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一种态制备误差容忍的量子数字签名协议

马洛嘉 丁华建 陈子骐 张春辉 王琴

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一种态制备误差容忍的量子数字签名协议

马洛嘉, 丁华建, 陈子骐, 张春辉, 王琴

A quantum digital signature protocol with state preparation error tolerance

Ma Luo-Jia, Ding Hua-Jian, Chen Zi-Qi, Zhang Chun-Hui, Wang Qin
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  • 量子数字签名(quantum digital signature, QDS)能够以信息论安全保证签名消息的不可伪造性、不可否认性和可转移性, 近年来备受关注与研究. 其中, 利用正交编码方式提出的信息论安全的实用化QDS协议, 成为目前QDS研究的主流范式. 然而, 现有QDS理论和实验都忽视了态制备过程中由于调制器件的不完美性可能引入调制误差. 本文针对此问题提出态制备误差容忍的QDS协议. 仿真结果表明, 相比原来的QDS协议, 本协议对态制备误差具有较好的容忍度, 能实现更高的签名率和签名距离. 另外, 本协议在密钥产生阶段只需要制备3个量子态, 降低了实验要求和难度. 因此, 本协议将对未来QDS的实际应用提供重要的参考价值.
    The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. (Phys. Rev. A 93 032325) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients.However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method.Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations.Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.
      通信作者: 王琴, qinw@njupt.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 12074194, 11774180) 、江苏省自然科学基金前沿技术项目(批准号: BK20192001)和江苏省重点研发计划产业前瞻与关键核心技术项目(批准号: BE2022071)资助的课题.
      Corresponding author: Wang Qin, qinw@njupt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074194, 11774180), the Leading-edge Technology Program of Natural Science Foundation, China (Grant No. BK20192001), and the Industrial Prospect and Key Core Technology Projects of Jiangsu Provincial key R & D Program, China(Grant No. BE2022071).
    [1]

    Diffie W, Helman M E 1976 IEEE Trans. Inf. Theory 22 644Google Scholar

    [2]

    Gottesman D, Chuang I 2001 arXiv: quant-ph/0105032v2

    [3]

    Clarke P J, Collins R J, Dunjko V, Andersson E, Jeffers J, Buller G S 2012 Nat. Commun. 3 1174Google Scholar

    [4]

    Collins R J, Donaldson R J, Dunjko V, Wallden P, Clarke P J, Andersson E, Jeffers J, Buller G S 2014 Phys. Rev. Lett. 113 040502Google Scholar

    [5]

    Amiri R, Wallden P, Kent A, Andersson E 2016 Phys. Rev. A 93 032325Google Scholar

    [6]

    Puthoor I V, Amiri R, Wallden P, Curty M, Andersson Erika 2016 Phys. Rev. A 94 022328Google Scholar

    [7]

    An X B, Zhang H, Zhang C M, Chen W, Wang S, Yin Z Q, Wang Q, He D Y, Hao P L, Liu S F, Zhou X Y, Guo G C, Han Z F 2019 Opt. Lett. 44 139Google Scholar

    [8]

    Zhang C H, Zhou X Y, Ding H J, Zhang C M, Guo G C, Wang Q 2018 Phys. Rev. Appl. 10 034033Google Scholar

    [9]

    Ding H J, Chen J J, Li J, Zhou X Y, Zhang C H, Zhang C M, Wang Q 2020 Opt. Lett. 45 1711Google Scholar

    [10]

    Yin H L, Fu Y, Li C L, Weng C X, Li B H, Gu J, Lu Y S, Huang S, Chen Z B 2023 Natl. Sci. Rev. 10 1093

    [11]

    Lo H K, Ma X F, Chen K 2005 Phys. Rev. Lett. 94 230504Google Scholar

    [12]

    Zeng G, Keitel C H 2002 Phys. Rev. A 65 042312Google Scholar

    [13]

    Tamaki K, Lo H K, Fung C H F, Qi B 2011 Phys. Rev. A 85 042307

    [14]

    Koashi M 2009 New J. Phys. 11 045018Google Scholar

    [15]

    Lo H K, Preskill J 2007 Quant. Inf. Comput. 8 431

    [16]

    Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quant. Inf. Comput. 4 325

    [17]

    Tamaki K, Curty M, Kato G, Lo H K, Azuma K 2014 Phys. Rev. A 90 052314Google Scholar

    [18]

    Serfling R J 1974 Ann. Statist. 2 39

    [19]

    马啸, 孙铭烁, 刘靖阳, 丁华建, 王琴 2022 物理学报 71 030301Google Scholar

    Ma X, Sun M S, Liu J Y, Ding H J, Wang Q 2022 Acta Phys. Sin. 71 030301Google Scholar

    [20]

    Hoeffding W 1994 Probability Inequalities for Sums of Bounded Random Variables (New York: Springer) pp409–426

    [21]

    Gobby C, Yuan Z L, Shields A J 2004 Appl. Phys. Lett. 84 3672Google Scholar

    [22]

    Zhang C H, Zhou X Y, Zhang C M, Li J, Wang Q 2021 Opt. Lett. 46 3757Google Scholar

  • 图 1  态制备误差容忍方法和GLLP分析方法签名率大小对比结果

    Fig. 1.  Comparison on the signature rate between the state-preparation-error tolerance scheme and GLLP method.

    图 2  态制备误差容忍方法和GLLP分析方法的错误率对比结果

    Fig. 2.  Comparison on the error rate between the state-preparation-error tolerance scheme and GLLP method.

    图 3  传输距离为20 km时, 不同总脉冲数下, 态制备误差容忍方法和GLLP分析方法签名率随着态制备误差变化对比

    Fig. 3.  The signature rate vs. state preparation error for the state-preparation-error tolerance scheme and GLLP method under different total number of pulses. Here the transmission distance is fixed at 20 km.

    表 1  基于量子数字签名的态制备误差容忍协议仿真使用的参数列表[21]

    Table 1.  The parameter list used for simulation of state preparation error tolerance protocol based on quantum digital signature protocol[21].

    接收方探测器
    暗计数率 Pd
    接收方探测器
    探测效率 ηd
    信道损耗系数
    α/(dB·km–1)
    KGP过程中估参
    长度比例 d
    发射的总
    脉冲数Ntot
    失败概率
    ${\varepsilon _{{\text{PE}}}}$
    最弱诱骗态
    强度 w
    1.5×10–6 0.145 0.2 1/21 1014 10–5 0.002
    下载: 导出CSV
  • [1]

    Diffie W, Helman M E 1976 IEEE Trans. Inf. Theory 22 644Google Scholar

    [2]

    Gottesman D, Chuang I 2001 arXiv: quant-ph/0105032v2

    [3]

    Clarke P J, Collins R J, Dunjko V, Andersson E, Jeffers J, Buller G S 2012 Nat. Commun. 3 1174Google Scholar

    [4]

    Collins R J, Donaldson R J, Dunjko V, Wallden P, Clarke P J, Andersson E, Jeffers J, Buller G S 2014 Phys. Rev. Lett. 113 040502Google Scholar

    [5]

    Amiri R, Wallden P, Kent A, Andersson E 2016 Phys. Rev. A 93 032325Google Scholar

    [6]

    Puthoor I V, Amiri R, Wallden P, Curty M, Andersson Erika 2016 Phys. Rev. A 94 022328Google Scholar

    [7]

    An X B, Zhang H, Zhang C M, Chen W, Wang S, Yin Z Q, Wang Q, He D Y, Hao P L, Liu S F, Zhou X Y, Guo G C, Han Z F 2019 Opt. Lett. 44 139Google Scholar

    [8]

    Zhang C H, Zhou X Y, Ding H J, Zhang C M, Guo G C, Wang Q 2018 Phys. Rev. Appl. 10 034033Google Scholar

    [9]

    Ding H J, Chen J J, Li J, Zhou X Y, Zhang C H, Zhang C M, Wang Q 2020 Opt. Lett. 45 1711Google Scholar

    [10]

    Yin H L, Fu Y, Li C L, Weng C X, Li B H, Gu J, Lu Y S, Huang S, Chen Z B 2023 Natl. Sci. Rev. 10 1093

    [11]

    Lo H K, Ma X F, Chen K 2005 Phys. Rev. Lett. 94 230504Google Scholar

    [12]

    Zeng G, Keitel C H 2002 Phys. Rev. A 65 042312Google Scholar

    [13]

    Tamaki K, Lo H K, Fung C H F, Qi B 2011 Phys. Rev. A 85 042307

    [14]

    Koashi M 2009 New J. Phys. 11 045018Google Scholar

    [15]

    Lo H K, Preskill J 2007 Quant. Inf. Comput. 8 431

    [16]

    Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quant. Inf. Comput. 4 325

    [17]

    Tamaki K, Curty M, Kato G, Lo H K, Azuma K 2014 Phys. Rev. A 90 052314Google Scholar

    [18]

    Serfling R J 1974 Ann. Statist. 2 39

    [19]

    马啸, 孙铭烁, 刘靖阳, 丁华建, 王琴 2022 物理学报 71 030301Google Scholar

    Ma X, Sun M S, Liu J Y, Ding H J, Wang Q 2022 Acta Phys. Sin. 71 030301Google Scholar

    [20]

    Hoeffding W 1994 Probability Inequalities for Sums of Bounded Random Variables (New York: Springer) pp409–426

    [21]

    Gobby C, Yuan Z L, Shields A J 2004 Appl. Phys. Lett. 84 3672Google Scholar

    [22]

    Zhang C H, Zhou X Y, Zhang C M, Li J, Wang Q 2021 Opt. Lett. 46 3757Google Scholar

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出版历程
  • 收稿日期:  2023-07-24
  • 修回日期:  2023-10-09
  • 上网日期:  2023-10-20
  • 刊出日期:  2024-01-20

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