Verifiable Secret Sharing and Distributed Key Generation Based on Hyperplane Geometry

Secret Sharing is an important building block in modern cryptography to ensure high level of data confidentiality and reliability. Most of the existing works in this topic are done using polynomial interpolation. In this paper, we extend Blakely's secret sharing and demonstrate that Verifiable Secret Sharing and Distributed Key Generation also can be designed using hyperplane geometry. In case if matrix inversion is implemented but polynomial interpolation is not, our proposed methods may be preferred than those that are based on polynomial interpolation.