Eprints of Rényi Institute

Secret sharing on infinite graphs

Csirmaz, László (2008) Secret sharing on infinite graphs. Tatra Mountains Mathematical Publication, 41 . pp. 1-18.

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We extend the notion of perfect secret sharing scheme for access structures with infinitely many participants. In particular we investigate cases when the participants are the vertices of an (infinite) graph, and the minimal qualified sets are the edges. The (worst case) information ratio of an access structure is the largest lower bound on the amount of information some participant must remember for each bit in the secret -- just the inverse of the information rate.
We determine this value for several infinite graphs: infinite path, two-dimensional square and honeycomb lattices; and give upper and lower bounds on the ratio for the triangular lattice.
It is also shown that the information ratio is not necessarily local, i.e. all finite spanned subgraphs have strictly smaller ratio than the whole graph. We conclude the paper by posing several open problems.

Item Type:Article
Keywords and phrases:secret sharing scheme, information theory, infinite graph, lattice
Subjects:68P25 Data encryption
94A60 Cryptography
Divisions:Research Groups > Theoretical cryptography
Last Modified:19 Nov 2009 15:32

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