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

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Abstract

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 \(\mathcal {M}_X\) or \(\mathcal {M}_Y\) 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.

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No datasets were generated or analysed during the current study.

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Acknowledgements

We would like to thank the anonymous referees for their helpful comments. This research was supported by Key Lab of Information Network Security, Ministry of Public Security (C21605).

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Authors and Affiliations

  1. The Third Research Institue of Ministry of Public Security, Shanghai, 200031, China

    Songyang Wu & Wenqi Sun

  2. Key Laboratory of Information Network Security of Ministry of Public Security, Third Research Institute of the Ministry of Public Security, Shanghai, 200031, China

    Songyang Wu, Wenqi Sun & Qingle Wang

  3. School of Control and Computer Engineering School of Energy, North China Electric Power University, Bei**g, 102206, China

    Yingying Wang, Jiawei Liu & Qingle Wang

Authors
  1. Songyang Wu
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Contributions

Songyang Wu, Wenqi Sun, and Qingle Wang wrote the main manuscript text. Songyang Wu and Qingle Wang designed the quantum private set computation protocol. Yingying Wang and Jiawei Liu performed the experiment and prepared figures 1-10. All authors reviewed the manuscript.

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Correspondence to Qingle Wang.

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Wu, S., Sun, W., Wang, Y. et al. A Secure Quantum Private Set Computation Protocol with Identity Authentication Utilizing GHZ States. Int J Theor Phys 63, 135 (2024). https://doi.org/10.1007/s10773-024-05672-1

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