本篇論文探討存在於現行量子私密比較協定中的兩種攻擊:幾乎不誠實的第三方可以從比較結果中獲得參與者的私密訊息，並且可以在不被偵測到的情況下，公布偽造的比較結果。
為了防止第三方的這兩種攻擊，本篇論文針對比較相等與比較大小的量子私密比較協定分別提出兩種新陷阱比較機制，並分別用來增強黃等人和盧等人的協定作為例。此機制可以防止第三方獲得實際的比較結果，且同時可以偵測第三方偽造的比較結果。除此之外，也將增強的協定拓展至適用於陌生人環境。

This thesis explores two attacks existing in various quantum private comparison (QPC) protocols where an almost dishonest third party (TP) can reveal the information of participants’ secrets from the comparison results or announce a fake comparison result without being detected.
To prevent these two attacks from the TP, two new trap comparison methods are proposed to prevent the TP from knowing the comparison result and to detect a fake comparison result. One for equality is used to enhance Huang et al.’s protocol and another for size relation is used to enhance Luo et al.’s protocol as examples. Moreover, the enhanced protocols will be extended to a stranger environment.

[1] Peter 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] Lov K Grover, "A fast quantum mechanical algorithm for database search," in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 1996, pp. 212-219.
[3] William K Wootters and Wojciech H Zurek, "A single quantum cannot be cloned," Nature, vol. 299, pp. 802-803, 1982.
[4] Charles H Bennett and Gilles Brassard, "Quantum cryptography: Public key distribution and coin tossing," Theoretical computer science, vol. 560, pp. 7-11, 1984.
[5] Yu-Guang Yang 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, vol. 42, p. 055305, 2009.
[6] Hsin-Yi Tseng, Jason Lin, and Tzonelih Hwang, "New quantum private comparison protocol using EPR pairs," Quantum Information Processing, vol. 11, pp. 373-384, 2012.
[7] Wen Liu, Yong-Bin Wang, and Zheng-Tao Jiang, "An efficient protocol for the quantum private comparison of equality with W state," Optics Communications, vol. 284, pp. 3160-3163, 2011.
[8] Liu Wen, Wang Yong-Bin, and Cui Wei, "Quantum private comparison protocol based on Bell entangled states," Communications in Theoretical Physics, vol. 57, p. 583, 2012.
[9] Wen Liu and Yong-Bin Wang, "Quantum private comparison based on GHZ entangled states," International Journal of Theoretical Physics, vol. 51, pp. 3596-3604, 2012.
[10] Wei-Wei Zhang and Ke-Jia Zhang, "Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party," Quantum information processing, vol. 12, pp. 1981-1990, 2013.
[11] Liu Wen-Jie, Liu Chao, Chen Han-Wu, Li Zhi-Qiang, and Liu Zhi-Hao, "Cryptanalysis and improvement of quantum private comparison protocol based on Bell entangled states," Communications in Theoretical Physics, vol. 62, p. 210, 2014.
[12] 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.
[13] 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.
[14] Zhiwei Sun, Jianping Yu, Ping Wang, Lingling Xu, and Chunhui Wu, "Quantum private comparison with a malicious third party," Quantum Information Processing, vol. 14, pp. 2125-2133, 2015.
[15] Tian-Yu Ye, "Multi-Party Quantum Private Comparison Protocol Based on Entanglement Swapping of Bell Entangled States," Communications in Theoretical Physics, vol. 66, p. 280, 2016.
[16] Yao-Jen Chang, Chia-Wei Tsai, and Tzonelih Hwang, "Multi-user private comparison protocol using GHZ class states," Quantum information processing, pp. 1-12, 2013.
[17] Chih-Hung Chang, Tzonelih Hwang, and Prosanta Gope, "An efficient quantum private comparison of equality over collective-noise channels," International Journal of Theoretical Physics, vol. 55, pp. 2125-2138, 2016.
[18] Qing-Le Wang, Hong-Xiang Sun, and Wei Huang, "Multi-party quantum private comparison protocol with n-level entangled states," Quantum information processing, vol. 13, pp. 2375-2389, 2014.
[19] Wen Liu, 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, vol. 53, pp. 1085-1091, 2014.
[20] Heng-Yue Jia, Qiao-Yan Wen, Ting-Ting Song, and Fei Gao, "Quantum protocol for millionaire problem," Optics communications, vol. 284, pp. 545-549, 2011.
[21] Qing-bin Luo, Guo-wu Yang, Kun She, Wei-na Niu, and Yu-qi Wang, "Multi-party quantum private comparison protocol based on d-dimensional entangled states," Quantum information processing, vol. 13, pp. 2343-2352, 2014.
[22] Sheng-Liang Huang, Tzonelih Hwang, and Prosanta Gope, "Multi-party quantum private comparison with an almost-dishonest third party," Quantum Information Processing, vol. 14, pp. 4225-4235, 2015.
[23] Song Lin, Ying Sun, Xiao-Fen Liu, and Zhi-Qiang Yao, "Quantum private comparison protocol with d-dimensional Bell states," Quantum information processing, vol. 12, 2013.
[24] Wei-Wei Zhang, Dan Li, Ke-Jia Zhang, and Hui-Juan Zuo, "A quantum protocol for millionaire problem with Bell states," Quantum information processing, vol. 12, pp. 2241-2249, 2013.
[25] Fen Zhuo Guo, Fei Gao, Su Juan Qin, Jie Zhang, and Qiao Yan Wen, "Quantum private comparison protocol based on entanglement swapping of d-level Bell states," Quantum information processing, vol. 12, pp. 2793-2802, 2013.
[26] Chao-Hua Yu, Gong-De Guo, and Song Lin, "Quantum private comparison with d-level single-particle states," Physica Scripta, vol. 88, p. 065013, 2013.
[27] Hoi-Kwong Lo, "Insecurity of quantum secure computations," Physical Review A, vol. 56, p. 1154, 1997.
[28] Chih-Yun Ho Jun Gu, Tzonelih Hwang, "Statistics Attack on "Quantum private comparison with a malicious third party"," in Cryptology and Information Security Conference 2016, Asia University, Taichung, Taiwan, 2016.
[29] Tzonelih Hwang, Tzu-Han Lin, and Shih-Hung Kao, "Quantum entanglement establishment between two strangers," Quantum Information Processing, vol. 15, pp. 385-403, 2016.
[30] XS Liu, GL Long, DM Tong, and Feng Li, "General scheme for superdense coding between multiparties," Physical Review A, vol. 65, p. 022304, 2002.
[31] 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.
[32] 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.
[33] Run-Hua Shi and Hong Zhong, "Multi-party quantum key agreement with bell states and bell measurements," Quantum information processing, pp. 1-12, 2013.
[34] Fei Gao, Su-Juan Qin, Qiao-Yan Wen, and Fu-Chen Zhu, "A simple participant attack on the brádler-dušek protocol," Quantum Information & Computation, vol. 7, pp. 329-334, 2007.
[35] Gao Fei, Lin Song, Wen Qiao-Yan, and Zhu Fu-Chen, "A special eavesdropping on one-sender versus N-receiver QSDC protocol," Chinese Physics Letters, vol. 25, p. 1561, 2008.
[36] 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.
[37] Qing-Yu Cai, "Eavesdropping on the two-way quantum communication protocols with invisible photons," Physics Letters A, vol. 351, pp. 23-25, 2006.
[38] Fu-Guo Deng, Xi-Han Li, Hong-Yu Zhou, and Zhan-jun Zhang, "Improving the security of multiparty quantum secret sharing against Trojan horse attack," Physical Review A, vol. 72, p. 044302, 2005.
[39] Xi-Han Li, Fu-Guo Deng, and Hong-Yu Zhou, "Improving the security of secure direct communication based on the secret transmitting order of particles," Physical Review A, vol. 74, p. 054302, 2006.