中文摘要：

可验证秘密共享（verifiable secret sharing,VSS）是一类重要的广义安全多方计算协议,轮复杂性和通信复杂性是其重要的复杂性度量.一些标准模型下的常数轮VSS协议在理论上具有较高的效率,但标准模型对秘密信道和广播信道的要求使得这些协议在现实网络中不具有实用性.安全群组通信对安全多方计算协议的安全性和性能有着重要影响,因此提出了安全多播与安全多方计算结合的体系结构——SMPC over SM.设计了两层分散式大规模安全多播组密钥管理方案,新方案所有组成员共享组密钥,在密钥更新过程中使用多播技术,使其达到了常数级的通信复杂性,并具有较好的可扩展性和容错性.基于上述体系结构SMPC over SM和组密钥管理方案,对Katz所提出的标准模型下常数轮VSS协议予以优化,继承了原协议最优轮复杂性优点,同时将其通信复杂性由O（n^3）降低为O（n^2）,节点的处理延迟降低为原来的1/n.

英文摘要：

VSS is an important generalized secure multi-party computation protocol,the round complexity and communication complexity are two of its most important complexity measures.Some existing VSS protocols with constant round under standard model that requires secure channel and broadcast channel are efficient theoretically,however,they can＇ t be applied to real point-to-point networks.Because secure group communication has significant influence on security and performance for secure multi-party computation protocols,an architecture—SMPC over SM was proposed.A two-level decentralized group key management scheme that shared a group key among all members was designed.By assembling those messages needed to be unicast respectively in the scheme,and then multicasting the assembled message,constant order communication complexity was achieved,better scalability and ability of fault tolerance were also obtained.Based on the proposed architecture—SMPC over SM and group key management,VSS with constant round under standard model in Katz et al was optimized,its communication complexity was reduced from O（n^3） to O（n^2）,optimum round complexity was inherited and processing delay of nodes was lowered to 1/n as well.