随着信息通信技术的不断突破与发展, 信息获取变得非常便利. 与此同时, 隐私信息也更容易泄露. 将智能领域与安全多方计算技术相结合, 有望解决隐私保护问题. 目前, 安全多方计算已经解决了许多不同隐私保护问题, 但还有更多的问题等待人们去解决. 对于极差、极值和的安全多方计算问题目前研究的结果很少, 极差、极值和作为统计学的常用工具在实际中有广泛的应用, 研究极差、极值和的保密计算具有重要意义. 本文提出了新编码方法, 用新编码方法解决了两种不同的安全多方计算问题, 一是极差的保密计算问题, 二是极值和的保密计算问题. 新编码方法结合Lifted ElGamal门限密码系统, 设计多方参与、每方拥有一个数据场景下分布式隐私数据集极差的保密计算协议; 将新编码方法稍作改动解决相同场景下保密计算极值和的问题. 以此为基础, 对新编码方法进一步修改, 结合Paillier密码系统设计了两方参与、每方拥有多个数据情况下分布式隐私数据集极差、极值和的保密计算协议. 用模拟范例方法证明协议在半诚实模型下的安全性. 最后, 用模拟实验测试协议的复杂性. 效率分析和实验结果表明本文协议简单高效, 可广泛用于实际应用中, 是解决其他很多安全多方计算问题的重要工具.
Due to the continuous breakthrough and development of information and communication technologies, information access has become convenient on the one hand. On the other hand, private information is now easier to leak than before. The combination of the intelligent field and secure multiparty computation (SMC) technology is expected to solve privacy protection problems. Although SMC has solved many different privacy protection problems so far, problems that remain to be settled are numerous. Research results about the SMC of range and the sum of extremums are currently seldom reported. As a common statistical tool, range and sum of extremums have been widely used in practice. Therefore, the secure computation of range and the sum of extremes are of great research significance. This study proposes a new encoding method and solves two types of SMC problems by the method: One is the secure computation of range, and the other is that of the sum of extremums. The new encoding method is combined with the Lifted ElGamal threshold cryptosystem to design a secure range computation protocol for distributed private datasets in the scenario in which multiple parties participate and each party has one data. Then, the new encoding method is slightly modified for the secure computation of the sum of extremums in the same scenario. On this basis, the study further modifies the new encoding method and combines it with the Paillier cryptosystem to design a protocol for the secure computation of range and the sum of extremums on distributed private datasets in the scenario in which two parties participate and each party has more than one data. Furthermore, this study proves that the proposed protocols are secure in the semi-honest model with the simulation paradigm. Finally, the complexities of these protocols are tested by simulation experiments. The results of the efficiency analysis and experiments show that the simple and efficient proposed protocols can be widely used in practical applications and are important tools for solving many other SMC problems.