Anonymous communication scheme based on quantum walk on Cayley graph

He Zhen-Xing; Fan Xing-Kui; Chu Peng-Cheng; Ma Hong-Yang

doi:10.7498/aps.69.20200333

Abstract

Information security is the cornerstone and lifeblood of national security in the information society, and anonymous quantum communication is one of the important ways to protect information security. Using quantum walk randomness to effectively solve sensitive problems such as leakage of identity information. In this paper, an anonymous communication scheme based on quantum walks on the Cayley graph is proposed. First, both parties in the communication hide their identity information, and the sender Alice anonymously selects the receiver Bob through logic or operation. Secondly, the trusted third party and the communicating parties use the BB84 protocol to generate and distribute the security key. Alice encrypts the information sequence according to the security key to obtain the blind information; Bob uses the joint Bell state measurement and security key to sign and the trusted third party verifies the signature information. Third, the trusted third party calculates the position probability distribution function of Bob’s quantum walk via the Fourier transform, converts the position information corresponding to the maximum probability into a confirmation frame and sends it to Alice; Alice uses the quantum compression algorithm by decreasing dimensions to reduce the number of transmitted information bits(the length of the information bit can be reduced by up to 37.5%) and uses the security key to complete the information encryption and then transmit the information to the location indicated by the confirmation frame. Bob uses quantum walks to search the location node to obtain the transmission information and complete the anonymous quantum communication. Finally, the security analysis of the scheme is carried out, and the numerical simulation results of the Cayley graph of 200 nodes are given. At the 10-step walk, the maximal probability of the 6th node is 45.31%. According to the simulation results, the probability that Bob is eavesdropped on the specific location at his 10-step walk during the communication of this scheme is approximately 6 × 10^–7%, so the receiver can avoid the identity information from the eavesdropping with a high probability, and the quantum network anonymity protocol is not broken.

Keywords:

Authors and contacts

School of Sciences, Qingdao University of Technology, Qingdao 266033, China

Corresponding author: Ma Hong-Yang, hongyang_ma@aliyun.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132, 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Project of Higher Educational Science and Technology Program of Shandong Province, China (Grant No. J18KZ012)

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References

[1]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[2]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1892
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[41]	Gong L, Qiu K, Deng C, Zhou N 2019 Opt. Laser Technol. 115 257 Google Scholar
[42]	Chen X B, Wang Y L, Xu G, Yang Y Y 2019 IEEE Access 7 13634 Google Scholar
[43]	Li H J, Chen X B, Wang Y L, Hou Y Y, Li J 2019 Quantum Inf. Process. 18 16 Google Scholar
[44]	Facer C, Twamley J, Cresser J 2008 Phys. Rev. A 77 012334 Google Scholar
[45]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[46]	龙桂鲁, 王川, 李岩松, 邓富国 2011 中国科学: 物理学力学天文学 41 332 Long G L, Wang C, Li Y S, Deng F G 2011 Sci. Sin. Phys. Mech. Astron. 41 332
[47]	Kempf A, Portugal R 2009 Phys. Rev. A 79 052317 Google Scholar
[48]	Childs A M 2010 Commun. Math. Phys. 294 281
[49]	刘欣, 梁燕霞, 聂敏, 魏媛媛 2017 光电子·激光 11 7 Liu X, Liang Y X, Nie M, Wei Y Y 2017 J. Optoelectron. Laser 11 7
[50]	马鸿洋, 张鑫, 徐鹏翱, 刘芬, 范兴奎 2020 通信学报 41 190 Google Scholar Ma H Y, Zhang X, Xu P A, Liu F, Fan X K 2020 J. Commun. 41 190 Google Scholar
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Cited By

图 1 匿名量子通信方案流程图

Figure 1. Flow chart of anonymous quantum communication scheme.

DownLoad: Full-Size Img PowerPoint

图 2 量子压缩过程

Figure 2. Quantum compression process.

DownLoad: Full-Size Img PowerPoint

图 3 匿名量子通信过程

Figure 3. Anonymous quantum communication process.

DownLoad: Full-Size Img PowerPoint

图 4 环形结构

Figure 4. Ring structure graph.

DownLoad: Full-Size Img PowerPoint

图 5 量子漫步10步时概率分布图

Figure 5. Probability distribution diagram for quantum walk in 10 steps.

DownLoad: Full-Size Img PowerPoint

表 1 信息N和签名Sor的对应关系

Table 1. Correspondence between information N and Sor signature

Alice信息序列$ N_{j} $	Bob签名序列$ Sor_{j} $
00	00 或 01
01	10 或 11
10	00 或 11
11	01 或 11

DownLoad: CSV

表 2 数值仿真结果

Table 2. Numerical simulation results

时间	节点总数	位置	概率/%
3	100	2	72.72
10	500	6	45.31
30	200 或 500	20	25.92
50	200 或 500	34	18.95
100	100	68	12.20
200	200	138	10.81

DownLoad: CSV

map

[1]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[2]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1892
[3]	胡钰安, 叶志清 2014 光子学报 43 827001 Google Scholar Hu Y A, Ye Z Q 2014 Acta Photon. Sin. 43 827001 Google Scholar
[4]	Unnikrishnan A, MacFarlane I J, Yi R, Diamanti E, Markham D, Kerenidis I 2019 Phys. Rev. Lett. 122 240510
[5]	Brassard G, Broadbent A, Fitzsimons J, Gambs S, Tapp A 2007 13 th International Conference on the Theory and Application of Cryptology and Information Security Kuching, Malaysia, December 2–6, 2007 pp460–473
[6]	陈鹏, 蔡有勋, 蔡晓菲, 施丽慧, 余旭涛 2015 64 040301 Chen P, Cai Y X, Cai X F, Shi L H, Yu X T 2015 Acta Phy. Sin. 64 040301
[7]	聂敏, 王林飞, 杨光, 张美玲, 裴昌幸 2015 64 210303 Google Scholar Nie M, Wang L F, Yang G, Zhang M L, Pei C X 2015 Acta Phy. Sin. 64 210303 Google Scholar
[8]	Wehner S 2004 Ph. D. Dissertation (Holland: Universiteit van Amsterdam)
[9]	Chaum D 1988 J. Cryptol. 1 1 Google Scholar
[10]	Chen X B, Sun Y R, Xu G 2019 Inf. Sci. 501 172 Google Scholar
[11]	Xu G, Xiao K, Li Z P, Niu X X, Ryan M 2019 CMC-Comput. Mater. Con. 58 809
[12]	Lipinska V, Murta G, Wehner S 2018 Phys. Rev. A 98 052320 Google Scholar
[13]	薛鹏, 郭光灿 2002 物理 31 385 Google Scholar Xue P, Guo G C 2002 Physics 31 385 Google Scholar
[14]	Boykin P O 2002 Ph. D. Dissertation (Los Angeles: University of California)
[15]	Christandl M, Wehner S 2005 11th International Conference on the Theory and Application of Cryptology and Information Chennai, India, December 4–8, 2005 pp217–235
[16]	Bouda J, Sprojcar J 2007 First International Conference on Quantum, Nano, and Micro Technologies Gosier, Guadeloupe, January 2–6, 2007 p12
[17]	Jiang L, He G Q, Nie D, Xiong J, Zeng G H 2012 Phys. Rev. A 85 042309 Google Scholar
[18]	周南润, 龚黎华, 刘三秋, 曾贵华 2007 56 5066 Google Scholar Zhou N R, Gong L H, Liu S Q, Zeng G H 2007 Acta Phys. Sin. 56 5066 Google Scholar
[19]	Montanaro A 2016 NPJ Quantum Inf. 2 15023 Google Scholar
[20]	杨乐, 李凯, 戴宏毅, 张明 2019 68 140301 Google Scholar Yang L, Li K, Dai H Y, Zhang M 2019 Acta Phys. Sin. 68 140301 Google Scholar
[21]	Travaglione B C, Milburn G J 2002 Phys. Rev. A 65 032310 Google Scholar
[22]	Childs A M, Goldstone J 2004 Phys. Rev. A 70 022314 Google Scholar
[23]	Childs A M, Cleve R, Deotto E, Farhi E, Gutmann S, Spielman D A 2003 Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing San Diego, America, June 9–11, 2003 pp59–68
[24]	Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R 2012 Phys. Rev. Lett. 108 010502 Google Scholar
[25]	Childs A M 2009 Phys. Rev. Lett. 102 180510
[26]	Zhan H 2019 Quantum Inf. Process. 18 369 Google Scholar
[27]	Costa P, de Melo F, Portugal R 2019 Phys. Rev. A 100 042320 Google Scholar
[28]	Di Molfetta G, Arrighi P 2020 Quantum Inf. Process. 19 47 Google Scholar
[29]	Wong T G 2019 Phys. Rev. A 100 062325 Google Scholar
[30]	Szigeti B E, Homa G, Zimborás Z, Barankai N 2019 Phys. Rev. A 100 062320 Google Scholar
[31]	Wang Y, Shang Y, Xue P 2017 Quantum Inf. Process. 16 221 Google Scholar
[32]	Feng Y Y, Shi R H, Shi J J, Zhou J, Guo Y 2019 Quantum Inf. Process. 18 154 Google Scholar
[33]	Li H J, Li J, Xiang N, Zheng Y, Yang Y G, Naseri M 2019 Quantum Inf. Process. 18 316 Google Scholar
[34]	Abd-El-Atty B, El-Latif A A A, Venegas-Andraca S E 2019 Quantum Inf. Process. 18 272 Google Scholar
[35]	Xu P A, He Z X, Qiu T H, Ma H Y 2020 Opt. Express 28 12508 Google Scholar
[36]	Shi P, Li N C, Wang S M, Liu Z, Ren M R, Ma H Y 2019 Sensors 19 5257 Google Scholar
[37]	Ma H Y, Teng J K, Hu T, Shi P, Wang S M 2020 Wireless. Pers. Commun. https://doi.org/10.1088/1674-1056/ab773 e [quant-ph]
[38]	Zhao J B, Zhang W B, Ma Y L, Zhang X H, Ma H Y 2020 Appl. Sci. 10 1935 Google Scholar
[39]	Ye C Q, Ye T Y 2019 Int. J. Theor. Phys. 58 1282 Google Scholar
[40]	Qin L G, Wang Z Y, Wu S C, Gong S Q, Ma H Y, Jing J 2018 Opt. Commun. 410 102 Google Scholar
[41]	Gong L, Qiu K, Deng C, Zhou N 2019 Opt. Laser Technol. 115 257 Google Scholar
[42]	Chen X B, Wang Y L, Xu G, Yang Y Y 2019 IEEE Access 7 13634 Google Scholar
[43]	Li H J, Chen X B, Wang Y L, Hou Y Y, Li J 2019 Quantum Inf. Process. 18 16 Google Scholar
[44]	Facer C, Twamley J, Cresser J 2008 Phys. Rev. A 77 012334 Google Scholar
[45]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[46]	龙桂鲁, 王川, 李岩松, 邓富国 2011 中国科学: 物理学力学天文学 41 332 Long G L, Wang C, Li Y S, Deng F G 2011 Sci. Sin. Phys. Mech. Astron. 41 332
[47]	Kempf A, Portugal R 2009 Phys. Rev. A 79 052317 Google Scholar
[48]	Childs A M 2010 Commun. Math. Phys. 294 281
[49]	刘欣, 梁燕霞, 聂敏, 魏媛媛 2017 光电子·激光 11 7 Liu X, Liang Y X, Nie M, Wei Y Y 2017 J. Optoelectron. Laser 11 7
[50]	马鸿洋, 张鑫, 徐鹏翱, 刘芬, 范兴奎 2020 通信学报 41 190 Google Scholar Ma H Y, Zhang X, Xu P A, Liu F, Fan X K 2020 J. Commun. 41 190 Google Scholar
[51]	Diaconis P, Rockmore D 1990 J. Am. Math. Soc. 3 297 Google Scholar
[52]	Hsiao H C, Kim T J, Perring A, Yamada A 2012 IEEE Secur. Privacy 19 506

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