两方有理数多重集的保密计算

集合的安全多方计算(SMC)在联合数据分析、敏感数据安全查询、数据可信交换等场景有着广泛的应用。该文基于有理数的几何编码，结合保密内积协议，首次提出了有理数域上两方多重集交集和并集的保密计算协议。应用模拟范例证明了协议在半诚实模型下的安全性，分别通过理论分析和仿真测试验证了协议的高效性。与现有协议相比，所设计协议无需给定包含所有集合元素的全集，可以保护集合势的隐私性，且在协议执行过程主要使用乘法运算，达到了信息论安全。

Secure Computation of Two-party Multisets with Rational Numbers

Secure Multiparty Computation (SMC) of sets has wide applications in joint data analysis, secure search over sensitive data, data security exchange. Based on geometric coding of rational numbers and the scalar product protocol, two secure computation protocols for computing the intersection and the union of two multisets with private rational numbers are proposed for the first time. The simulation paradigm is used to prove the privacy- preserving properties of proposed protocols in the semi-honest model, and the protocols’ efficiency is verified by theoretical analysis and programming test. Compared with existing protocols, the proposed protocols do not need to specify a universal set, which can protect the privacy of set potential. Moreover, the multiplication operation is mainly used in the implementation of the protocols, which achieves the security of information theory.