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多数在理想条件下设计的量子密码协议没有考虑实际通信中噪音的影响, 可能造成机密信息不能被准确传输, 或可能存在窃听隐藏在噪音中的风险, 因此分析噪音条件下量子密码协议的安全性具有重要的意义. 为了分析量子BB84协议在联合旋转噪音信道上的安全性, 本文采用粒子偏转模型, 对量子信道中的联合噪音进行建模, 定量地区分量子信道中噪音和窃听干扰; 并且采用冯诺依曼熵理论建立窃听者能窃取的信息量与量子比特误码率、噪音水平三者之间的函数关系, 定量地分析噪音条件下量子信道的安全性; 最后根据联合噪音模型及窃听者能窃取的信息量与量子比特误码率、噪音水平三者之间的关系, 定量地分析了量子BB84协议在联合噪音条件下的安全性并计算噪音临界点. 通过分析可知, 在已有噪音水平条件下, 窃听者最多能够从通信双方窃取25%的密钥, 但是Eve 的窃听行为会被检测出来, 这样Alice和Bob会放弃当前协商的密钥, 重新进行密钥协商, 直至确认没有Eve的窃听为止. 这个结果说明量子BB84协议在联合旋转噪音信道下的通信是安全的.Most of quantum cryptography protocols are designed under the ideal conditions without considering the impact of noise in actual communication; thus they may result in that the confidential information cannot be transmitted to the receiver accurately or eavesdroppers can steal the confidential information by mixing in noise. Therefore, analyzing the security of quantum cryptography protocols under noise conditions is of great significance. For the purpose of analyzing the security of quantum BB84 protocol in collective-rotation noise, firstly this paper introduces the quantum BB84 protocol, and considers the influence of environmental noise on it. An explanation should be stated that in a noise environment, the effects of noise and eavesdropping cannot be distinguished between each other. So the mechanism for which the error bit is simply used as the criterion to judge whether there exists eavesdropping in the BB84 protocol, cannot be used in the noise environment. The mechanism to judge whether there exists eavesdropping in quantum noise channel needs to be modified and improved for protecting the information. An initial qubit error rate can be set according to the noisy quantum channel. If the qubit error rate of the quantum communication channel is larger than that, it can be determined that the quantum channel is not secure and exists eavesdropping, no matter what the reason is. And on this basis, the collective-rotation noise model will be established in quantum channel by using the particle deflection model and distinguish the noise from the eavesdropping in quantum channel quantitatively, and the relationship of the amount of information that eavesdroppers can steal, the quantum bits error rate and the noise level will be analyzed by using the von Neumann entropy. Finally, the noise critical point will be calculated by using the collective noise model and the relationship between the amount of information that eavesdroppers can steal, at the quantum bits error rate, and the noise level. Through the analysis, we can know that in the existing noise level, the most of the eavesdropping can steal 25% of the key from the communication. However, the Eve's eavesdropping behavior will be detected, so that Alice and Bob will give up the current consultation key, and restart the key negotiation. This result shows that the quantum BB84 protocol is safe and secure in the collective-rotation noise channel. The research results of this paper will enrich the theory of quantum cryptography, and the innovation of security detection methods in quantum cryptographic protocols will help promote the process of practical quantum cryptography.
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Keywords:
- quantum security communication /
- collective-rotation noise /
- security analysis /
- quantum bit error rate
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[1] Bennett C H, Brassard G 1984 Theor. Comput. Sci. 560 175
[2] Bennett C H, Bessette F, Brassard G, Salvail L, Smolin J 1992 J. Cryptology 5 3
[3] Muller A, Breguet J, Gisin N 1993 Europhys. Lett. 23 383
[4] Boileau J C, Gottesman D, Laflamme R, Poulin D, Spekkens R W 2004 Phys. Rev. Lett. 92 017901
[5] Gottesman D, Hoi-Kwong L, Lu kenhaus N, Preskill J 2002 Quant. Inf. Comput. 4 325
[6] Watanabe S, Matsumoto R, Uyematsu T 2005 Int. J. Quantum. Inf. 4 935
[7] Wang Y, Wang H D, Li Z H, Huang J X 2009 Computer Science and Information Technology Beijing, August 8-11, 2009 p438
[8] Aizan N H K, Zukarnain Z A, Zainuddin H 2010 Network Applications Protocols and Services (NETAPPS) Kedah, September 22-23, 2010 p130
[9] Winiarczyk P, Zabierowski W 2011 CAD Systems in Microelectronics (CADSM) Polyana-Svalyava, February 23-25, 2011 p23
[10] Buhari A, Zukarnain Z A, Subramaniam S K, Zainuddin H, Saharudin S 2012 Industrial Electronics and Applications (ISIEA) Bandung, September 23-26, 2012 p84
[11] Yang F, Hao Y J 2013 Wavelet Active Media Technology and Information Processing (ICCWAMTIP) Chengdu, December 17-19, 2013 p29
[12] Rostom R, Bakhache B, Salami H, Awad A 2014 Mediterranean Electrotechnical Conference (MELECON) Beirut, April 13-16, 2014 p350
[13] Halip N H M, Mokhtar M, Buhari A 2014 Photonics (ICP) Kuala Lumpur, September 2-4, 2014 p29
[14] Lucamarini M, Dynes J F, Frohlich B, Zhiliang Y, Shields A J 2015 Select. Topics in Quantum Electron. 21 6601408
[15] Archana B, Krithika S 2015 Electronics and Communication Systems (ICECS) Coimbatore, February 26-27, 2015 p457
[16] Jasper R, Nicolas P, Ronald F 2015 Broadband Coverage in Germany 9th ITG Symposium Proceedings Berlin, Germany, April 20-21, 2015 p1
[17] Zhao N, Pei C X, Liu D, Quan D X, Sun X N 2011 Acta Phys. Sin. 60 090307 (in Chinese) [赵楠, 裴昌幸, 刘丹, 权东晓, 孙晓楠 2011 物理学报 60 090307]
[18] Chen M J, Liu X 2011 Chin. Phys. B 20 100305
[19] Zhou F, Yong H L, Li D D, Yin J, Ren J G, Peng C Z 2014 Acta Phys. Sin. 63 140303 (in Chinese) [周飞, 雍海林, 李东东, 印娟, 任继刚, 彭承志 2014 物理学报 63 140303]
[20] Ma H Q, Wei K J, Yang J H, Li R X, Zhu W 2014 Chin. Phys. B 23 100307
[21] Zhao L Y, Li H W, Yin Z Q, Chen W, You J, Han Z F 2014 Chin. Phys. B 23 100304
[22] Ren C B, Xu Q L, Ren G Z 2003 Comput. Eng. Appl. J. 13 177
[23] Deng F G, Li X H, Li C Y, Zhou P, Zhou H Y 2007 Chin. Phys. 16 277
[24] Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. 78 022321
[25] Niu H C, Ren B C, Wang T J, Hua M, Deng F G 2012 Internal J. Theor. Phys. 51 2346
[26] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) chaper 8
[27] Zeng G H, Wang X M, Zhu H W 2000 J. China Inst. Commun. 21 70
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