关于两个不同访问群体的秘密共享方案  

On secret sharing scheme for two different access clusters

作　　者：李滨[1] 

机构地区：[1]成都师范学院数学系,成都611130

出　　处：《四川大学学报（自然科学版）》2016年第3期534-541,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科研项目(12ZB276)

摘　　要：根据秘密共享的含义,针对目前秘密共享方案不能解决两个具有不同访问权限的群体的秘密共享问题,引入(s+q,m+n)(q<min{n,s})门限秘密共享的概念;结合微分几何和密码学理论,提出有限域Zp上的参数曲线在实数区间(a,b)内可微的思想.利用平面上曲线的主密钥点Q(k)处的法线与切线的交点来构建(2+1,m+n)情形的门限体制;利用空间曲线的主密钥点Q(k)处的超法面与切线的交点来构建(s+q,m+n)(s≥3)情形的门限体制.经证明该门限方案满足秘密共享的重构要求和安全性要求,是一个完备的秘密共享方案.结果显示,该门限方案具有几何直观、主密钥的单参数表示、可扩充新的秘密共享参与者的优点,是一个具体实用且易于实现的秘密共享方案.Secret sharing is a nuclear kind of technique in key management.The construction of its scheme is one of hot questions for cryptography researches at present.In this paper,the concept of（s＋q,m＋n）（qmin{n,s}）threshold secret sharing was introduced in the light of the problem that two clusters with different access right can not be solved in secret sharing scheme so far and on the basis of secret sharing meaning.The thought that the parameter curve over finite field Zpis differentiable in real number interval（a,b）was proposed to combine differential geometry with cryptography.A threshold scherne with（2＋1,m＋n）situation was constructed by using the intersection point of normal line and tangent at master key point Q（k）on plane curve.A threshold scheme with（s＋q,m＋n）（s≥3）situation was constructed by using the intersection point of hypernormal plane and tangent at master key point Q（k）on space curve.This threshold scheme was proved to satisfy the requirement of reconstruction and security feature as a perfect secret sharing scheme.The results reveal that this secret sharing scheme has its own advantage of geometric visual and one-parameter representation for a master key as well as extensible new shadow holder.So it is concrete practical and easy to implementation.

关 键 词：可微曲线 正则曲线 门限秘密共享 切线 超法面 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]