基于多维空间参数曲线的门限秘密共享方案

引入了多维空间参数曲线的概念，提出了有限域Fp上参数曲线在实数域〖WTHZ〗R〖WTBX〗上可微的思想，并给出了参数曲线上整数点的超法面方程.利用多维空间参数曲线与超法面的交点来构建参与者共享的主密钥，设计出一个直观的、安全完备的（s,n）门限秘密共享方案.结果表明，此方案在几何法中具有主密钥的单参数表示的特点，较Blakley门限秘密共享方案更具体实用，且易于实现.

The threshold secret sharing scheme based on hyperspace parameter curve

The notion of hyperspace parameter curve is introduced. The theory that the parameter curve in finite field Fp is differentiable in real number field R is proposed. Furthermore, the hypernormal plane equation of the integral point on the parameter curve is given. Then a participants sharing master key is constructed by using the intersection point of hyperspace parameter curve and hypernormal plane. At last, a （s, n）-threshold secret sharing scheme that is secure perfect and visual is designed. The results reveal that this secret sharing scheme has its own advantage of one-parameter representation for a master key in the geometric method. So it can be carried out easily and more concrete practical compared with the Blakley threshold secret sharing scheme.