Private set intersection (PSI) allows participants to securely compute the intersection of their inputs, which has a wide range of applications such as privacy-preserving contact tracing of COVID-19. Most existing PSI protocols were based on asymmetric/symmetric cryptosystem. Therefore, keys-related operations would burden these systems. In this paper, we transform the problem of the intersection of sets into the problem of finding roots of polynomials by using point-value polynomial representation, blind polynomials’ point-value pairs for secure transportation and computation with the pseudorandom function, and then propose an efficient PSI protocol without any cryptosystem. We optimize the protocol based on the permutation-based hash technique which divides a set into multisubsets to reduce the degree of the polynomial. The following advantages can be seen from the experimental result and theoretical analysis: (1) there is no cryptosystem for data hiding or encrypting and, thus, our design provides a lightweight system; (2) with set elements less than , our protocol is highly efficient compared to the related protocols; and (3) a detailed formal proof is given in the semihonest model.

中文翻译：

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使用点值多项式表示的有效专用集相交

专用集交集（PSI）使参与者可以安全地计算其输入的交集，该交集具有广泛的应用程序，例如COVID-19的隐私保护联系人跟踪。现有的大多数PSI协议都基于非对称/对称密码系统。因此，与密钥相关的操作会给这些系统带来负担。在本文中，我们使用点值多项式表示，盲多项式的点值对进行安全传输和使用伪随机函数进行计算，将集合的交集问题转换为寻找多项式根的问题，然后提出高效的PSI协议，无需任何密码系统。我们基于基于置换的哈希技术优化协议，该算法将集合分为多个子集以减少多项式的次数。从实验结果和理论分析可以看出以下优点：（1）没有用于数据隐藏或加密的密码系统，因此，我们的设计提供了一种轻量级的系统；（2）集合元素少于，与相关协议相比，我们的协议效率很高；（3）在半诚实模型中给出了详细的形式证明。