Some New Results About Secret Sharing Schemes Based On MSPs

Secret sharing schemes is one of the important research subjects in cryptography. It mainly solves the security of the secret and how to protect the secret efficiently. First, this paper introduces the concept of secret sharing schemes. Then we introduce monotone span programs (MSPs) and two operations of access structure to build large MSPs from small MSPs. Many scholars consider and give some solutions to construct the secret sharing realizing any access structure. In this paper we use the special threshold secret sharing schemes in order to gain perfect secret sharing schemes realizing any access structure. The new method is not only simple but also doesn't depend on the complexity of access structure.Some secret sharing schemes exist the " faulty " places when we estimate whether the scheme is optimal using the ideal secret sharing schemes. Whether is there ideal secret sharing scheme realizing some access structure? We apply the equivalence relation in algebra to dividing some different entities for the set of players, we construct a special threshold access structure; then we consider their composite access structure of these access structures; when this composite access structure is equal to original access structure, we give ideal secret sharing schemes realizing it.