A verifiable \((k,n)\)-threshold quantum secure multiparty summation protocol. (English) Zbl 1526.81021
Summary: Quantum secure multiparty summation plays an important role in quantum cryptography. In the existing quantum secure multiparty summation protocols, the \((n,n)\)-threshold protocol has been given extensive attention. To increase the applicability of quantum secure multiparty summation protocols, a new quantum secure multiparty summation protocol based on Shamir’s threshold scheme and \(d\)-dimensional GHZ state is proposed in this paper. In the proposed protocol, i) it has a \((k,n)\)-threshold approach; ii) in the result output phase, it can not only detect the existence of deceptive behavior but also determine the specific cheaters; iii) compared with the \((n,n)\)-threshold quantum secure multiparty summation protocols, it needs less computation cost when \(L\) satisfies \(L > 4\), where \(L\) is the length of each participant’s secret. In addition, the security analysis shows that our protocol can resist intercept-resend attack, entangle-measure attack, Trojan horse attack, and participant attack.
MSC:
| 81P94 | Quantum cryptography (quantum-theoretic aspects) |
| 65B10 | Numerical summation of series |
| 68M25 | Computer security |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 94A40 | Channel models (including quantum) in information and communication theory |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 93C65 | Discrete event control/observation systems |
| 68P30 | Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) |
Keywords:
quantum secure multiparty summation; \(d\)-dimensional GHZ state; Shamir’s threshold scheme; hash function; securityReferences:
| [1] | Yao, A.C.: Protocols for secure computations. In: 23rd IEEE Symposium on Foundations of Computer Science, pp. 160-164 (1982) |
| [2] | Hamada, K., Kikuchi, R., Ikarashi, D., Chida, K., Takahashi, K.: Practically efficient multi-party sorting protocols from comparison sort algorithms. In: Information Security and cryptology-ICISC 2012. 15th International Conference, pp. 202-216 (2013) · Zbl 1342.68121 |
| [3] | Laud, P.; Pettai, M., Secure multiparty sorting protocols with covert privacy, Secure IT systems NordSec 2016, 10014, 216-231 (2016) |
| [4] | Maheshwari, N., Kiyawat, K.: Structural framing of protocol for secure multiparty cloud computation. In: 2011 Fifth Asia Modelling Symposium IEEE, pp. 187-192 (2011) |
| [5] | Lopez-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption. In: Proceedings of the 2012 ACM Symposium on Theory of Computing, pp. 1219-1234 (2012) · Zbl 1286.68114 |
| [6] | Jung, T.; Li, XY; Wan, M., Collusion-tolerable privacy-preserving sum and product calculation without secure channel, IEEE Trans. Dependable Secure Comput., 12, 1, 45-57 (2015) · doi:10.1109/TDSC.2014.2309134 |
| [7] | Mehnaz, S., Bellala, G., Bertino, E.: A secure sum protocol and its application to privacy-preserving multiparty analytics. In: Proceedings of the 22nd ACM on Symposium on Access Control Models and Technologies, pp. 219-230. ACM (2017) |
| [8] | Ashouri, TM; Baraani, DA, Cryptographic collusion-resistant protocols for secure sum, Int. J. Electron. Secur. Digit. Forensic., 9, 1, 19-34 (2017) · doi:10.1504/IJESDF.2017.081753 |
| [9] | Kantarcioglu, M.; Clifton, C., Privacy-preserving distributed mining of association rules on horizontally partitioned data, IEEE Trans. Knowl. Data Eng., 16, 9, 1026-1037 (2004) · doi:10.1109/TKDE.2004.45 |
| [10] | Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium of Foundation of Computer Science, pp. 124-134 (1994) |
| [11] | Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium Computing, pp. 212-219. ACM (1996) · Zbl 0922.68044 |
| [12] | Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 643-652 (2002) · Zbl 1192.94115 |
| [13] | Chen, XB; Xu, G.; Yang, YX; Wen, QY, An efficient protocol for the secure multi-party quantum summation, Int. J. Theor. Phys., 49, 11, 2793-2804 (2010) · Zbl 1203.81047 · doi:10.1007/s10773-010-0472-5 |
| [14] | Wang, QL; Sun, HX; Huang, W., Multi-party quantum private comparison protocol with n-level entangled states, Quant. Inf. Process., 13, 11, 2375-2389 (2014) · Zbl 1305.81070 · doi:10.1007/s11128-014-0774-2 |
| [15] | Liu, B.; Zhang, MW; Shi, RH, Quantum secure multi-party private set intersection cardinality, Int. J. Theor. Phys., 59, 7, 1992-2007 (2020) · Zbl 1447.81096 · doi:10.1007/s10773-020-04471-8 |
| [16] | Dou, Z.; Chen, XB; Xu, G.; Liu, W.; Yang Y. X.; Yang, Y., An attempt at universal quantum secure multi-party computation with graph state, Phys. Scr., 95, 5, 055106 (2020) · doi:10.1088/1402-4896/ab73d5 |
| [17] | Shi, RH; Zhang, S., Quantum solution to a class of two-party private summation problems, Quantum Inf. Process., 16, 9, 225 (2017) · Zbl 1387.81193 · doi:10.1007/s11128-017-1676-x |
| [18] | Ye, TY; Xu, TJ, A lightweight three-user secure quantum summation protocol without a third party based on single-particle states, Quant. Inf. Process., 21, 9, 309 (2022) · Zbl 1508.81808 · doi:10.1007/s11128-022-03652-0 |
| [19] | Liu, W.; Wang, YB; Fan, WQ, An novel protocol for the quantum secure multi-party summation based on two-particle bell states, Int. J. Theor. Phys., 56, 9, 2783-2791 (2017) · Zbl 1379.81039 · doi:10.1007/s10773-017-3442-3 |
| [20] | Yang, HY; Ye, TY, Secure multi-party quantum summation based on quantum Fourier transform, Quant. Inf. Process., 17, 6, 129 (2018) · Zbl 1448.81176 · doi:10.1007/s11128-018-1890-1 |
| [21] | Lv, SX; Jiao, XF; Zhou, P., Multiparty quantum computation for summation and multiplication with mutually unbiased bases, Int. J. Theor. Phys., 58, 2872-2882 (2019) · Zbl 1433.81054 · doi:10.1007/s10773-019-04170-z |
| [22] | Wang, YL; Hu, PC; Xu, QL, Quantum secure multi-party summation based on entanglement swapping, Quant. Inf. Process., 20, 10, 319 (2021) · Zbl 1509.81425 · doi:10.1007/s11128-021-03262-2 |
| [23] | Song, X.; Gou, R.; Wen, A., Secure multiparty quantum computation based on Lagrange unitary operator, Sci. Rep., 10, 7921 (2020) · doi:10.1038/s41598-020-64538-8 |
| [24] | Sutradhar, K.; Om, H., A generalized quantum protocol for secure multiparty summation, IEEE Trans. Circuits Syst. II Express Briefs, 67, 12, 2978-2982 (2020) |
| [25] | Qin, H.; Dai, Y., Dynamic quantum secret sharing by using d-dimensional GHZ state. Quantum Inf, Process., 16, 3, 64 (2017) · Zbl 1373.81181 |
| [26] | Cai, QY; Li, WB, Deterministic secure communication without using entanglement, Chin. Phys. Lett., 21, 601-603 (2004) · doi:10.1088/0256-307X/21/4/003 |
| [27] | Deng, FG; Long, GL, Secure direct communication with a quantum one-time pad, Phys. Rev. A., 69, 2004, 98-106 (2016) |
| [28] | Wang, P.; Zhang, R.; Sun, ZW, Practical quantum key agreement protocol based on BB84, Quant. Inf. Comput., 22, 3-4, 241-250 (2022) |
| [29] | Li, YB; Qin, SJ; Yuan, Z.; Huang, W.; Sun, Y., Quantum private comparison against decoherence noise, Quant. Inf. Process., 12, 6, 2191-2205 (2013) · Zbl 1267.81128 · doi:10.1007/s11128-012-0517-1 |
| [30] | Yang, YG; Xia, J.; Jia, X.; Zhang, H., Comment on quantum private comparison protocols with a semi-honest third party, Quantum Inf. Process., 12, 2, 877-885 (2013) · Zbl 1264.81159 · doi:10.1007/s11128-012-0433-4 |
| [31] | Shamir, A., How to share a secret, Commun. ACM, 22, 11, 612-613 (1979) · Zbl 0414.94021 · doi:10.1145/359168.359176 |
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