实现分离多级存取结构的黑盒密钥共享体制

黑盒密钥共享体制和有限域上的密钥共享体制是不同的.该体制只要求主密钥空间是一个有限交换群,并且可以将群运算和随机挑选群元素等过程作为黑盒调用.尤其是,它与群的结构和除数无关.迄今为止,还没有造出有效的实现非门限存取结构的黑盒密钥共享体制.文中给出了任意交换群上的实现一类非门限存取结构的黑盒密钥共享体制的构造方法.作者使用的工具是环上单调张成方案.首先,作者提出弱单调张成方案的概念,并给出了使用弱单调张成方案构造单调张成方案的方法.然后,利用有理数域上的单调张成方案和有限域上的单调张成方案,构造出了一对互素的弱单调张成方案,最终构造出了实现一类非门限存取结构——分离多级存取结构的有效黑盒密钥共享体制.作者构造的新体制可用于构造新的实现分离多级存取结构的环上安全多方计算协议、线性整密钥共享体制、分布式RSA签名协议和新的零知识证明协议.

Black-Box Secret Sharing Scheme for Disjunctive Multi-Level Access Structure

A black-box secret sharing scheme(BBSSS) differs from an ordinary linear secret sharing scheme over finite field.It works in exactly the same way over any finite Abelian group,as it only requires black-box access to group operations and to random group elements.In particular,there is no dependence on e.g.the structure of the group or its order.Until now,the efficient BBSSS for non-threshold access structure has not been constructed.In this paper,we give an approach to construct BBSSS for some non-threshold over arbitrary Abelian group by making use of the technique of monotone span scheme(MSP).First,we introduce the notation of weak MSPs and give the technique to construct the MSP based on weak MSPs.Then,we construct a pair of coprime weak MSPs by using the MSP over rational field and the MSP over finite field.Finally,we construct an efficient non-threshold BBSSS such as BBSSS for disjunctive multi-level access structure.Our new scheme can be applied to construct the new secure multi-party computation protocol over rings,linear integer secret sharing scheme,and distributed RSA signature for disjunctive multi-level access structure,and new zero-knowledge protocol.