What is Prohibited Structure

Secret sharing aims at distributing and sharing a secret among a group of participants efficiently. In this chapter, we propose a plane-based access structure for secret sharing. Specifically, if any two among a set of three participants in a graph contain an edge, these participants constitute a prohibited structure which is not able to recover the master key. Otherwise, the set of three participants constitute an access structure which can recover the master key. Subsequently, we extend the plane-based scheme and propose a generic k-dimensional secret sharing scheme. Finally, we analyze the performance of the proposed scheme and reveal its advantages compared to existing schemes.