TITLE:
Secret Sharing Scheme Based on the Differential Manifold
AUTHORS:
Bin Li
KEYWORDS:
Topological Space, Differential Manifold, Secret Sharing, Tangent Plane, Hypernormal
JOURNAL NAME:
Applied Mathematics,
Vol.14 No.3,
March
20,
2023
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.