Distributed Secret Sharing Scheme Based on Personalized Spherical Coordinates Space

Threshold secret sharing schemes are ideal to protect confidential information. In this paper, the authors propose a novel distributed (k, n) threshold secret sharing scheme based on spherical coordinates. As four non-coplanar points can determine a unique sphere, they 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 proactively secret sharing are considered during the procedures of generating shadows and recovering secret and four or more participants could recover secret in their scheme.

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