On the bound for anonymous secret sharing schemes

In anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k, n)threshold schemes with 1 < k < n. Our bound is tight for k = 2. We also show a close relationship between optimum anonymous (2, n)threshold secret schemes and combinatorial designs.