On Hierarchical Threshold Access Structures

One of the recent generalizations of (t, n) secret sharing for hierarchical threshold access structures is given by Tassa, where he answers the natural question of sharing a secret among a set of participants, say military officers, so that the secret can be constructed by a group of participants, some of whom are hierarchically superior to others. Both recent schemes proposed by Tassa for addressing this problem require some significant amount of theoretical background. We give a conceptually simpler alternative for the understanding of the realization of hierarchical threshold access structures and we consider perfectness of our scheme with the help of computer experiments. Our simple scheme employs a slightly different approach than previous works, as it involves a certain distribution of polynomials, where members of higher compartments are given a summation of evaluations of higher number of polynomials, resulting in a hierarchical effect. We further consider some alternative hierarchical access structures having potential to be applied in military. The access structures that we consider are realized herein with a simple employment of the well known building blocks such as Lagrange interpolation and access structure product and can be realized with an information rate at worst 1/m.