Private Set Intersection: a Systematic Review

Various services, such as search engines, are increasingly deployed in cloud-based and distributed systems. However, data are typically managed by trusted servers, making user privacy and data security critical concerns. Private Set Intersection (PSI) is a powerful cryptographic primitive that enables multiple parties to compute the intersection of their datasets without revealing private inputs. It has been extensively studied over the past two decades, leading to significant gains in computational and communication efficiency. Yet, in many real-world scenarios, revealing the raw intersection may still leak sensitive information. To address this, numerous PSI variants have been developed to meet different application needs. In this paper, we present a comprehensive survey of PSI and its variants. We categorize existing protocols by functionality and underlying cryptographic techniques and analyze their theoretical properties. We focus on recent developments from the last five years, including emerging directions such as fuzzy PSI and updatable PSI. We also explore applications of these protocols across various domains. Finally, we identify key research challenges, including improving privacy guarantees, enhancing computational efficiency, and ensuring scalability for large-scale datasets. These findings aim to guide future research, as PSI and its variants play a central role in advancing privacy-preserving applications.