Improved Scheme of Distributed Secret Sharing Based on Personalized Spherical Coordinates Space

Threshold secret sharing schemes are ideal to protect confidential information. In this paper, we give a better -reconstructed algorithm of the distributed threshold secret sharing scheme based on spherical coordinates. In TAN’s scheme, during secret sharing procedures of proposed scheme, they designed algorithm to convert secret to sphere center. And then they designed an algorithm to all the participants on the same sphere surface. Because four non-coplanar points determine a unique sphere, the dealer and other four participants could reconstruct the secret. Cramer rule is used to calculus and reconstruct the secret. In our scheme, we have found that Gaussian elimination is a better way to calculus and reconstruct the secret. Performance analysis proves that the proposed scheme has relatively advantage in computation complexity, storage space and communication amounts during distribution and reconstruction processes.