Skip to main content
Log in

Secure multi-party convex hull protocol based on quantum homomorphic encryption

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Secure multi-party computational geometry (SMCG) is a branch of secure multi-party computing (SMC). The protocol is designed for secure multi-party convex hull computation in SMCG. Firstly, a secure two-party value comparison protocol based on quantum homomorphic encryption is proposed. Due to the nature of quantum homomorphic encryption, the protocol can well protect the security of data in the execution of quantum circuits and the interaction between parties. The result is announced by a semi-trusted third party. Using the value comparison protocol designed above, a secure multi-party convex hull protocol is proposed, which can safely solve the common convex hull of multiple user point sets. Then the correctness and security analysis are carried out, which proves that the protocol is safe and reliable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in the article.

References

  1. Yao, A.C.: Protocols for secure computations. Annu. Symp. Found. Comput. Sci. Proc. (1982). https://doi.org/10.1109/sfcs.1982.38

    Article  Google Scholar 

  2. Atallah, M.J., Du, W.: Secure multi-party computational geometry. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) Algorithms and data structures, pp. 165–179. Springer, Berlin (2001)

    Chapter  Google Scholar 

  3. Troncoso-Pastoriza, J.R., Katzenbeisser, S., Celik, M., Lemma, A.: A secure multidimensional point inclusion protocol. MM Sec’07 Proc. Multimed. Secur. Work. (2007). https://doi.org/10.1145/1288869.1288884

    Article  Google Scholar 

  4. Luo, Y.-L., Huang, L.-S., Zhong, H.: Secure two-party point-circle inclusion problem. J. Comput. Sci. Technol. 22, 88–91 (2007). https://doi.org/10.1007/s11390-007-9011-0

    Article  Google Scholar 

  5. Pawlik, A., Kozik, J., Krawczyk, T., Lasoń, M., Micek, P., Trotter, W.T., Walczak, B.: Triangle-free geometric intersection graphs with large chromatic number. Discret. Comput. Geom. 50, 714–726 (2013). https://doi.org/10.1007/s00454-013-9534-9

    Article  MathSciNet  MATH  Google Scholar 

  6. Boneh, D.A.N., Franklin, M.: Polynomial-time approximation schemes for geometric intersection graphs. 32, 586–615 (2003)

  7. Tao, Y., Yi, K., Sheng, C., Kalnis, P.: Efficient and accurate nearest neighbor and closest pair search in high-dimensional space. ACM Trans. Database Syst. (2010). https://doi.org/10.1145/1806907.1806912

    Article  Google Scholar 

  8. Li, C., Ni, R.: Derivatives of generalized distance functions and existence of generalized nearest points. J. Approx. Theory. 115, 44–55 (2002). https://doi.org/10.1006/jath.2001.3651

    Article  MathSciNet  MATH  Google Scholar 

  9. Qi, W., Yonglong, L., Liusheng, H.: Privacy-preserving protocols for finding the convex hulls. ARES 2008-3rd Int. Conf. Availab. Secur. Reliab. Proc. (2008). https://doi.org/10.1109/ARES.2008.11

    Article  Google Scholar 

  10. Assarf, B., Gawrilow, E., Herr, K., Joswig, M., Lorenz, B., Paffenholz, A., Rehn, T.: Computing convex hulls and counting integer points with polymake. Math. Program. Comput. 9, 1–38 (2017). https://doi.org/10.1007/s12532-016-0104-z

    Article  MathSciNet  MATH  Google Scholar 

  11. Löffler, M., Van Kreveld, M.: Largest and smallest convex hulls for imprecise points. Algorithmica (New York). 56, 235–269 (2010). https://doi.org/10.1007/s00453-008-9174-2

    Article  MathSciNet  MATH  Google Scholar 

  12. Park, C.S., Park, R., Krishna, G.: Constitutive expression and structural diversity of inducible isoform of nitric oxide synthase in human tissues. Life Sci. 59, 219–225 (1996). https://doi.org/10.1016/0024-3205(96)00287-1

    Article  Google Scholar 

  13. Demartin, F., Maltoni, F., Mawatari, K., Zaro, M.: Higgs production in association with a single top quark at the LHC. Eur. Phys. J. C. 75, 212–219 (2015). https://doi.org/10.1140/epjc/s10052-015-3475-9

    Article  ADS  Google Scholar 

  14. Shi, R., Mu, Y., Zhong, H., Cui, J., Zhang, S.: Privacy-preserving point-inclusion protocol for an arbitrary area based on phase-encoded quantum private query. Quantum Inf. Process. (2017). https://doi.org/10.1007/s11128-016-1476-8

    Article  MATH  Google Scholar 

  15. wan Peng, Z., Shi, R., Zhong, H., Cui, J., Zhang, S.: A novel quantum scheme for secure two-party distance computation. Quantum Inf. Process. 16, 1–12 (2017). https://doi.org/10.1007/s11128-017-1766-9

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Chen, B., Yang, W., Huang, L.: Cryptanalysis and improvement of the novel quantum scheme for secure two-party distance computation. Quantum Inf. Process. 18, 1–14 (2019). https://doi.org/10.1007/s11128-018-2148-7

    Article  ADS  MATH  Google Scholar 

  17. Peng, Z., Shi, R., Wang, P., Zhang, S.: A novel quantum solution to secure two-party distance computation. Quantum Inf. Process. 17, 1–12 (2018). https://doi.org/10.1007/s11128-018-1911-0

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, W., Xu, Y., Yang, J.C.N., Yu, W., Chi, L.: Privacy-preserving quantum two-party geometric intersection. Comput Mater Contin. 60, 1237–1250 (2019)

    Google Scholar 

  19. Liang, M.: Quantum fully homomorphic encryption scheme based on universal quantum circuit. Quantum Inf. Process. 14, 2749–2759 (2015). https://doi.org/10.1007/s11128-015-1034-9

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Boykin, P.O., Roychowdhury, V.: Optimal encryption of quantum bits. Phys. Rev. A At. Mol. Opt. Phys. (2003). https://doi.org/10.1103/PhysRevA.67.042317

    Article  Google Scholar 

  21. Nielsen, M.A., Chuang, I., Grover, L.K.: Quantum computation and quantum information. Am. J. Phys. 70(5), 558–559 (2002). https://doi.org/10.1119/1.1463744

    Article  ADS  Google Scholar 

  22. Yuan, S., Gao, S., Wen, C., Wang, Y., Qu, H., Wang, Y.: A novel fault-tolerant quantum divider and its simulation. Quantum Inf. Process. 2, 1–15 (2022). https://doi.org/10.1007/s11128-022-03523-8

    Article  MathSciNet  MATH  Google Scholar 

  23. Xu, G., Yun, F., Chen, X.B., Xu, S., Wang, J., Shang, T., Chang, Y., Dong, M.: Secure multi-party quantum summation based on quantum homomorphic encryption. Intell. Autom. Soft Comput. 34, 531–541 (2022)

    Article  Google Scholar 

  24. Gong, C., Du, J., Dong, Z., Guo, Z., Gani, A., Zhao, L., Qi, H.: Grover algorithm-based quantum homomorphic encryption ciphertext retrieval scheme in quantum cloud computing. Quantum Inf. Process. 19, 105 (2020). https://doi.org/10.1007/s11128-020-2603-0

    Article  ADS  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 6217070290 and Shanghai Science and Technology Project under Grant No. 21JC1402800 and 20040501500.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ri-Gui Zhou.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Zhou, RG. Secure multi-party convex hull protocol based on quantum homomorphic encryption. Quantum Inf Process 22, 24 (2023). https://doi.org/10.1007/s11128-022-03779-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03779-0

Keywords

Navigation