Secure three-party semi-quantum summation using single photons. (English) Zbl 1528.81050
Summary: We first propose a three-party semi-quantum summation protocol with an almost-dishonest third party (TP) using single photons. TP who has full quantum power helps three classical users compute the summation of their private bit strings while the privacy of their inputs is preserved. For a particle from TP, three users’ operations are limited either to (1) reflect the particle without disturbance back to TP or to (2) measure the particle in the \(Z\) basis and resend the measured particle back to TP. We also show that our protocol is secure against both outside and participant attacks.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
References:
| [1] | Heinrich, S., Quantum summation with an application to integration, J. Complex., 18, 1, 1-50 (2002) · Zbl 1050.68043 · doi:10.1006/jcom.2001.0629 |
| [2] | Heinrich, S.; Novak, E., On a problem in quantum summation, J. Complex., 19, 1, 1-18 (2003) · Zbl 1051.68066 · doi:10.1016/S0885-064X(02)00003-1 |
| [3] | Heinrich, S., Kwas, M., Wozniakowski, H.: Quantum boolean summation with repetitions in the worst-average setting. arXiv:quant-ph/0311036 (2003) · Zbl 1044.65003 |
| [4] | Du, JZ; Chen, XB; Wen, QY; Zhu, FC, Secure multiparty quantum summation, Acta Phys. Sin., 56, 11, 6214 (2007) |
| [5] | Chen, XB; Xu, G.; Yang, YX; Wen, QY, An efficient protocol for the secure multi-party quantum summation, Int. J. Theo. Phy., 49, 11, 2793-2804 (2010) · Zbl 1203.81047 · doi:10.1007/s10773-010-0472-5 |
| [6] | Lo, HK, Insecurity of quantum secure computations, Phys. Rev. A, 56, 1154-1162 (1997) · doi:10.1103/PhysRevA.56.1154 |
| [7] | Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing, pp 643-652. ACM (2002) · Zbl 1192.94115 |
| [8] | Chau, HF, Quantum-classical complexity-security tradeoff in secure multiparty computations, Phys. Rev. A, 61, 032308 (2000) · doi:10.1103/PhysRevA.61.032308 |
| [9] | Ben-Or, M., Crepeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: 47th Annual IEEE Symposium on Foundations of Computer Science, 2006. FOCS’06, pp 249-260 (2006) |
| [10] | Smith, A.: Multi-party quantum computation. arXiv:quant-ph/0111030 (2010) |
| [11] | Sun, Z.; Yu, J.; Wang, P.; Xu, L.; Wu, C., Quantum private comparison with a malicious third party, Quantum Inf. Process, 14, 6, 2125-2133 (2015) · Zbl 1317.81087 · doi:10.1007/s11128-015-0956-6 |
| [12] | Hung, SM; Hwang, SL; Hwang, T.; Kao, SH, Multiparty quantum private comparison with almost dishonest third parties for strangers, Quantum Inf. Process, 16, 2, 36 (2017) · Zbl 1383.81071 · doi:10.1007/s11128-016-1498-2 |
| [13] | He, GP, Quantum private comparison protocol without a third party, Int. J. Quantum Inf., 15, 2, 1750014 (2017) · Zbl 1375.81076 · doi:10.1142/S0219749917500149 |
| [14] | Hillery, M.; Ziman, M.; Bužek, V.; Bieliková, M., Towards quantum-based privacy and voting, Phys. Lett. A, 349, 1-4, 75-81 (2006) · Zbl 1195.81032 · doi:10.1016/j.physleta.2005.09.010 |
| [15] | Li, Y.; Zeng, G., Quantum anonymous voting systems based on entangled state, Optical Review, 15, 5, 219-223 (2008) · doi:10.1007/s10043-008-0034-8 |
| [16] | Wang, Q.; Yu, C.; Gao, F.; Qi, H.; Wen, Q., Self-tallying quantum anonymous voting, Phys. Rev. A, 94, 2, 022333 (2016) · doi:10.1103/PhysRevA.94.022333 |
| [17] | Xue, P.; Zhang, X., A simple quantum voting scheme with multi-qubit entanglement, Scientific Reports, 7, 1, 7586 (2017) · doi:10.1038/s41598-017-07976-1 |
| [18] | Bao, N.; Halpern, NY, Quantum voting and violation of arrow’s impossibility theorem, Phys. Rev. A, 95, 6, 062306 (2017) · doi:10.1103/PhysRevA.95.062306 |
| [19] | Zhang, C.; Sun, Z.; Huang, Y.; Long, D., 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) · Zbl 1284.81079 · doi:10.1007/s10773-013-1884-9 |
| [20] | Zhang, C.; Sun, ZW; Huang, X.; Long, DY, Three-party quantum summation without a trusted third party, Int. J. Quantum Inf., 13, 2, 1550011 (2015) · Zbl 1328.81076 · doi:10.1142/S0219749915500112 |
| [21] | Shi, RH; Mu, Y.; Zhong, H.; Cui, J.; Zhang, S., Secure multiparty quantum computation for summation and multiplication, Sci. Rep., 6, 19655 (2016) · doi:10.1038/srep19655 |
| [22] | 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 |
| [23] | Zhang, C., Situ, H., Huang, Q., Yang, P.: Multi-party quantum summation without a trusted third party based on single particles. Int. J. Quantum Inf.: 1750010 (2017) · Zbl 1375.81079 |
| [24] | 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 |
| [25] | Yang, HY; Ye, TY, Secure multi-party quantum summation based on quantum fourier transform, Quantum Inf. Process, 17, 6, 129 (2018) · Zbl 1448.81176 · doi:10.1007/s11128-018-1890-1 |
| [26] | Ji, Z.; Zhang, H.; Wang, H.; Wu, F.; Jia, J.; Wu, W., Quantum protocols for secure multi-party summation, Quantum Inf. Process, 18, 6, 168 (2019) · Zbl 1504.94214 · doi:10.1007/s11128-018-2141-1 |
| [27] | Julsgaard, B.; Sherson, J.; Cirac, JI; Fiurášek, J.; Polzik, ES, Experimental demonstration of quantum memory for light, Nature, 432, 7016, 482 (2004) · doi:10.1038/nature03064 |
| [28] | Yao, XC; Wang, TX; Xu, P.; Lu, H.; Pan, GS; Bao, XH; Peng, CZ; Lu, CY; Chen, YA; Pan, JW, Observation of eight-photon entanglement, Nature Photonics, 6, 4, 225 (2012) · doi:10.1038/nphoton.2011.354 |
| [29] | Nielson, M. A., Chuang, I.L.: Quantum computation and quantum information (2000) · Zbl 1049.81015 |
| [30] | Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical bob. In: 2007 First International Conference on Quantum, Nano, and Micro Technologies (ICQNM’07), pp 10-10. IEEE (2007) · Zbl 1228.81142 |
| [31] | Zou, X.; Qiu, D.; Li, L.; Wu, L.; Li, L., Semiquantum-key distribution using less than four quantum states, Phy. Rev. A, 79, 5, 052312 (2009) · doi:10.1103/PhysRevA.79.052312 |
| [32] | Jian, W.; Sheng, Z.; Quan, Z.; Chao-Jing, T., Semiquantum key distribution using entangled states, Chinese Phys. Lett., 28, 10, 100301 (2011) · doi:10.1088/0256-307X/26/10/100301 |
| [33] | Krawec, WO, Mediated semiquantum key distribution, Phys. Rev. A, 91, 3, 032323 (2015) · doi:10.1103/PhysRevA.91.032323 |
| [34] | Li, Q.; Chan, WH; Zhang, S., Semiquantum key distribution with secure delegated quantum computation, Scientific Reports, 6, 19898 (2016) · doi:10.1038/srep19898 |
| [35] | Liu, ZR; Hwang, T., Mediated semi-quantum key distribution without invoking quantum measurement, Annalen der Physik, 530, 4, 1700206 (2018) · Zbl 07754524 · doi:10.1002/andp.201700206 |
| [36] | Li, Q.; Chan, WH; Long, DY, Semiquantum secret sharing using entangled states, Phys. Rev. A, 82, 022303 (2010) · doi:10.1103/PhysRevA.82.022303 |
| [37] | Wang, J.; Zhang, S.; Zhang, Q.; Tang, CJ, Semiquantum secret sharing using two-particle entangled state, Int. J. Quantum Inf., 10, 5, 1250050 (2012) · Zbl 1260.94059 · doi:10.1142/S0219749912500505 |
| [38] | Li, L.; Qiu, D.; Mateus, P., Quantum secret sharing with classical bobs, J. Phys. A: Mathematical and Theoretical, 46, 4, 045304 (2013) · Zbl 1341.81020 · doi:10.1088/1751-8113/46/4/045304 |
| [39] | Yang, CW; Hwang, T., Efficient key construction on semi-quantum secret sharing protocols, Int. J. Quantum Inf., 11, 5, 1350052 (2013) · Zbl 1287.81042 · doi:10.1142/S0219749913500524 |
| [40] | Chou, W. H., Hwang, T., Gu, J.: Semi-quantum private comparison protocol under an almost-dishonest third party. arXiv:1607.07961 (2016) |
| [41] | Yan-Feng, L., Semi-quantum private comparison using single photons, Int. J. Theor. Phys., 57, 10, 3048-3055 (2018) · Zbl 1412.81068 · doi:10.1007/s10773-018-3823-2 |
| [42] | Lin, PH; Hwang, T.; Tsai, CW, Efficient semi-quantum private comparison using single photons, Quantum Inf. Process, 18, 7, 207 (2019) · Zbl 1508.81706 · doi:10.1007/s11128-019-2251-4 |
| [43] | Shukla, C.; Thapliyal, K.; Pathak, A., Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue, Quantum Inf. Process, 16, 12, 295 (2017) · Zbl 1382.81077 · doi:10.1007/s11128-017-1736-2 |
| [44] | Dür, W.; Vidal, G.; Cirac, JI, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A, 62, 6, 062314 (2000) · doi:10.1103/PhysRevA.62.062314 |
| [45] | Cai, QY, Eavesdropping on the two-way quantum communication protocols with invisible photons, Phys. Lett. A, 351, 1-2, 23-25 (2006) · Zbl 1234.68031 · doi:10.1016/j.physleta.2005.10.050 |
| [46] | Kraus, B.; Tittel, W.; Gisin, N.; Nilsson, M.; Kröll, S.; Cirac, J., Quantum memory for nonstationary light fields based on controlled reversible inhomogeneous broadening, Phys. Rev. A, 73, 2, 020302 (2006) · doi:10.1103/PhysRevA.73.020302 |
| [47] | Deng, FG; Li, XH; Zhou, HY; Zhang, ZJ, Improving the security of multiparty quantum secret sharing against trojan horse attack, Phys. Rev. A, 72, 4, 044302 (2005) · doi:10.1103/PhysRevA.72.044302 |
| [48] | Li, XH; Deng, FG; Zhou, HY, Improving the security of secure direct communication based on the secret transmitting order of particles, Phys. Rev. A, 74, 5, 054302 (2006) · doi:10.1103/PhysRevA.74.054302 |
| [49] | Gu, J.; Ho, CY; Hwang, T., Statistics attack on ’quantum private comparison with a malicious third party’and its improvement, Quantum Inf. Process, 17, 2, 23 (2018) · Zbl 1402.81110 · doi:10.1007/s11128-017-1788-3 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
