**Secret sharing schemes on graphs**

*Laszlo Csirmaz*

**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

**Available format(s): **PDF | BibTeX Citation

**Version: **20050225:155546 (All versions of this report)

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