Secure Multi-party Computation (SMPC) is a family of protocols which allow some parties to compute a function on their private inputs, obtaining the output at the end and nothing more. In this work, we focus on a particular SMPC problem named Private Set Intersection (PSI). The challenge in PSI is how two or more parties can compute the intersection of their private input sets, while the elements that are not in the intersection remain private. This problem has attracted the attention of many researchers because of its wide variety of applications, contributing to the proliferation of many different approaches. Despite that, current PSI protocols still require heavy cryptographic assumptions that may be unrealistic in some scenarios. In this paper, we perform a Systematic Literature Review of PSI solutions, with the objective of analyzing the main scenarios where PSI has been studied and giving the reader a general taxonomy of the problem together with a general understanding of the most common tools used to solve it. We also analyze the performance using different metrics, trying to determine if PSI is mature enough to be used in realistic scenarios, identifying the pros and cons of each protocol and the remaining open problems.

安全多方计算 (SMPC) 是一系列协议，它允许某些方根据其私有输入计算函数，最后获得输出，仅此而已。在这项工作中，我们专注于一个名为私有集交集 (PSI) 的特定 SMPC 问题。PSI 中的挑战是两方或多方如何计算其私有输入集的交集，同时不在交集中的元素保持私有。这个问题因其广泛的应用而引起了许多研究人员的注意，促进了许多不同方法的扩散。尽管如此，当前的 PSI 协议仍然需要大量的密码假设，这在某些情况下可能是不现实的。在本文中，我们对 PSI 解决方案进行了系统的文献回顾，目的是分析研究 PSI 的主要场景，并为读者提供问题的一般分类以及对用于解决该问题的最常用工具的一般理解。我们还使用不同的指标分析性能，试图确定 PSI 是否足够成熟以用于现实场景，确定每个协议的优缺点以及剩余的未解决问题。