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 物理学报 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 物理学报 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	${1}/({ {3 k} })$

下载: 导出CSV

[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 物理学报 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 物理学报 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

[1]	贺英, 王天一, 李莹莹. 线性光学克隆机改进的离散极化调制连续变量量子密钥分发可组合安全性分析. 物理学报, 2024, 73(23): . doi: 10.7498/aps.20241094
[2]	贺英, 王天一, 李莹莹. 线性光学克隆机改进的离散极化调制连续变量量子密钥分发可组合安全性分析. 物理学报, 2024, 73(23): 230303. doi: 10.7498/aps.73.20241094
[3]	龚黎华, 陈振泳, 徐良超, 周南润. 基于高维单粒子态的双向半量子安全直接通信协议. 物理学报, 2022, 71(13): 130304. doi: 10.7498/aps.71.20211702
[4]	荣民希, 辛向军, 李发根. 具有强安全性的指定验证者量子签名方案. 物理学报, 2020, 69(19): 190302. doi: 10.7498/aps.69.20200244
[5]	李津, 王海燕, 李优, 张秋月, 贾瑜. 氧族元素对D-A和D--A共聚物光吸收谱红移的第一性原理研究. 物理学报, 2016, 65(10): 103101. doi: 10.7498/aps.65.103101
[6]	谢天婷, 邓科, 罗懋康. 二维非对称周期时移波状通道中的粒子定向输运问题. 物理学报, 2016, 65(15): 150501. doi: 10.7498/aps.65.150501
[7]	李剑, 陈彦桦, 潘泽世, 孙风琪, 李娜, 黎雷蕾. 量子BB84协议在联合旋转噪音信道上的安全性分析. 物理学报, 2016, 65(3): 030302. doi: 10.7498/aps.65.030302
[8]	尹逊汝, 马文平, 申冬苏, 王丽丽. 基于Bell态的三方量子密钥协商. 物理学报, 2013, 62(17): 170304. doi: 10.7498/aps.62.170304
[9]	陆鸢, 黄鹏, 朱俊, 代文超, 曾贵华. 基于αη协议的量子数据流加密系统实际安全与性能分析. 物理学报, 2012, 61(8): 080301. doi: 10.7498/aps.61.080301
[10]	赵楠, 裴昌幸, 刘丹, 权东晓, 孙晓楠. 基于BB84协议的量子密钥分发安全门限研究. 物理学报, 2011, 60(9): 090307. doi: 10.7498/aps.60.090307
[11]	王静, 蒋国平. 一种超混沌图像加密算法的安全性分析及其改进. 物理学报, 2011, 60(6): 060503. doi: 10.7498/aps.60.060503
[12]	沈咏, 邹宏新. 离散调制连续变量量子密钥分发的安全边界. 物理学报, 2010, 59(3): 1473-1480. doi: 10.7498/aps.59.1473
[13]	王天银, 秦素娟, 温巧燕, 朱甫臣. 多方控制的量子安全直接通信协议的分析及改进. 物理学报, 2008, 57(12): 7452-7456. doi: 10.7498/aps.57.7452
[14]	杜建忠, 陈秀波, 温巧燕, 朱甫臣. 保密多方量子求和. 物理学报, 2007, 56(11): 6214-6219. doi: 10.7498/aps.56.6214
[15]	王剑, 陈皇卿, 张权, 唐朝京. 多方控制的量子安全直接通信协议. 物理学报, 2007, 56(2): 673-677. doi: 10.7498/aps.56.673
[16]	王开, 裴文江, 邹留华, 何振亚. 一种多混沌系统公钥密码算法的安全性分析. 物理学报, 2006, 55(12): 6243-6247. doi: 10.7498/aps.55.6243
[17]	杨宇光, 温巧燕, 朱甫臣. 基于纠缠交换的多方多级量子密钥分配协议. 物理学报, 2005, 54(12): 5544-5548. doi: 10.7498/aps.54.5544
[18]	白丽华, 张庆刚, 刘新国. D+CD4→CD3+D2反应的四维量子散射计算. 物理学报, 2003, 52(11): 2774-2780. doi: 10.7498/aps.52.2774
[19]	张权, 唐朝京, 张森强. B92量子密钥分配协议的变形及其无条件安全性证明. 物理学报, 2002, 51(7): 1439-1447. doi: 10.7498/aps.51.1439
[20]	杨理, 吴令安, 刘颂豪. 复合量子密钥分发系统双速协议及其安全性分析. 物理学报, 2002, 51(11): 2446-2451. doi: 10.7498/aps.51.2446

计量

文章访问数: 5878
PDF下载量: 105
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

基于d维GHZ态的多方量子密钥协商