International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Secret sharing on the infinite ladder

Laszlo Csirmaz
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Abstract: The notion of perfect secret sharing scheme has been extended to encompass infinite access structures, in particular infinite graphs. The participants are the vertices of the graph $G$ and the edges are the minimal qualified subsets. The information ratio (the inverse of the information rate) of $G$ is the largest lower bound on the amount of information by secret bits some vertex must receive in each scheme realizing this access structure. We show that this value is 7/4 for the infinite ladder, solving an open problem from. We give bounds for other infinite graphs as well.
  title={Secret sharing on the infinite ladder},
  booktitle={IACR Eprint archive},
  keywords={foundations / secret sharing scheme; information theory; infinite graph; information rate},
  note={ 13763 received 7 Sep 2007},
  author={Laszlo Csirmaz},