Secret Sharing in the Rank Metric
By: Johan Vester Dinesen , Eimear Byrne , Ragnar Freij-Hollanti and more
Potential Business Impact:
Makes secret codes work better with math.
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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