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Secret sharing schemes on graphs
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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. |
BibTeX
@misc{eprint-2005-12396, title={Secret sharing schemes on graphs}, booktitle={IACR Eprint archive}, keywords={foundations / secret sharing, polymatroid, information theory}, url={http://eprint.iacr.org/2005/059}, note={ laci@degas.ceu.hu 12839 received 25 Feb 2005}, author={Laszlo Csirmaz}, year=2005 }