Ideal and Computationally Perfect Secret Sharing Schemes for Generalized Access Structures

A secret sharing scheme is proposed in this paper. The scheme is ideal and uses computationally perfect concept. It uses a one way function and realizes generalized access structure. The scheme is useful for non-ideal access structures. For example, Stinson[14] has identified eighteen possible non-isomorphic monotone access structures with four participants. Fourteen of them admit ideal and perfect secret sharing schemes. The remaining four cannot be made both perfect and ideal. By making use of the computationally perfect concept, we propose ideal scheme for those four access structures. Novelty of the scheme is that it is applicable for any number of participants and generates the least amount of public information. In fact, we show results that establish that the proposed scheme is optimal for access structures consisting of four or less number of participants. Our scheme can be extended to multiple secrets. Since some applications require that a secret sharing scheme designed for it be extended to the case of multiple secrets, our approach finds it useful in such scenarios.