| Derived from effective management to the key, Secret Sharing is an important branch of Cryptology. With the deepening research to theory, Secret Sharing applies increasingly widespread and is involved in e-commerce, privacy protection, data security and secure multi-party computation and so on. Delving into threshold Secret Sharing algorithm not only promotes the Secret Sharing theoretical research, but also holds great practical significance.By widely reading Chinese and foreign references, this paper introduces components and critical stages of threshold Secret Sharing scheme, describes the current station at home and abroad in this field, studies deeply on the ideologies, key technologies, advantages and shortcomings of classic threshold schemes. All these lay the foundation for writing this paper. By extensively learning, this paper made the following work:(1)A threshold Secret Sharing scheme based on cube is proposed. In this scheme, participants’ shares are the points mapped into the surfaces of the cube, and the cube’s geometric center is used to place the secret.(2)Relying on the cube scheme, a modal on the threshold Secret Sharing scheme based on sphere is raised. In this scheme, n participants’shares are the points belong to a sphere, n participants maintain the sphere jointly, and the secret is placed in the center of the sphere.(3)A specific threshold Secret Sharing scheme based on sphere is put forward. The secret distribution algorithm is mainly responsible for mapping the secret into a point, and mapping the participants’ shares into the sphere whose center is the point. Depending on known points, the secret reconstruction algorithm rebuilds the sphere, and then calculates the center.(4)The threshold Secret Sharing scheme based on sphere is analyzed mainly on false data and collusion attack. Against the false data, this scheme applies digital signature to participants, which makes the scheme be identifiable to the false data and the provider. |
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