Secret Sharing Schemes with General Access Structures (Full version)

Secret sharing schemes with general monotone access structures have been widely discussed in the literature. But in some scenarios, non-monotone access structures may have more practical significance. In this paper, we shed a new light on secret sharing schemes realizing general (not necessarily monotone) access structures. Based on an attack model for secret sharing schemes with general access structures, we redefine perfect secret sharing schemes, which is a generalization of the known concept of perfect secret sharing schemes with monotone access structures. Then, we provide for the first time two constructions of perfect secret sharing schemes with general access structures. The first construction can be seen as a democratic scheme in the sense that the shares are generated by the players themselves. Our second construction significantly enhance the efficiency of the system, where the shares are distributed by the trusted center (TC).