基于多维空间参数曲线的门限秘密共享方案

The threshold secret sharing scheme based on hyperspace parameter curve

引入了多维空间参数曲线的概念,提出了有限域Fp上参数曲线在实数域R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 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.