## Cryptology ePrint Archive: Report 2007/355

**Secret sharing on the infinite ladder**

*Laszlo Csirmaz*

**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.

**Category / Keywords: **foundations / secret sharing scheme; information theory; infinite graph; information rate

**Date: **received 7 Sep 2007

**Contact author: **csirmaz at renyi hu

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

**Version: **20070913:195735 (All versions of this report)

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