Secret sharing on the infinite ladder

The notion of perfect secret sharing scheme has been extended to encompass infinite access structures, in particular infinite graphs, in [2]. The participants are the vertices of the graph G and the edges are the minimal qualified subsets. The information ratio 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 [2]. We give bounds for other infinite graphs as well.