x

留言板

Arbitrated quantum signature scheme based on quantum walks

Arbitrated quantum signature scheme based on quantum walks

Feng Yan-Yan, Shi Rong-Hua, Shi Jin-Jing, Guo Ying
PDF
HTML
• Abstract

Quantum signature is quantum counterpart of classical digital signature, which has been widely applied to modern communication, such as electronic payment, electronic voting and electronic medical, owing to its great implication in ensuring the authenticity and the integrity of the message and the non-repudiation. Arbitrated quantum signature (AQS) is an important and practical type of quantum signature. The AQS algorithm is a symmetric key cryptography-based quantum signature algorithm, and its implementation requires the trusted arbitrator to be directly involved. In this paper, employing the key-controlled chained CNOT (KCCC) operation as the appropriate encryption (decryption) algorithm, we suggest an AQS scheme based on teleportation of quantum walks with two coins on a four-vertex cycle, which is used to transfer the message copy from the sender to the receiver. In light of the model of teleportation of quantum walks, the sender encodes the message to be signed into her or his coin state, and the necessary entangled states can be created as a result of the conditional shift between the coin state and the position state. The measurements performed on the generated entangled states are the bases of signature production and message recovery. Then according to the classical measurement results from the sender, the receiver performs the appropriate local unitary operations (i.e., Pauli operations) on his own coin state to recover the original message and further verifies the validity of the completed signature by using the appropriate verification algorithms under the aid of the trustworthy arbitrator. The suggested AQS scheme makes the following contributions: 1) the necessary entangled states for quantum teleportation of message copy do not need preparing in advance, and they can be produced automatically by the first step of quantum walks; 2) the scheme satisfies the features of non-repudiation, un-forgeability and non-disavowal due to the use of the KCCC operation; 3) the scheme may be achieved by linear optical elements such as beam splitters, wave plates, etc., because quantum walks have proven to be realizable in different physical systems and experiments.Analysis and discussion show that the proposed AQS scheme possesses the impossibility of disavowals by the signer and the receiver and impossibility of forgeries by anyone. Comparisons reveal that the designed AQS protocol is favorable. Furthermore, it provides an idea by employing the quantum computing model into quantum communication protocols with a possible improvement with respect to its favorable properties, for example, the automatic generation of entangled states via the first step of quantum walks on different models. In the near future, we will further investigate the production of entanglement by quantum walks and its applications with some improvements in designing the quantum communication protocols.

References

 [1] Meijer H, Akl S 1981 ACM SIGCOMM Comp. Com. 11 37 [2] Zeng G, Keitel C H 2002 Phys. Rev. A 65 042312 [3] Nielsen M A, Chuang I, Grover L K 2002 Am. J. Phys. 70 558 [4] Guo Y, Xie C L, Liao Q, Zhao W, Zeng G H, Huang D 2017 Phys. Rev. A 96 022320 [5] Guo Y, Liao Q, Wang Y, Wang Y J, Huang D, Huang P, Zeng G H 2017 Phys. Rev. A 95 032304 [6] Xu G, Chen X B, Dou Z, Yang Y X, Li Z 2015 Quantum Inf. Process. 14 2959 [7] Chen X B, Sun Y R, Xu G, Jia H Y, Qu Z, Yang Y X 2017 Quantum Inf. Process. 16 244 [8] Chen X B, Tang X, Xu G, Dou Z, Chen Y L, Yang Y X 2018 Quantum Inf. Process. 17 225 [9] Curty M, Lütkenhaus N 2008 Phys. Rev. A 77 046301 [10] Zeng G 2008 Phys. Rev. A 78 016301 [11] Li Q, Chan W H, Long D Y 2009 Phys. Rev. A 79 054307 [12] Zou X, Qiu D 2010 Phys. Rev. A 82 042325 [13] Gao F, Qin S J, Guo F Z, Wen Q Y 2011 Phys. Rev. A 84 022344 [14] Choi J W, Chang K Y, Hong D 2011 Phys. Rev. A 84 062330 [15] 张骏, 吴吉义 2013 北京邮电大学学报 36 113 Zhang J, Wu J Y 2013 J. Beijing Univ. Posts Telecommun. 36 113 [16] Li F G, Shi J H 2015 Quantum Inf. Process. 14 2171 [17] Yang Y G, Lei H, Liu Z C, Zhou Y H, Shi W M 2016 Quantum Inf. Process. 15 2487 [18] Zhang L, Sun H W, Zhang K J, Jia H Y 2017 Quantum Inf. Process. 16 70 [19] Zhang Y, Zeng J 2018 Int. J. Theor. Phys. 57 994 [20] Guo Y, Feng Y Y, Huang D Z, Shi J J 2016 Int. J. Theor. Phys. 55 2290 [21] Feng Y Y, Shi R H, Guo Y 2018 Chin. Phys. B 27 020302 [22] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687 [23] Venegas-Andraca S E 2012 Quantum Inf. Process. 11 1015 [24] Kempe J 2003 Contemp. Phys. 44 307 [25] Wang Y, Shang Y, Xue P 2017 Quantum Inf. Process. 16 221 [26] Shang Y, Wang Y, Li M, Lu R Q 2019 EPL- Europhys. Lett. 124 60009 [27] Chen X B, Wang Y L, Xu G, Yang Y X 2019 IEEE Access 7 13634 [28] Zou X, Dong Y, Guo G 2006 New J. Phys. 8 81 [29] Bian Z H, Li J, Zhan X, Twamley J, Xue P 2017 Phys. Rev. A 95 052338 [30] Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 eaat3174 [31] Aharonov D, Ambainis A, Kempe J, Vazirani U 2001 Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing New York, USA, 2001 p50 [32] Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J, Sanders Barry C 2015 Phys. Rev. Lett. 114 140502

Cited By

• 图 1  具有四个顶点的环及其相移规则

Figure 1.  Shift regulations on a cycle with four vertexes.

图 2  两个硬币的环上的量子游走线路原理图

Figure 2.  Circuit diagram of quantum walks on cycles with two coins.

图 3  签名方案原理图(QKD代表量子密钥分发)

Figure 3.  Schematic of the suggested arbitrated quantum signature scheme. QKD is short for quantum key distribution.

图 4  n = 50, 100, 150三种情况下Alice成功抵赖签名的概率${P_{{\rm{disavowal}}}}(m)$

Figure 4.  Alice’s disavowal probability ${P_{{\rm{disavowal}}}}(m)$ as a function of the amount m of the disavowed qubit in the signature state $|{S_a}\rangle$ for the respective $n = 50$, $n = 100$ and $n = 150$.

•  [1] Meijer H, Akl S 1981 ACM SIGCOMM Comp. Com. 11 37 [2] Zeng G, Keitel C H 2002 Phys. Rev. A 65 042312 [3] Nielsen M A, Chuang I, Grover L K 2002 Am. J. Phys. 70 558 [4] Guo Y, Xie C L, Liao Q, Zhao W, Zeng G H, Huang D 2017 Phys. Rev. A 96 022320 [5] Guo Y, Liao Q, Wang Y, Wang Y J, Huang D, Huang P, Zeng G H 2017 Phys. Rev. A 95 032304 [6] Xu G, Chen X B, Dou Z, Yang Y X, Li Z 2015 Quantum Inf. Process. 14 2959 [7] Chen X B, Sun Y R, Xu G, Jia H Y, Qu Z, Yang Y X 2017 Quantum Inf. Process. 16 244 [8] Chen X B, Tang X, Xu G, Dou Z, Chen Y L, Yang Y X 2018 Quantum Inf. Process. 17 225 [9] Curty M, Lütkenhaus N 2008 Phys. Rev. A 77 046301 [10] Zeng G 2008 Phys. Rev. A 78 016301 [11] Li Q, Chan W H, Long D Y 2009 Phys. Rev. A 79 054307 [12] Zou X, Qiu D 2010 Phys. Rev. A 82 042325 [13] Gao F, Qin S J, Guo F Z, Wen Q Y 2011 Phys. Rev. A 84 022344 [14] Choi J W, Chang K Y, Hong D 2011 Phys. Rev. A 84 062330 [15] 张骏, 吴吉义 2013 北京邮电大学学报 36 113 Zhang J, Wu J Y 2013 J. Beijing Univ. Posts Telecommun. 36 113 [16] Li F G, Shi J H 2015 Quantum Inf. Process. 14 2171 [17] Yang Y G, Lei H, Liu Z C, Zhou Y H, Shi W M 2016 Quantum Inf. Process. 15 2487 [18] Zhang L, Sun H W, Zhang K J, Jia H Y 2017 Quantum Inf. Process. 16 70 [19] Zhang Y, Zeng J 2018 Int. J. Theor. Phys. 57 994 [20] Guo Y, Feng Y Y, Huang D Z, Shi J J 2016 Int. J. Theor. Phys. 55 2290 [21] Feng Y Y, Shi R H, Guo Y 2018 Chin. Phys. B 27 020302 [22] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687 [23] Venegas-Andraca S E 2012 Quantum Inf. Process. 11 1015 [24] Kempe J 2003 Contemp. Phys. 44 307 [25] Wang Y, Shang Y, Xue P 2017 Quantum Inf. Process. 16 221 [26] Shang Y, Wang Y, Li M, Lu R Q 2019 EPL- Europhys. Lett. 124 60009 [27] Chen X B, Wang Y L, Xu G, Yang Y X 2019 IEEE Access 7 13634 [28] Zou X, Dong Y, Guo G 2006 New J. Phys. 8 81 [29] Bian Z H, Li J, Zhan X, Twamley J, Xue P 2017 Phys. Rev. A 95 052338 [30] Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 eaat3174 [31] Aharonov D, Ambainis A, Kempe J, Vazirani U 2001 Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing New York, USA, 2001 p50 [32] Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J, Sanders Barry C 2015 Phys. Rev. Lett. 114 140502
•  [1] Zhang Sheng, Wang Jian, Zhang Quan, Tang Chao-Jing. An analysis of the model of the error bits of quantum cryptography protocol. Acta Physica Sinica, 2009, 58(1): 73-77. doi: 10.7498/aps.58.73 [2] Li Wei, Fan Ming-Yu, Wang Guang-Wei. Arbitrated quantum signature scheme based on entanglement swapping. Acta Physica Sinica, 2011, 60(8): 080302. doi: 10.7498/aps.60.080302 [3] Wang Jian, Chen Huang-Qing, Zhang Quan, Tang Chao-Jing. Multiparty controlled quantum secure direct communication protocol. Acta Physica Sinica, 2007, 56(2): 673-677. doi: 10.7498/aps.56.673 [4] Quan Dong-Xiao, Pei Chang-Xing, Liu Dan, Zhao Nan. One-way deterministic secure quantum communication protocol based on single photons. Acta Physica Sinica, 2010, 59(4): 2493-2497. doi: 10.7498/aps.59.2493 [5] Lin Qing-Qun, Wang Fa-Qiang, Mi Jing-Long, Liang Rui-Sheng, Liu Song-Hao. Deterministic quantum key distribution based on random phase coding. Acta Physica Sinica, 2007, 56(10): 5796-5801. doi: 10.7498/aps.56.5796 [6] Liu Song-Hao, Wu Ling-An, Yang Li. . Acta Physica Sinica, 2002, 51(11): 2446-2451. doi: 10.7498/aps.51.2446 [7] Liu Song-Hao, Wu Ling-An, Yang Li. . Acta Physica Sinica, 2002, 51(5): 961-965. doi: 10.7498/aps.51.961 [8] Chen Li-Bing, Tan Peng, Dong Shao-Guang, Lu Hong. Controlled implementation of a nonlocal and open-target destination quantum controlled-Not （CNOT） gate using partially entangled pairs. Acta Physica Sinica, 2009, 58(10): 6772-6778. doi: 10.7498/aps.58.6772 [9] Ding Dong, Yan Feng-Li. Implementation of the scheme of a quantum information signature based on weak nonlinearity. Acta Physica Sinica, 2013, 62(1): 010302. doi: 10.7498/aps.62.010302 [10] Liu Chuan-Long, Zheng Yi-Zhuang. Teleportation of entangled coherent state through bipartite entangled quantum channels. Acta Physica Sinica, 2006, 55(12): 6222-6228. doi: 10.7498/aps.55.6222 [11] He Rui, Bing He. A new quantum teleportation protocal. Acta Physica Sinica, 2011, 60(6): 060302. doi: 10.7498/aps.60.060302 [12] Yang Lu, Ma Hong-Yang, Zheng Chao, Ding Xiao-Lan, Gao Jian-Cun, Long Gui-Lu. Quantum communication scheme based on quantum teleportation. Acta Physica Sinica, 2017, 66(23): 230303. doi: 10.7498/aps.66.230303 [13] Zhang Guo-Feng, Xing Zhao. Swap operation in a two-qubit anisotropy XYZ model in the presence of an inhomogeneous magnetic field. Acta Physica Sinica, 2010, 59(3): 1468-1472. doi: 10.7498/aps.59.1468 [14] Zhou Xiao-Qing, Wu Yun-Wen, Zhao Han. Quantum teleportation internetworking and routing strategy. Acta Physica Sinica, 2011, 60(4): 040304. doi: 10.7498/aps.60.040304.2 [15] Zhou Xiao-Qing, Wu Yun-Wen. Broadcast and multicast in quantum teleportation internet. Acta Physica Sinica, 2012, 61(17): 170303. doi: 10.7498/aps.61.170303 [16] Qiao Pan-Pan, Ahmad Abliz, Cai Jiang-Tao, Lu Jun-Zhe, Maimaitiyiming Tusun, Ribigu Maimaitiming. Quantum teleportation using superconducting charge qubits in thermal equilibrium. Acta Physica Sinica, 2012, 61(24): 240303. doi: 10.7498/aps.61.240303 [17] Wu Ying, Li Jin-Fang, Liu Jin-Ming. Enhancement of quantum Fisher information of quantum teleportation by optimizing partial measurements. Acta Physica Sinica, 2018, 67(14): 140304. doi: 10.7498/aps.67.20180330 [18] WEN YANG-JING, FENG YU, FU CHUAN-HONG. QUANTUM TREATMENT OF OPTICAL SOLITON PROPAGATION. Acta Physica Sinica, 1993, 42(12): 1942-1949. doi: 10.7498/aps.42.1942 [19] Zhang Wei, Han Zheng-Fu. Quantum broadcasting multiple blind signature protocol based on three-particle partial entanglement. Acta Physica Sinica, 2019, 68(7): 070301. doi: 10.7498/aps.68.20182044 [20] Wang Yu-Wu, Wei Xiang-He, Zhu Zhao-Hui. Quantum voting protocols based on the non-symmetric quantum channel with controlled quantum operation teleportation. Acta Physica Sinica, 2013, 62(16): 160302. doi: 10.7498/aps.62.160302
•  Citation:
Metrics
• Abstract views:  165
• Cited By: 0
Publishing process
• Received Date:  27 February 2019
• Accepted Date:  15 April 2019
• Available Online:  16 August 2019
• Published Online:  01 June 2019

Arbitrated quantum signature scheme based on quantum walks

Corresponding author: Shi Jin-Jing, shijinjing@csu.edu.cn;
• School of Computer Science and Engineering, Central South University, Changsha 410083, China

Abstract: Quantum signature is quantum counterpart of classical digital signature, which has been widely applied to modern communication, such as electronic payment, electronic voting and electronic medical, owing to its great implication in ensuring the authenticity and the integrity of the message and the non-repudiation. Arbitrated quantum signature (AQS) is an important and practical type of quantum signature. The AQS algorithm is a symmetric key cryptography-based quantum signature algorithm, and its implementation requires the trusted arbitrator to be directly involved. In this paper, employing the key-controlled chained CNOT (KCCC) operation as the appropriate encryption (decryption) algorithm, we suggest an AQS scheme based on teleportation of quantum walks with two coins on a four-vertex cycle, which is used to transfer the message copy from the sender to the receiver. In light of the model of teleportation of quantum walks, the sender encodes the message to be signed into her or his coin state, and the necessary entangled states can be created as a result of the conditional shift between the coin state and the position state. The measurements performed on the generated entangled states are the bases of signature production and message recovery. Then according to the classical measurement results from the sender, the receiver performs the appropriate local unitary operations (i.e., Pauli operations) on his own coin state to recover the original message and further verifies the validity of the completed signature by using the appropriate verification algorithms under the aid of the trustworthy arbitrator. The suggested AQS scheme makes the following contributions: 1) the necessary entangled states for quantum teleportation of message copy do not need preparing in advance, and they can be produced automatically by the first step of quantum walks; 2) the scheme satisfies the features of non-repudiation, un-forgeability and non-disavowal due to the use of the KCCC operation; 3) the scheme may be achieved by linear optical elements such as beam splitters, wave plates, etc., because quantum walks have proven to be realizable in different physical systems and experiments.Analysis and discussion show that the proposed AQS scheme possesses the impossibility of disavowals by the signer and the receiver and impossibility of forgeries by anyone. Comparisons reveal that the designed AQS protocol is favorable. Furthermore, it provides an idea by employing the quantum computing model into quantum communication protocols with a possible improvement with respect to its favorable properties, for example, the automatic generation of entangled states via the first step of quantum walks on different models. In the near future, we will further investigate the production of entanglement by quantum walks and its applications with some improvements in designing the quantum communication protocols.

Reference (32)

/