本論文試圖利用新發現之量子互換特性，在「半量子」環境中設計安全的協定。本論文首先推導出廣義GHZ-like States之間的糾纏互換關係。利用這些關係，提出了一個含第三方的半量子私密比較協議，在近乎不誠實的第三方幫助下，使兩個只具備基本量子能力的「古典」參與者可以安全的比較秘密。此外，將此協定衍生並提出了一個多方半量子私密求和協議，在近乎不誠實的第三方幫助下，使三個或更多的「古典」參與者可以安全的進行私密求和。此外，本文提出的協定可以簡單的調整成為不同的量子密碼學協定，如半量子金鑰分配協議、半量子多方私密分享協議與可控制式半量子直接通訊協議。

This thesis develops some new properties of entanglement swapping of generalized Greenberger–Horne–Zeilinger-like (GHZ-like) states to design secure protocols in the “semi-quantum” environment. We first derive the entanglement swapping correlations of generalized Greenberger–Horne–Zeilinger-like states. By utilizing the properties of entanglement swapping, we propose a semi-quantum private comparison protocol (SQPC) that allows two classical participants to compare the equality of their secret information securely with the help of an almost-dishonest third party (TP). We then extend the SQPC to propose the first multi-party semi-quantum summation protocol (MSQS), which allows three or more classical participants to compute the summation of their secret information securely with the help of an almost-dishonest TP. In addition, we show that the proposed protocols can be easily converted to other quantum cryptography protocols, such as mediated semi-quantum key distribution, multi-party semi-quantum secret sharing, and controlled deterministic secure semi-quantum communication.

[1] Yang, Yu-Guang, and Qiao-Yan Wen. "An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement." Journal of Physics A: Mathematical and Theoretical 42.5 (2009): 055305.
[2] Jia, Heng-Yue, et al. "Quantum protocol for millionaire problem." Optics communications 284.1 (2011): 545-549.
[3] Chen, Xiu-Bo, et al. "An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement." Optics communications 283.7 (2010): 1561-1565.
[4] Lin, Jason, Hsin-Yi Tseng, and Tzonelih Hwang. "Intercept–resend attacks on Chen et al.'s quantum private comparison protocol and the improvements." Optics Communications 284.9 (2011): 2412-2414.
[5] Zhang, Wei-Wei, Dan Li, and Yan-Bing Li. "Quantum private comparison protocol with W States." International Journal of Theoretical Physics 53.5 (2014): 1723-1729.
[6] Chang, Yao-Jen, Chia-Wei Tsai, and Tzonelih Hwang. "Multi-user private comparison protocol using GHZ class states." Quantum information processing 12.2 (2013): 1077-1088.
[7] Xu, Ling, and Zhiwen Zhao. "Quantum private comparison protocol based on the entanglement swapping between χ+ state and W-Class state." Quantum Information Processing 16.12 (2017): 302.
[8] Luo, Qing-bin, et al. "Multi-party quantum private comparison protocol based on d-dimensional entangled states." Quantum information processing 13.10 (2014): 2343-2352.
[9] Liu, Wen, Yong-Bin Wang, and Xiao-Mei Wang. "Multi-party quantum private comparison protocol using d-dimensional basis states without entanglement swapping." International Journal of Theoretical Physics 53.4 (2014): 1085-1091.
[10] Zhang, Wei-Wei, and Ke-Jia Zhang. "Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party." Quantum information processing 12.5 (2013): 1981-1990.
[11] Tseng, Hsin-Yi, Jason Lin, and Tzonelih Hwang. "New quantum private comparison protocol using EPR pairs." Quantum Information Processing 11.2 (2012): 373-384.
[12] Wang, Cong, Gang Xu, and Yi-Xian Yang. "Cryptanalysis and improvements for the quantum private comparison protocol using EPR pairs." International Journal of Quantum Information 11.04 (2013): 1350039.
[13] Wang, Qing-Le, Hong-Xiang Sun, and Wei Huang. "Multi-party quantum private comparison protocol with n-level entangled states." Quantum information processing 13.11 (2014): 2375-2389.
[14] Huang, Sheng-Liang, Tzonelih Hwang, and Prosanta Gope. "Multi-party quantum private comparison protocol with an almost-dishonest third party using GHZ states." International Journal of Theoretical Physics 55.6 (2016): 2969-2976.
[15] Hung, Shih-Min, et al. "Multiparty quantum private comparison with almost dishonest third parties for strangers." Quantum Information Processing 16.2 (2017): 36.
[16] Ye, Tian-Yu, and Chong-Qiang Ye. "Measure-Resend Semi-Quantum Private Comparison Without Entanglement." International Journal of Theoretical Physics 57.12 (2018): 3819-3834.
[17] Yan-Feng, Lang. "Semi-Quantum Private Comparison Using Single Photons." International Journal of Theoretical Physics 57.10 (2018): 3048-3055.
[18] Du Jian-Zhong, Chen Xiu-Bo, Wen Qiao-Yan et al. “Secure multiparty quantum summation.” Acta Phys. Sin., 2007, 56(11): 6214-6219.
[19] Chen, Xiu-Bo, et al. "An efficient protocol for the secure multi-party quantum summation." International Journal of Theoretical Physics 49.11 (2010): 2793-2804.
[20] Shi, Run-hua, et al. "Secure multiparty quantum computation for summation and multiplication." Scientific reports 6 (2016): 19655.
[21] Zhang, Cai, et al. "High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom." International Journal of Theoretical Physics 53.3 (2014): 933-941.
[22] Liu, Wen, Yong-Bin Wang, and Wen-Qin Fan. "An novel protocol for the quantum secure multi-party summation based on two-particle bell states." International Journal of Theoretical Physics 56.9 (2017): 2783-2791.
[23] Zhang, Cai, et al. "Multi-party quantum summation without a trusted third party based on single particles." International Journal of Quantum Information 15.02 (2017): 1750010.
[24] Tang, Xin, et al. "Secure Multiparty Quantum Summation Based on d-Level Single Particles." International Conference on Cloud Computing and Security. Springer, Cham, 2018.
[25] Yang, Hui-Yi, and Tian-Yu Ye. "Secure multi-party quantum summation based on quantum Fourier transform." Quantum Information Processing 17.6 (2018): 129.
[26] Julsgaard, Brian, et al. "Experimental demonstration of quantum memory for light." Nature 432.7016 (2004): 482.
[27] Yao, Xing-Can, et al. "Observation of eight-photon entanglement." Nature photonics 6.4 (2012): 225-228.
[28] Nielsen, Michael A., and Isaac Chuang. "Quantum computation and quantum information." (2002): 558-559.
[29] Boyer, Michel, Dan Kenigsberg, and Tal Mor. "Quantum key distribution with classical Bob." Quantum, Nano, and Micro Technologies, 2007. ICQNM'07. First International Conference on. IEEE, 2007.
[30] Boyer, Michel, et al. "Semiquantum key distribution." Physical Review A 79.3 (2009): 032341.
[31] Li, Qin, W. H. Chan, and Dong-Yang Long. "Semiquantum secret sharing using entangled states." Physical Review A 82.2 (2010): 022303.
[32] Zou, XiangFu, and DaoWen Qiu. "Three-step semiquantum secure direct communication protocol." Science China Physics, Mechanics & Astronomy 57.9 (2014): 1696-1702.
[33] Zou, Xiangfu, et al. "Semiquantum-key distribution using less than four quantum states." Physical Review A 79.5 (2009): 052312.
[34] Yu, Kun-Fei, et al. "Authenticated semi-quantum key distribution protocol using Bell states." Quantum Information Processing 13.6 (2014): 1457-1465.
[35] Yu, Kun-Fei, et al. "Multi-party semi-quantum key distribution-convertible multi-party semi-quantum secret sharing." Quantum Information Processing 16.8 (2017): 194.
[36] Liu, Zhi‐Rou, and Tzonelih Hwang. "Mediated Semi‐Quantum Key Distribution Without Invoking Quantum Measurement." Annalen der Physik 530.4 (2018): 1700206.
[37] Lu, Hua, and Qing-Yu Cai. "Quantum key distribution with classical Alice." International Journal of Quantum Information 6.06 (2008): 1195-1202.
[38] Xian-Zhou, Zhang, et al. "Quantum key distribution series network protocol with M-classical Bobs." Chinese Physics B 18.6 (2009): 2143.
[39] Tan, Yong-gang, Hua Lu, and Qing-yu Cai. "Comment on “Quantum key distribution with classical Bob”." Physical review letters 102.9 (2009): 098901.
[40] Jian, Wang, et al. "Semiquantum key distribution using entangled states." Chinese Physics Letters 28.10 (2011): 100301.
[41] Li, Lvzhou, Daowen Qiu, and Paulo Mateus. "Quantum secret sharing with classical Bobs." Journal of Physics A: Mathematical and Theoretical 46.4 (2013): 045304.
[42] Nie, Yi-you, Yuan-hua Li, and Zi-sheng Wang. "Semi-quantum information splitting using GHZ-type states." Quantum information processing 12.1 (2013): 437-448.
[43] Krawec, Walter O. "Mediated semiquantum key distribution." Physical Review A 91.3 (2015): 032323.
[44] Boyer, Michel, and Tal Mor. "Comment on “Semiquantum-key distribution using less than four quantum states”." Physical Review A 83.4 (2011): 046301.
[45] Sun, Zhi-Wei, Rui-Gang Du, and Dong-Yang Long. "Quantum key distribution with limited classical bob." International Journal of Quantum Information 11.01 (2013): 1350005.
[46] Wang, Jian, et al. "Semiquantum secret sharing using two-particle entangled state." International Journal of Quantum Information 10.05 (2012): 1250050.
[47] Xie, Chen, Lvzhou Li, and Daowen Qiu. "A novel semi-quantum secret sharing scheme of specific bits." International Journal of Theoretical Physics 54.10 (2015): 3819-3824.
[48] Zou, Xiangfu, et al. "Semiquantum key distribution without invoking the classical party’s measurement capability." Quantum Information Processing 14.8 (2015): 2981-2996.
[49] Luo, Yi-Ping, and Tzonelih Hwang. "Authenticated semi-quantum direct communication protocols using Bell states." Quantum Information Processing 15.2 (2016): 947-958.
[50] Shukla, Chitra, Kishore Thapliyal, and Anirban Pathak. "Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue." Quantum Information Processing 16.12 (2017): 295.
[51] Li, Qin, Wai Hong Chan, and Shengyu Zhang. "Semiquantum key distribution with secure delegated quantum computation." Scientific reports 6 (2016): 19898.
[52] Zou, Xiangfu, and Daowen Qiu. "Reply to “Comment on ‘Semiquantum-key distribution using less than four quantum states’”." Physical Review A 83.4 (2011): 046302.
[53] Zhang, Wei, Daowen Qiu, and Paulo Mateus. "Security of a single-state semi-quantum key distribution protocol." Quantum Information Processing 17 (2018): 1-21.
[54] Gao, Gan, Yue Wang, and Dong Wang. "Multiparty semiquantum secret sharing based on rearranging orders of qubits." Modern Physics Letters B 30.10 (2016): 1650130.
[55] Li, Chuan-Ming, et al. "Authenticated semi-quantum key distributions without classical channel." Quantum Information Processing 15.7 (2016): 2881-2893.
[56] Gao, Xiang, Shibin Zhang, and Yan Chang. "Cryptanalysis and improvement of the semi-quantum secret sharing protocol." International Journal of Theoretical Physics 56.8 (2017): 2512-2520.
[57] Gu, Jun, Po-hua Lin, and Tzonelih Hwang. "Double C-NOT attack and counterattack on ‘Three-step semi-quantum secure direct communication protocol’." Quantum Information Processing 17.7 (2018): 182.
[58] Meslouhi, A., and Yassine Hassouni. "Cryptanalysis on authenticated semi-quantum key distribution protocol using Bell states." Quantum Information Processing 16.1 (2017): 18.
[59] Yan, LiLi, et al. "Semi-quantum protocol for deterministic secure quantum communication using Bell states." Quantum Information Processing 17.11 (2018): 315.
[60] Gao, Gan, Yue Wang, and Dong Wang. "Cryptanalysis of a semi-quantum secret sharing scheme based on Bell states." Modern Physics Letters B 32.09 (2018): 1850117.
[61] Ye, Tian-Yu, and Chong-Qiang Ye. "Semi-quantum Dialogue Based on Single Photons." International Journal of Theoretical Physics 57.5 (2018): 1440-1454.
[62] Li, Zhulin, et al. "Limited resource semiquantum secret sharing." Quantum Information Processing 17.10 (2018): 285.
[63] Xie, Chen, et al. "Semi-quantum Secure Direct Communication Scheme Based on Bell States." International Journal of Theoretical Physics 57.6 (2018): 1881-1887.
[64] Yin, Ai Han, and Yan Tong. "A novel semi-quantum secret sharing scheme using entangled states." Modern Physics Letters B 32.22 (2018): 1850256.
[65] Chen, Bingren, Wei Yang, and Liusheng Huang. "Cryptanalysis and improvement of the novel semi-quantum secret sharing scheme based on Bell states." Modern Physics Letters B 32.25 (2018): 1850294.
[66] Bennett, Charles H. "Quantum crytography." Proc. IEEE Int. Conf. Computers, Systems, and Signal Processing, Bangalore, India, 1984. 1984.
[67] Pan, Jian-Wei, et al. "Experimental entanglement swapping: entangling photons that never interacted." Physical Review Letters 80.18 (1998): 3891.
[68] Zukowski, Marek, et al. "``Event-ready-detectors'Bell experiment via entanglement swapping." Physical Review Letters 71 (1993): 4287-4290.
[69] Karimipour, Vahid, Alireza Bahraminasab, and Saber Bagherinezhad. "Entanglement swapping of generalized cat states and secret sharing." Physical Review A 65.4 (2002): 042320.
[70] Cai, Qing-Yu. "Eavesdropping on the two-way quantum communication protocols with invisible photons." Physics Letters A 351.1-2 (2006): 23-25.
[71] Deng, Fu-Guo, et al. "Improving the security of multiparty quantum secret sharing against Trojan horse attack." Physical Review A 72.4 (2005): 044302.
[72] Gisin, Nicolas, et al. "Quantum cryptography." Reviews of modern physics 74.1 (2002): 145.
[73] Lucamarini, Marco, and Stefano Mancini. "Secure deterministic communication without entanglement." Physical review letters 94.14 (2005): 140501.
[74] Peres, Asher. Quantum theory: concepts and methods. Vol. 57. Springer Science & Business Media, 2006.
[75] Gu, Jun, Chih-Yung Ho, and Tzonelih Hwang. "Statistics attack on ‘quantum private comparison with a malicious third party’and its improvement." Quantum Information Processing 17.2 (2018): 23.
[76] Peter W Shor, "Algorithms for quantum computation: Discrete logarithms and factoring," in Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on, pp. 124-134, 1994.
[77] Lo Hoi-Kwong, Xiongfeng Ma and Kai Chen, "Decoy state quantum key distribution." Physical review letters 94.23: 230504 (2005).
[78] Bennett Charles H, "Quantum cryptography using any two nonorthogonal states." Physical review letters 68.21: 3121 (1992).
[79] Bennett Charles H., Gilles Brassard and N. David Mermin, "Quantum cryptography without Bell’s theorem." Physical Review Letters 68.5: 557 (1992).
[80] Long Gui-Lu and Xiao-Shu Liu, "Theoretically efficient high-capacity quantum-key-distribution scheme." Physical Review A 65.3: 032302 (2002).
[81] Nicolas J. Cerf, Mohamed Bourennane, Anders Karlsson and Nicolas Gisin, "Security of quantum key distribution using d-level systems." Physical Review Letters 88.12: 127902 (2002).
[82] Lo Hoi-Kwong, Marcos Curty and Bing Qi, "Measurement-device-independent quantum key distribution." Physical review letters 108.13: 130503 (2012).
[83] Fre´de´ric Grosshans, Gilles Van Assche, Je´roˆme Wenger, Rosa Brouri, Nicolas J. Cerf and Philippe Grangier, "Quantum key distribution using gaussian-modulated coherent states." Nature 421.6920: 238 (2003).
[84] Boström Kim and Timo Felbinger, "Deterministic secure direct communication using entanglement." Physical Review Letters 89.18: 187902 (2002).
[85] Deng Fu-Guo and Gui Lu Long, "Secure direct communication with a quantum one-time pad." Physical Review A 69.5: 052319 (2004).
[86] Chuan Wang, Fu-Guo Deng, Yan-Song Li, Xiao-Shu Liu and Gui Lu Long, "Quantum secure direct communication with high-dimension quantum superdense coding." Physical Review A 71.4: 044305 (2005).
[87] Beller Mara, “Quantum dialogue: The making of a revolution.” University of Chicago Press, 2001.
[88] Nguyen Ba An, "Quantum dialogue." Physics Letters A 328.1: 6-10 (2004).
[89] Hillery Mark, Vladimír Bužek, and André Berthiaume, "Quantum secret sharing." Physical Review A 59.3: 1829 (1999).
[90] Li Xiao, Gui Lu Long, Fu-Guo Deng and Jian-Wei Pan, "Efficient multiparty quantum-secret-sharing schemes." Physical Review A 69.5: 052307 (2004).
[91] Karlsson, Anders, Masato Koashi, and Nobuyuki Imoto, "Quantum entanglement for secret sharing and secret splitting." Physical Review A 59.1: 162 (1999).
[92] Yan Feng-Li and Ting Gao, "Quantum secret sharing between multiparty and multiparty without entanglement." Physical Review A 72.1: 012304 (2005).
[93] Krawec, Walter O. "Restricted attacks on semi-quantum key distribution protocols." Quantum information processing 13.11 (2014): 2417-2436.