Distributed secret sharing scheme based on personalized spherical coordinates space

Threshold secret sharing schemes are ideal to protect confidential information. In this paper, we propose a novel distributed threshold secret sharing scheme based on spherical coordinates. As four non-coplanar points can determine a unique sphere, we design transformation algorithms to generate secret as sphere center and mapping algorithms to convert participants to be sphere surface points. An algorithm to generate shadow secrets is proposed based on spherical coordinates. Verifiability and proactivity secret sharing are considered during the procedures of generating shadows and recovering secret and four or more participants could recover secret in our scheme. Performance analysis proves that the proposed scheme has relatively advantage in computation complexity, storage space and communication amounts during distribution and reconstruction processes, and it can tolerate collusion attacks and detect dishonest participants.