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Multi-party quantum private comparison based on the entanglement swapping of d-level cat states and d-level Bell states

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Abstract

In this paper, a novel multi-party quantum private comparison protocol with a semi-honest third party (TP) is proposed based on the entanglement swapping of d-level cat states and d-level Bell states. Here, TP is allowed to misbehave on his own, but will not conspire with any party. In our protocol, n parties employ unitary operations to encode their private secrets and can compare the equality of their private secrets within one time execution of the protocol. Our protocol can withstand both the outside attacks and the participant attacks on the condition that none of the QKD methods is adopted to generate keys for security. One party cannot obtain other parties’ secrets except for the case that their secrets are identical. The semi-honest TP cannot learn any information about these parties’ secrets except the end comparison result on whether all private secrets from n parties are equal.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments that help enhancing the quality of this paper. Funding by the National Natural Science Foundation of China (Grant Nos. 61402407 and 11375152) is gratefully acknowledged.

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Authors and Affiliations

  1. College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou, 310018, People’s Republic of China

    Ji Zhao-Xu & Ye Tian-Yu

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  1. Ji Zhao-Xu
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  2. Ye Tian-Yu
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Correspondence to Ye Tian-Yu.

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Appendix

Appendix

See Figs. 1, 2, 3 and Table 1

Fig. 1
figure 1

Graphical description of entanglement swapping between one d-level n-particle cat state and one d-level Bell state (Here, one d-level n-particle cat state is depicted by a line with n nodes on it where the first node is solid and other nodes are empty. And one d-level Bell state is depicted by a line with two nodes on it where one node is solid and the other node is empty)

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Fig. 2
figure 2

Graphical description of entanglement swapping process of our protocol for three parties and for qubits

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Fig. 3
figure 3

Graphical description of entanglement swapping process of our protocol for n parties and for qudits

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Table 1 Comparison results between our protocol and the previous MQPC protocols
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Zhao-Xu, J., Tian-Yu, Y. Multi-party quantum private comparison based on the entanglement swapping of d-level cat states and d-level Bell states. Quantum Inf Process 16, 177 (2017). https://doi.org/10.1007/s11128-017-1628-5

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