Secret Sharing Schemes for (k, n)-Consecutive Access Structures

We consider access structures over a set \(\mathcal {P}\) of n participants, defined by a parameter k with \(1 \le k \le n\) in the following way: a subset is authorized if it contains participants \(i,i+1,\ldots ,i+k-1\), for some \(i \in \{1,\ldots ,n-k+1\}\). We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)-consecutive.

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