Paper Info
Title
Secret sharing on infinite graphs.
Abstract
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.
Year
Venue
Keywords
2007
Tatra Mountains Mathematical Publications
secret sharing scheme,information theory,infinite graph,lattice
Field
DocType
Volume
Inverse,Discrete mathematics,Combinatorics,Secret sharing,Code rate,Lattice (order),Vertex (geometry),Upper and lower bounds,Access structure,Mathematics,Information ratio
Journal
41
ISSN
Citations 
PageRank 
1210-3195
1
0.37
References 
Authors
0
1
Name
Order
Citations
PageRank
László Csirmaz116315.86