基于<i>d</i>维GHZ态的多方量子密钥协商

唐杰; 石磊; 魏家华; 于惠存; 薛阳; 武天雄

doi:10.7498/aps.69.20200799

摘要

提出了一个基于d维多粒子GHZ (Greenberger-Horne-Zeilinger) 态作为量子信道的多方量子密钥协商协议. 该方案充分利用时移操作将密钥编码到量子态序列中, 通过d维Z基测量得到密钥. 除此之外, 本方案确保多个参与者是完全对等且公平的, 对最终密钥生成的贡献是平等的. 安全性分析表明本方案能够有效抵抗内部参与者和外部窃听者的攻击.

关键词:

A multi-party quantum key agreement protocol based on d-level multi-particle GHZ states is proposed. The “d-level” is common in other quantum cryptographic protocols, but there are few researches in the field of quantum key agreement. In our scheme, we introduce two indistinguishable orthogonal bases, i.e. the quantum Fourier transform and shift operation, into a d-level quantum system. In addition, we make full use of shift operation to encode the key into the sequence of quantum states, and the key can be measured by the d-level Z-basis. By decoding and calculating, each participant can equally extract other participants’ key and obtain the final shared key $ K = {K_0} \oplus {K_1} \oplus \cdots \oplus {K_{k - 1}}$. The protocol resists external eavesdropping by inserting decoy states and conducting two security checks. Furthermore, we present an example by assigning certain values to parameters for illustrative purpose. Finally, QKA protocol mainly involves two types of attacks: participant attack and external attack. The external attack can be divided into Trojan attack, intercept-resend attack, and entangle-measure attack. To demonstrate the security of the scheme, we analyze the two types of attacks. The results show that the scheme can effectively resist the attack from internal participants and external eavesdroppers. However, the premise of our protocol is based on the ideal quantum channel. In practical applications, particles are usually affected by noise in the process of quantum channel transmission. Therefore, how the agreement adapts itself to a more complicated environment is our main work in the future.

Keywords:

作者及机构信息

空军工程大学信息与导航学院, 西安　710077

通信作者: 魏家华, weijiahua@126.com

基金项目: 国家自然科学基金(批准号: 61971436)和国家自然科学基金青年科学基金(批准号: 61803382)资助的课题

Authors and contacts

Institute of Information and Navigation, Air Force Engineering University, Xi’an 710077, China

Corresponding author: Wei Jia-Hua, weijiahua@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61971436) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61803382)

文章全文 : translate this paragraph

参考文献

[1]	Zhou N, Zeng G, Xiong J 2004 Electron. Lett. 40 1149 Google Scholar
[2]	Chong S K, Hwang, T 2010 Opt. Commun. 283 1192 Google Scholar
[3]	Huang W, Su Q, Wu X, Li Y B, Sun L 2014 Int. J. Theor. Phys. 53 2891 Google Scholar
[4]	Shen D S, Ma W P, Wang L L 2014 Quantum Inf. Process. 13 2313 Google Scholar
[5]	He Y F, Ma W P 2015 Quantum Inf. Process. 14 3483 Google Scholar
[6]	He Y F, Ma W P 2017 Int. J. Quantum Inf. 3 1750018 Google Scholar
[7]	Yang Y G, Li B R, Li D, Zhou Y H, Shi W M 2019 Quantum Inf. Process. 18 322 Google Scholar
[8]	Zhou Y H, Wang M F, Shi W M, Yang Y G, Zhang J 2020 Quantum Inf. Process. 19 100 Google Scholar
[9]	Shi R H, Zhong H 2013 Quantum Inf. Process 12 921 Google Scholar
[10]	Liu B, Gao F, Huang W, Wen Q Y 2013 Quantum Inf. Process. 12 1797 Google Scholar
[11]	Sun Z, Zhang C, Wang B H, Li Q, Long D Y 2013 Quantum Inf. Process. 12 3411 Google Scholar
[12]	尹逊汝, 马文平, 申冬苏, 王丽丽 2013 62 170304 Google Scholar Yin X R, Ma W P, Shen D S, Wang L L 2013 Acta Phys. Sin. 62 170304 Google Scholar
[13]	Xu G B, Wen Q Y, Gao F, Qin S J 2014 Quantum Inf. Process. 13 2587 Google Scholar
[14]	Sun Z, Zhang C, Wang P, Yu J P, Zhang Y, Long D Y 2016 Int. J. Theor. Phys. 55 1920 Google Scholar
[15]	Sun Z, Yu J, Wang P 2016 Quantum Inf. Process. 15 373 Google Scholar
[16]	Cai T, Jiang M, Cao G 2018 Quantum Inf. Process. 17 103 Google Scholar
[17]	Lin S, Guo G D, Chen A M, Liu X F 2019 Quantum Inf. Process. 18 1 Google Scholar
[18]	Liu H N, Liang X Q, Jiang D H, Zhang Y H, Xu G B 2019 Quantum Inf. Process. 18 242 Google Scholar
[19]	Zhou N R, Zhu K N, Wang Y Q 2020 Int. J. Theor. Phys. 59 663 Google Scholar
[20]	Huang W, Wen Q Y, Liu B, Su Q, Gao F 2014 Quantum Inf. Process. 13 1651 Google Scholar
[21]	Cai B B, Guo G D, Lin S 2017 Int. J. Theor. Phys. 56 1039 Google Scholar
[22]	Min S Q, Chen H Y, Gong L H 2018 Int. J. Theor. Phys. 57 1811 Google Scholar
[23]	Wang S S, Xu G B, Liang X Q 2018 Int. J. Theor. Phys. 57 3716 Google Scholar
[24]	Zhao X Q, Zhou N R, Chen H Y, Gong L H 2019 Int. J. Theor. Phys. 58 436 Google Scholar
[25]	Liu H N, Liang X Q, Jiang D H, Zhang Y H, Xu G B 2019 Int. J. Theor. Phys. 58 1659 Google Scholar
[26]	Yin X R, Ma W P 2019 Int. J. Theor. Phys. 58 631 Google Scholar
[27]	Zhou Y H, Zhang J, Shi W M, Yang Y G 2020 Mod. Phys. Lett. B 4 2050083 Google Scholar
[28]	Wang W, Zhou B M, Zhang L 2020 Int. J. Theor. Phys. 59 1944 Google Scholar
[29]	Tang J, Shi L, Wei J H 2020 Mod. Phys. Lett. B 49 2050201 Google Scholar
[30]	Bouwmeester D, Pan J W, Daniell M, Weinfurte H, Zeilinger A 1999 Phys. Rev. Lett. 82 1345 Google Scholar
[31]	周南润, 宋汉冲, 龙黎华, 刘晔 2012 61 214203 Google Scholar Zhou N R, Chong S H, Gong L H, Liu Y 2012 Acta Phys. Sin. 61 214203 Google Scholar
[32]	Zhang Z J, Man Z X, Shi S H 2005 Int. J. Quantum Inf. 03 555 Google Scholar
[33]	Hwang T, Hwang C C, Li C M 2011 Phys. Scripta 83 045004 Google Scholar
[34]	Kao S H, Tsai C W, Tzonelih H 2011 Commun. Theor. Phys. 55 1007 Google Scholar
[35]	Cai Q Y 2006 Phys. Lett. A 351 23 Google Scholar
[36]	Deng F G, Li X H, Zhou H Y, Zhang Z J 2005 Phys. Rev. A 72 044302 Google Scholar
[37]	Cabello A 2000 Phys. Rev. Lett. 85 5633 Google Scholar

施引文献

表 1 本文协议和其他协议比较

Table 1. Comparison between our protocols and the other protocols.

QKA protocol	Quantum resource	Qubit efficiency
Liu et al.’s protocols^[10]	GHZ states	${1}/[{ {2 k\left( {k - 1} \right)} }]$
Xu et al.’s protocols^[12]	Single photons	${1}/[{ {2 k\left( {k - 1} \right)} }]$
Sun et al.’s protocols^[14]	Six-qubit states	${1}/({ {2 k} })$
Our protocol	GHZ states	${1}/({ {3 k} })$

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[1]	Zhou N, Zeng G, Xiong J 2004 Electron. Lett. 40 1149 Google Scholar
[2]	Chong S K, Hwang, T 2010 Opt. Commun. 283 1192 Google Scholar
[3]	Huang W, Su Q, Wu X, Li Y B, Sun L 2014 Int. J. Theor. Phys. 53 2891 Google Scholar
[4]	Shen D S, Ma W P, Wang L L 2014 Quantum Inf. Process. 13 2313 Google Scholar
[5]	He Y F, Ma W P 2015 Quantum Inf. Process. 14 3483 Google Scholar
[6]	He Y F, Ma W P 2017 Int. J. Quantum Inf. 3 1750018 Google Scholar
[7]	Yang Y G, Li B R, Li D, Zhou Y H, Shi W M 2019 Quantum Inf. Process. 18 322 Google Scholar
[8]	Zhou Y H, Wang M F, Shi W M, Yang Y G, Zhang J 2020 Quantum Inf. Process. 19 100 Google Scholar
[9]	Shi R H, Zhong H 2013 Quantum Inf. Process 12 921 Google Scholar
[10]	Liu B, Gao F, Huang W, Wen Q Y 2013 Quantum Inf. Process. 12 1797 Google Scholar
[11]	Sun Z, Zhang C, Wang B H, Li Q, Long D Y 2013 Quantum Inf. Process. 12 3411 Google Scholar
[12]	尹逊汝, 马文平, 申冬苏, 王丽丽 2013 62 170304 Google Scholar Yin X R, Ma W P, Shen D S, Wang L L 2013 Acta Phys. Sin. 62 170304 Google Scholar
[13]	Xu G B, Wen Q Y, Gao F, Qin S J 2014 Quantum Inf. Process. 13 2587 Google Scholar
[14]	Sun Z, Zhang C, Wang P, Yu J P, Zhang Y, Long D Y 2016 Int. J. Theor. Phys. 55 1920 Google Scholar
[15]	Sun Z, Yu J, Wang P 2016 Quantum Inf. Process. 15 373 Google Scholar
[16]	Cai T, Jiang M, Cao G 2018 Quantum Inf. Process. 17 103 Google Scholar
[17]	Lin S, Guo G D, Chen A M, Liu X F 2019 Quantum Inf. Process. 18 1 Google Scholar
[18]	Liu H N, Liang X Q, Jiang D H, Zhang Y H, Xu G B 2019 Quantum Inf. Process. 18 242 Google Scholar
[19]	Zhou N R, Zhu K N, Wang Y Q 2020 Int. J. Theor. Phys. 59 663 Google Scholar
[20]	Huang W, Wen Q Y, Liu B, Su Q, Gao F 2014 Quantum Inf. Process. 13 1651 Google Scholar
[21]	Cai B B, Guo G D, Lin S 2017 Int. J. Theor. Phys. 56 1039 Google Scholar
[22]	Min S Q, Chen H Y, Gong L H 2018 Int. J. Theor. Phys. 57 1811 Google Scholar
[23]	Wang S S, Xu G B, Liang X Q 2018 Int. J. Theor. Phys. 57 3716 Google Scholar
[24]	Zhao X Q, Zhou N R, Chen H Y, Gong L H 2019 Int. J. Theor. Phys. 58 436 Google Scholar
[25]	Liu H N, Liang X Q, Jiang D H, Zhang Y H, Xu G B 2019 Int. J. Theor. Phys. 58 1659 Google Scholar
[26]	Yin X R, Ma W P 2019 Int. J. Theor. Phys. 58 631 Google Scholar
[27]	Zhou Y H, Zhang J, Shi W M, Yang Y G 2020 Mod. Phys. Lett. B 4 2050083 Google Scholar
[28]	Wang W, Zhou B M, Zhang L 2020 Int. J. Theor. Phys. 59 1944 Google Scholar
[29]	Tang J, Shi L, Wei J H 2020 Mod. Phys. Lett. B 49 2050201 Google Scholar
[30]	Bouwmeester D, Pan J W, Daniell M, Weinfurte H, Zeilinger A 1999 Phys. Rev. Lett. 82 1345 Google Scholar
[31]	周南润, 宋汉冲, 龙黎华, 刘晔 2012 61 214203 Google Scholar Zhou N R, Chong S H, Gong L H, Liu Y 2012 Acta Phys. Sin. 61 214203 Google Scholar
[32]	Zhang Z J, Man Z X, Shi S H 2005 Int. J. Quantum Inf. 03 555 Google Scholar
[33]	Hwang T, Hwang C C, Li C M 2011 Phys. Scripta 83 045004 Google Scholar
[34]	Kao S H, Tsai C W, Tzonelih H 2011 Commun. Theor. Phys. 55 1007 Google Scholar
[35]	Cai Q Y 2006 Phys. Lett. A 351 23 Google Scholar
[36]	Deng F G, Li X H, Zhou H Y, Zhang Z J 2005 Phys. Rev. A 72 044302 Google Scholar
[37]	Cabello A 2000 Phys. Rev. Lett. 85 5633 Google Scholar

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