A survey on secure multi-party computation techniques based on private set intersection

With the increasing emphasis on data circulation and value realization, privacy-preserving computation has become a critical enabler for cross-organizational data collaboration. This survey focuses on Private Set Intersection (PSI) techniques within the framework of Secure Multi-Party Computation (SMPC), systematically reviewing the theoretical foundations and technological evolution of PSI as a fundamental privacy-preserving protocol. We first construct a technical stack of PSI protocols, elucidating the cryptographic principles that enable efficient set operations while preserving data confidentiality. Furthermore, we explore the synergistic integration of PSI with blockchain and federated learning, highlighting innovative paradigms for addressing privacy challenges in decentralized environments. Notably, in response to emerging threats posed by quantum computing, this work analyzes the design of post-quantum PSI protocols based on pseudorandom quantum states. Through empirical studies in representative application scenarios – such as collaborative medical analytics, financial risk modeling, and government data sharing – this survey not only demonstrates the practical value of PSI but also underscores its pivotal role in building a trustworthy data collaboration ecosystem. As computational paradigms continue to evolve, PSI is poised to achieve breakthroughs in the multi-objective optimization of privacy, efficiency, and security, thereby offering robust privacy-preserving solutions across various industries.