Abstract
This paper presents a novel n-party quantum summation protocol without the help of a third party via using d-dimensional Bell states. The proposed protocol has inserted decoy photons to prevent various types of the outsider attacks. All participants, respectively, perform the shifting operation to encode their private secrets on quantum particle sequences composed of the first particles of all d-dimensional Bell states. Then, the proposed n-party quantum summation protocol can resist individual attack and \((n-2)\)-party collusion attack. As an example, this paper compares the presented multi-party quantum summation protocol with other schemes in terms of different indicators.
Similar content being viewed by others
References
He, G.P.: Quantum private comparison protocol without a third party. Int. J. Quantum Inf. 15(2), 1750014 (2016)
Wu, W.Q., Cai, Q.Y., Wu, S.M., et al.: Cryptanalysis and improvement of Ye et al’s quantum private comparison protocol. Int. J. Theor. Phys. 58(6), 1892–1900 (2019)
Wu, W.Q., Zhang, H.G.: Cryptanalysis of Zhang et al’s Quantum Private Comparison and the Improvement. Int. J. Theor. Phys. 58(6), 1854–1860 (2019)
Wu, W.Q., Ma, X.X.: Quantum private comparison protocol without a third party. Int. J. Theor. Phys. 59(6), 1854–1865 (2020)
Xu, T.T., Li, Z.H., Bai, C.M., et al.: A New Improving Quantum Secret Sharing Scheme. Int. J. Theor. Phys. 56, 1–10 (2017)
Bai, C.M., Li, Z.H., Xu, T.T., et al.: Quantum secret sharing using the d-dimensional GHZ state. Quantum Inf. Process. 16(3), 59 (2017)
Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Quantum public key cryptosystem based on bell states. Int. J. Theor. Phys. 56(11), 3431–3440 (2017)
Wu, W.Q., Cai, Q.Y., Zhang, H.G., et al.: Bit-oriented quantum public-key cryptosystem based on bell states. Int. J. Theor. Phys. 57(12), 1–11 (2018)
Hillery, M., Ziman, M., Buz̆ek, V., et al.: Towards quantum-based privacy and voting. Phys. Lett. A 349(1–4), 75–81 (2006)
Chen, X.B., Xu, G., Yang, Y.X., et al.: An efficient protocol for the secure multi-party quantum summation. Int. J. Theor. Phys. 49(11), 2793–2804 (2010)
Zhang, C., Sun, Z., Huang, Y., et al.: High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 53(3), 933–941 (2014)
Shi, R.H., Mu, Y., Zhong, H., et al.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)
Zhang, C., Razavi, M., Sun, Z.W., et al.: Improvements on “Secure multi-party quantum summation based on quantum Fourier transform.” Quantum Inf. Process. 18, 336 (2019)
Zhang, C., Situ, H., Huang, Q., et al.: Multi-party quantum summation with a single d-level quantum system. Int. J. Quantum Inf. 17(03), 1154–652 (2019)
Zhang, C., Sun, Z.W., Huang, X., et al.: Three-party quantum summation without a trusted third party. Int. J. Quantum Inf. 13(2), 1550011 (2015)
Zhang, C., Situ, H., Huang, Q., et al.: Multi-party quantum summation without a trusted third party based on single particles. Int. J. Quantum Inf. 15(2), 1750010 (2017)
Yang, H.Y., Ye, T.Y.: Secure multi-party quantum summation based on quantum Fourier transform. Quantum Inf. Process. 17(6), 129 (2018)
Wu, W.Q., Zhang, H.G.: A quantum query algorithm for computing the degree of a perfect nonlinear Boolean function. Quantum Inf. Process. 18(3), 62 (2019)
Bennett C.H., Brassard G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179 (1984)
Gao, F., Qin, S.J., Wen, Q.Y., et al.: A simple participant attack on the Bradler-Dusek protocol. Quantum Inf. Comput. 7(4), 329–334 (2007)
Liu, B., Xiao, D., Jia, H.Y., et al.: Collusive attacks to circle-type multi-party quantum key agreement protocols. Quantum Inf. Process. 15, 2113–2124 (2016)
Zhang, C., Razavi, M., Sun, Z.W., et al.: Multi-party quantum summation based on quantum teleportation. Entropy 21(7), 719 (2019)
Zhang, C., Sun, Z., Huang, Y., et al.: High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 53(3), 933–941 (2014)
Acknowledgements
The authors are supported by the Natural Science Foundation of HeBei Province Nos. F2021201199, Science and technology research project of Hebei higher education Nos. ZD2021011.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, W., Ma, X. Multi-party quantum summation without a third party based on d-dimensional Bell states. Quantum Inf Process 20, 200 (2021). https://doi.org/10.1007/s11128-021-03142-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-021-03142-9