Quantum Secret Sharing by applying Analytic Geometry

In this paper, we investigate a novel $(2,2)$-threshold scheme and then generalize this to a $(n,n)$-threshold scheme for quantum secret sharing (QSS) which makes use of the fundamentals of Analytic Geometry. The dealer aptly selects GHZ states related to the coefficients which determine straight lines on a two-dimension plane. Then by computing each two of the lines intercept or not, we obtain a judging matrix whose rank can be used to determine the secret stored in entangled bits. Based on the database technology, authorized participants access to the database to obtain the secret information and hence the secret never appears in the channel. In this way, the eavesdroppers fail to obtain any secret by applying various attack strategies.