Secret Sharing Scheme Based on the Differential Manifold

Abstract

In this paper, the concepts of topological space and differential manifold are introduced, and it is proved that the surface determined by function F (x2, x2, …, xt) of class Cr in Euelidean Rt is a differential manifold. Using the intersection of the tangent plane and the hypernormal of the differential manifold to construct the shared master key of participants, an intuitive, secure and complete (t,n)-threshold secret sharing scheme is designed. The paper is proved to be safe, and the probability of successful attack of attackers is only 1/pt-1. When the prime number p is sufficiently large, the probability is almost 0. The results show that this scheme has the characteristics of single-parameter representation of the master key in the geometric method, and is more practical and easy to implement than the Blakley threshold secret sharing scheme.