中文摘要：

集合成员关系的安全多方计算在保密数据挖掘和保密数据查询等方面有着重要的应用价值.针对以往方案在集合规模较大时的低效问题,本文将原问题转化成多项式一次性求值问题,在此基础上共设计了四个协议.利用同态加密设计了平凡协议1;利用离散对数设计了高效协议2,此协议非常简洁.最后,针对不同的应用场景又分别设计了云计算环境下外包用户计算的协议3和抗抵赖环境下可公开保密判定的协议4.通过分析和比较显示,我们的方案除了集合的势,其余任何信息都没有泄露,并且在集合规模较大时,相比以往方案高效而简洁.

英文摘要：

Secure multiparty computation of set membership is significant to privacy-preserving data mining, data query, etc. In this paper, we first transform the original problem into the one-time evaluation problem for polynomial, and then construct four protocols. We design the trivial protocol 1 using homomorphic encryption and construct the efficient protocol 2 using discrete logarithm instead of encryption, which is very concise. Lastly, according to the different application scenarios, we also propose protocol 3 and protocol 4 ： the former can be used to outsource computation in cloud computing environment;the latter can be used for public secure computation against repudiation. The analysis and comparison show that our protocols are more efficient and concise than previously known.