. Secret Sharing in the Rank Metric. https://doi.org/10.1109/isit63088.2025.11195478

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