本論文試圖利用量子力學基礎定律，在「半量子」環境中設計安全密鑰分配協定。本論文提出GHZ糾結態間Entanglement Swapping的數學通式，亦分別提出了Z基底光子和Bell糾結態以及Z基底光子和GHZ糾結態的兩種糾纏相關性。基於這些性質，本論文提出了兩個半量子金鑰分配協定，允許兩個或多個只具備基本量子能力的「古典」參與者，在近乎不誠實的量子密鑰分配中心下建立共享會話密鑰。此近乎不誠實的量子密鑰分配中心除了不能與任何參與者合作之外可以執行任何攻擊來獲取「古典」參與者的秘密信息。此外，本文提出的半量子金鑰分配協議可以經由些微的調整而適用於更實用的環境，如陌生人環境、量子集合相位雜訊環境與量子易丟落的環境。

This thesis attempts to utilize the laws of fundamental quantum mechanism for architecting secure key distribution protocols in the “semi-quantum” environments. In this thesis, the entanglement swapping formula among the GHZ states, the entanglement correlations of the Z-basis photons and the Bell states, and the entanglement correlations of the Z-basis photons and the GHZ states are presented. Based on these properties, this thesis proposes two mediated SQKD protocols that allow two or multiple “classical” participants with basic quantum capabilities to establish a shared session key under an almost dishonest quantum key distribution center that can perform any attack to obtain the secret information of classical participants except in collaboration with any participants. Moreover, the proposed SQKD protocols can be applied to more realistic environments (i.e., the stranger environment, the collective-dephasing noise, and the lossy quantum channel) with small adjustments.

[1] P. W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring," in Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on, 1994, pp. 124-134.
[2] Artur K. Ekert, "Quantum cryptography based on Bell’s theorem," Physical Review Letters, vol. 67, pp. 661-663, 08/05/ 1991.
[3] C. H. Bennett and G. Brassard, "Quantum Cryptography: Public Key Distribution and Coin Tossing," presented at the Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984.
[4] Charles H. Bennett, Gilles Brassard, and N. David Mermin, "Quantum cryptography without Bell’s theorem," Physical Review Letters, vol. 68, pp. 557-559, 02/03/ 1992.
[5] A. Cabello, "Quantum key distribution without alternative measurements," Physical Review A, vol. 61, pp. art. no.-052312, May 2000.
[6] G. L. Long and X. S. Liu, "Theoretically efficient high-capacity quantum-key-distribution scheme," Physical Review A, vol. 65, p. 032302, 02/01/ 2002.
[7] C. Li, H. S. Song, L. Zhou, and C. F. Wu, "A random quantum key distribution achieved by using Bell states," Journal of Optics B-Quantum and Semiclassical Optics, vol. 5, pp. 155-157, Apr 2003.
[8] D. G. Song, "Secure key distribution by swapping quantum entanglement," Physical Review A, vol. 69, Mar 2004.
[9] X. H. Li, F. G. Deng, and H. Y. Zhou, "Efficient quantum key distribution over a collective noise channel," Physical Review A, vol. 78, Aug 2008.
[10] Chang Ho Hong, Jin O. Heo, Gyong Luck Khym, Jongin Lim, Suc-Kyung Hong, and Hyung Jin Yang, "quantum channels are sufficient for Multi-user Quantum Key Distribution protocol between users," Optics Communications, vol. 283, pp. 2644-2646, 6/15/ 2010.
[11] Nan-Run Zhou, Li-Jun Wang, Jie Ding, and Li-Hua Gong, "Quantum deterministic key distribution protocols based on the authenticated entanglement channel," Physica Scripta, vol. 81, p. 045009, 2010.
[12] Nan-Run Zhou, Li-Jun Wang, Jie Ding, Li-Hua Gong, and Xiang-Wu Zuo, "Novel Quantum Deterministic Key Distribution Protocols with Entangled States," International Journal of Theoretical Physics, vol. 49, pp. 2035-2044, 2010/09/01 2010.
[13] N. Zhou, G. Zeng, and J. Xiong, "Quantum key agreement protocol," Electronics Letters, vol. 40, p. 1149, 2004.
[14] Song-Kong Chong and Tzonelih Hwang, "Quantum key agreement protocol based on BB84," Optics Communications, vol. 283, pp. 1192-1195, 2010.
[15] Song-Kong Chong, Chia-Wei Tsai, and Tzonelih Hwang, "Improvement on “Quantum Key Agreement Protocol with Maximally Entangled States”," International Journal of Theoretical Physics, vol. 50, pp. 1793-1802, 2011.
[16] Run-Hua Shi and Hong Zhong, "Multi-party quantum key agreement with bell states and bell measurements," Quantum Information Processing, vol. 12, pp. 921-932, 2013/02/01 2013.
[17] Bin Liu, Fei Gao, Wei Huang, and Qiao-yan Wen, "Multiparty quantum key agreement with single particles," Quantum Information Processing, vol. 12, pp. 1797-1805, 2013/04/01 2013.
[18] Zhiwei Sun, Cai Zhang, Banghai Wang, Qin Li, and Dongyang Long, "Improvements on “multiparty quantum key agreement with single particles”," Quantum Information Processing, vol. 12, pp. 3411-3420, 2013.
[19] Xun-Ru Yin, Wen-Ping Ma, and Wei-Yan Liu, "Three-Party Quantum Key Agreement with Two-Photon Entanglement," International Journal of Theoretical Physics, vol. 52, pp. 3915-3921, 2013.
[20] Wei Huang, Qiao-Yan Wen, Bin Liu, Fei Gao, and Ying Sun, "Quantum key agreement with EPR pairs and single-particle measurements," Quantum Information Processing, vol. 13, pp. 649-663, 2014/03/01 2014.
[21] Mark Hillery, Vladimír Bužek, and André Berthiaume, "Quantum secret sharing," Physical Review A, vol. 59, p. 1829, 1999.
[22] Yongmin Li, Kuanshou Zhang, and Kunchi Peng, "Multiparty secret sharing of quantum information based on entanglement swapping," Physics Letters A, vol. 324, pp. 420-424, 4/26/ 2004.
[23] Zhan-jun Zhang, Yong Li, and Zhong-xiao Man, "Multiparty quantum secret sharing," Physical Review A, vol. 71, p. 044301, 04/11/ 2005.
[24] Run-hua Shi and Hong Zhong, "Multiparty quantum secret sharing with the pure entangled two-photon states," Quantum Information Processing, vol. 11, pp. 161-169, 2012/02/01 2012.
[25] Shih-Min Hung, Sheng-Liang Hwang, Tzonelih Hwang, and Shih-Hung Kao, "Multiparty quantum private comparison with almost dishonest third parties for strangers," Quantum Information Processing, vol. 16, p. 36, 2017.
[26] Bin Liu, Di Xiao, Wei Huang, Heng-Yue Jia, and Ting-Ting Song, "Quantum private comparison employing single-photon interference," Quantum Information Processing, vol. 16, p. 180, 2017.
[27] Ji Zhao-Xu and Ye Tian-Yu, "Multi-party quantum private comparison based on the entanglement swapping of d-level cat states and d-level Bell states," Quantum Information Processing, vol. 16, p. 177, 2017.
[28] Michel Boyer, Dan Kenigsberg, and Tal Mor, "Quantum Key Distribution with Classical Bob," Physical Review Letters, vol. 99, p. 140501, 10/05/ 2007.
[29] Michel Boyer, Ran Gelles, Dan Kenigsberg, and Tal Mor, "Semiquantum key distribution," Physical Review A, vol. 79, p. 032341, 2009.
[30] Zhang Xian-Zhou, Gong Wei-Gui, Tan Yong-Gang, Ren Zhen-Zhong, and Guo Xiao-Tian, "Quantum key distribution series network protocol with M -classical Bobs," Chinese Physics B, vol. 18, p. 2143, 2009.
[31] Xiangfu Zou, Daowen Qiu, Lvzhou Li, Lihua Wu, and Lvjun Li, "Semiquantum-key distribution using less than four quantum states," Physical Review A, vol. 79, p. 052312, 05/12/ 2009.
[32] Wang Jian, Zhang Sheng, Zhang Quan, and Tang Chao-Jing, "Semiquantum key distribution using entangled states," Chinese Physics Letters, vol. 28, p. 100301, 2011.
[33] K. F. Yu, C. W. Yang, C. H. Liao, and T. Hwang, "Authenticated semi-quantum key distribution protocol using Bell states," Quantum Information Processing, vol. 13, pp. 1457-1465, Jun 2014.
[34] Qin Li, W. H. Chan, and Dong-Yang Long, "Semiquantum secret sharing using entangled states," Physical Review A, vol. 82, p. 022303, 2010.
[35] Jian Wang, Sheng Zhang, Quan Zhang, and Chao-Jing Tang, "Semiquantum secret sharing using two-particle entangled state," International Journal of Quantum Information, vol. 10, p. 1250050, 2012.
[36] Lvzhou Li, Daowen Qiu, and Paulo Mateus, "Quantum secret sharing with classical Bobs," Journal of Physics A: Mathematical and Theoretical, vol. 46, p. 045304, 2013.
[37] Chun-Wei Yang and Tzonelih Hwang, "Efficient key construction on semi-quantum secret sharing protocols," International Journal of Quantum Information, vol. 11, p. 1350052, 2013.
[38] B. S. Shi, J. Li, J. M. Liu, X. F. Fan, and G. C. Guo, "Quantum key distribution and quantum authentication based on entangled state," Physics Letters A, vol. 281, pp. 83-87, Mar 19 2001.
[39] H. C. Shih, K. C. Lee, and T. Hwang, "New Efficient Three-Party Quantum Key Distribution Protocols," Ieee Journal of Selected Topics in Quantum Electronics, vol. 15, pp. 1602-1606, Nov-Dec 2009.
[40] Brian Julsgaard, Jacob Sherson, J Ignacio Cirac, Jaromír Fiurášek, and Eugene S Polzik, "Experimental demonstration of quantum memory for light," Nature, vol. 432, pp. 482-486, 2004.
[41] Michael A Nielsen and Isaac Chuang, "Quantum computation and quantum information," ed: AAPT, 2002.
[42] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, et al., "Observation of eight-photon entanglement," Nature Photonics, vol. 6, pp. 225-228, 2012.
[43] Xi-Lin Wang, Luo-Kan Chen, Wei Li, H-L Huang, Chang Liu, Chao Chen, et al., "Experimental ten-photon entanglement," Physical Review Letters, vol. 117, p. 210502, 2016.
[44] Michel Boyer, Dan Kenigsberg, and Tal Mor, "Quantum key distribution with classical Bob," in Quantum, Nano, and Micro Technologies, 2007. ICQNM'07. First International Conference on, 2007, pp. 10-10.
[45] Xiangfu Zou, Daowen Qiu, Shengyu Zhang, and Paulo Mateus, "Semiquantum key distribution without invoking the classical party’s measurement capability," Quantum Information Processing, vol. 14, pp. 2981-2996, 2015.
[46] Chuan-Ming Li, Kun-Fei Yu, Shih-Hung Kao, and Tzonelih Hwang, "Authenticated semi-quantum key distributions without classical channel," Quantum Information Processing, vol. 15, pp. 2881-2893, 2016.
[47] B Clifford Neuman and Theodore Ts'o, "Kerberos: An authentication service for computer networks," IEEE Communications magazine, vol. 32, pp. 33-38, 1994.
[48] Nigel Jefferies, Chris Mitchell, and Michael Walker, "A proposed architecture for trusted third party services," in Cryptography: Policy and Algorithms, 1996, pp. 98-104.
[49] Xiu-Bo Chen, Gang Xu, Xin-Xin Niu, Qiao-Yan Wen, and Yi-Xian Yang, "An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement," Optics communications, vol. 283, pp. 1561-1565, 2010.
[50] Sheng-Liang Huang, 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, vol. 55, pp. 2969-2976, 2016.
[51] Tzonelih Hwang, Tzu-Han Lin, and Shih-Hung Kao, "Quantum entanglement establishment between two strangers," Quantum Information Processing, vol. 15, pp. 385-403, 2016.
[52] Warren P Grice, "Arbitrarily complete Bell-state measurement using only linear optical elements," Physical Review A, vol. 84, p. 042331, 2011.
[53] Jian-Wei Pan, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger, "Experimental entanglement swapping: Entangling photons that never interacted," Physical Review Letters, vol. 80, p. 3891, 1998.
[54] M Zukowski, A Zeilinger, MA Horne, and AK Ekert, "" Event-ready-detectors" Bell experiment via entanglement swapping," Physical Review Letters, vol. 71, pp. 4287-4290, 1993.
[55] Charles H Bennett, Gilles Brassard, and Jean-Marc Robert, "Privacy amplification by public discussion," SIAM journal on Computing, vol. 17, pp. 210-229, 1988.
[56] Charles H Bennett, Gilles Brassard, Claude Crépeau, and Ueli M Maurer, "Generalized privacy amplification," IEEE Transactions on Information Theory, vol. 41, pp. 1915-1923, 1995.
[57] Fei Gao, Fen-Zhuo Guo, Qiao-Yan Wen, and Fu-Chen Zhu, "Comment on “Experimental demonstration of a quantum protocol for byzantine agreement and liar detection”," Physical review letters, vol. 101, p. 208901, 2008.
[58] F. G. Deng, Zhou, P., Li, X. H., Li, C. Y., Zhou, H. Y., "Robustness of two-way quantum communication protocols against trojan horse attack," Quantum Physics, 2005.
[59] Q. Y. Cai, "Eavesdropping on the two-way quantum communication protocols with invisible photons," Physics Letters A, vol. 351, pp. 23-25, Feb 20 2006.
[60] C. W. Yang, T. Hwang, and Y. P. Luo, "Enhancement on "quantum blind signature based on two-state vector formalism"," Quantum Information Processing, vol. 12, pp. 109-117, Jan 2013.
[61] F. G. Deng, X. H. Li, H. Y. Zhou, and Z. J. Zhang, "Improving the security of multiparty quantum secret sharing against Trojan horse attack," Physical Review A, vol. 72, Oct 2005.
[62] X. H. Li, F. G. Deng, and H. Y. Zhou, "Improving the security of secure direct communication based on the secret transmitting order of particles," Physical Review A, vol. 74, Nov 2006.
[63] Walter O Krawec, "Mediated semiquantum key distribution," Physical Review A, vol. 91, p. 032323, 2015.
[64] Jason Lin and Tzonelih Hwang, "An enhancement on Shi et al.'s multiparty quantum secret sharing protocol," Optics Communications, vol. 284, pp. 1468-1471, 2011.
[65] Chun-Wei Yang and Tzonelih Hwang, "Quantum dialogue protocols immune to collective noise," Quantum information processing, vol. 12, pp. 2131-2142, 2013.
[66] TianYu Ye, "Information leakage resistant quantum dialogue against collective noise," SCIENCE CHINA Physics, Mechanics & Astronomy, vol. 57, pp. 2266-2275, 2014.
[67] TianYu Ye, "Fault tolerant channel-encrypting quantum dialogue against collective noise," SCIENCE CHINA Physics, Mechanics & Astronomy, vol. 58, pp. 1-10, 2015.
[68] Shih-Hung Kao, Chun-Wei Yang, and Tzonelih Hwang, "Fault-tolerant controlled deterministic secure quantum communication using EPR states against collective noise," Quantum Information Processing, vol. 15, pp. 4711-4727, 2016.