Cryptology ePrint Archive: Report 2005/059
Secret sharing schemes on graphs
Abstract: Given a graph $G$, a perfect secret sharing scheme based on $G$ is a method to distribute a secret data among the vertices of $G$, the participants, so that a subset of participants can recover the secret if they contain an edge of $G$, otherwise they can obtain no information regarding the secret. The average information rate is the ratio of the size of the secret and the average size of the share a participant must remember. The information rate of $G$ is the supremum of the information rates realizable by perfect secret sharing schemes.
We construct a graph on $n$ vertices with average information rate below $4/\log n$. We obtain this result by determining, up to a constant factor, the average information rate of the $d$/dimensional cube.
Category / Keywords: foundations / secret sharing, polymatroid, information theory
Date: received 25 Feb 2005
Contact author: laci at degas ceu hu
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Version: 20050225:155546 (All versions of this report)
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