International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Secret sharing schemes on graphs

Authors:
Laszlo Csirmaz
Download:
URL: http://eprint.iacr.org/2005/059
Search ePrint
Search Google
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
}