CryptoDB
Secret sharing on trees: problem solved
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Abstract: | We determine the worst case information rate for all secret sharing schemes based on trees. It is the inverse of $2-1/c$, where $c$ is the size of the maximal core in the tree. A {\it core} is a connected subset of the vertices so that every vertex in the core has a neighbor outside the core. The upper bound comes from an application of the entropy method, while the lower bound is achieved by a construction using Stinson's decomposition theorem. It is shown that $2-1/c$ is also the {\it fractional cover number} of the tree where the edges of the tree are covered by stars, and the vertex cover should be minimized. We also give an $O(n^2)$ algorithm which finds an optimal cover on any tree, and thus a perfect secret sharing scheme with optimal rate. |
BibTeX
@misc{eprint-2009-18222, title={Secret sharing on trees: problem solved}, booktitle={IACR Eprint archive}, keywords={foundations / Secret sharing scheme; information rate; graph;}, url={http://eprint.iacr.org/2009/071}, note={ csirmaz@degas.ceu.hu 14287 received 12 Feb 2009}, author={Laszlo Csirmaz and Gabor Tardos}, year=2009 }