Ideal hierarchical secret sharing and lattice path matroids

By a fundamental result by Brickell and Davenport (J Cryptol 4:123–134, 1991), the access structures of ideal secret sharing schemes are matroid ports. Farràs and Padró (IEEE Trans Inf Theory 58(5):3273–3286, 2012) presented a characterization of ideal hierarchical access structures. In this paper, we provide a different characterization. Specifically, we show that an access structure is ideal and hierarchical if and only if it is a port of a lattice path matroid at some specific points.