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Secret Sharing Schemes for (kn)-Consecutive Access Structures

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11124)

Abstract

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, (kn)-consecutive.

We prove that these access structures are only ideal when \(k=1,n-1,n\). Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than \(\frac{2}{3}\). For the non-ideal cases, we give either the exact value of the optimal information rate, for \(k=n-2\) and \(k=n-3\), or some bounds on it.

Keywords

Secret sharing schemes Ideal access structures Information rate 

Notes

Acknowledgments

This work is partially supported by Spanish Ministry of Economy and Competitiveness, under Project MTM2016-77213-R.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dept. MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.CYBERCAT-Center for Cybersecurity Research of CataloniaBarcelonaSpain

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