A Secure Quantum Private Set Computation Protocol with Identity Authentication Utilizing GHZ States

Private set computation (PSC) represents a pivotal technology in the information age, facilitating the processing of sensitive datasets while safeguarding privacy. In this paper, we propose a secure quantum protocol theoretically to achieve private set computation, utilizing the quantum entanglement correlations of Greenberger-Horne-Zeilinger (GHZ) states, and applicable to computations such as Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA). This protocol incorporates an identity verification mechanism, ensuring that only authenticated users can engage in the computation process. It is designed to specifically cater to the computational requirements of PSI-CA or PSU-CA applications, while maintaining the privacy of each element within the data sets. Our approach utilizes tripartite GHZ states alongside single qubit preparations, which are notably straightforward to generate. Furthermore, the quantum operations required from users are confined to \(\mathcal {M}_X\) ${\mathcal{M}}_X$ or \(\mathcal {M}_Y\) ${\mathcal{M}}_Y$ measurements, thereby enhancing the protocol’s practical feasibility. The proposed protocol is secure and can resist attacks from both internal and external attackers, such as user impersonation attacks, user collusion attacks, etc. To substantiate the practical applicability, we employ an example of two private data sets for experimental verification on the IBM quantum computing platform. This work further illustrates the advantages of the GHZ state in private set computing and explores the quantum benefits of entanglement in such computations.