Quantum Secret Sharing Schemes Based on a Class of Restricted Access Structures

doi:10.3969/j.issn.1671-1122.2023.08.003

Abstract

Abstract:

In this paper, a multi-party quantum secret sharing based on a restricted access structure was designed using the quantum correlation of GHZ entangled state. In this paper, firstly, the participants were divided into two mutually disjoint subsets with three particles of the $d$-dimensional GHZ state as information carriers, and the participants in the two mutually disjoint subsets held the second and third particles of the GHZ state, respectively, and these participants hide their secret shares in quantum states which were acted the unitary transformations.Then, the participants in the subsets recovered the secret with the aid of the classical model. Finally, this scheme is more economical in terms of quantum resources compared to the same type of schemes, and the scheme is simpler and more efficient.

Key words: access structure, monotone span program, quantum secret sharing

CLC Number:

TP309

LI Zhihui, LUO Shuangshuang, WEI Xingjia. Quantum Secret Sharing Schemes Based on a Class of Restricted Access Structures[J]. Netinfo Security, 2023, 23(8): 32-40.

Figures/Tables 2

References 28

[1]	BENNETT C, BRASSARD G. WITHDRAWN: Quantum Cryptography:Public Key Distribution and Coin Tossing[C]//IEEE. Proceedings of IEEE International Conference on Computers,Systems, and Signal Processing. New York: IEEE, 1984, 175-179.
[2]	LO H K, CURTY M, QI M. Measurement-Device-Independent Quantum Key Distribution[EB/OL]. (2012-05-28)[2023-05-10]. https://doi.org/10.48550/arXiv.1109.1473.
[3]	TANG Yanlin, YIN Hualei, MA Xiongfeng, et al. Source Attack of Decoy-State Quantum Key Distribution Using Phase Information[EB/OL]. (2013-04-09)[2023-05-10]. https://doi.org/10.1103/PhysRevA.88.022308.
[4]	LO H K, MA Xiongfeng, CHEN Kai. Decoy State Quantum Key Distribution[EB/OL]. (2005-06-16)[2023-05-10]. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.94.230504.
[5]	NAM S W, NORDHOLT J E, RICE P R, et al. Long Distance Decoy State Quantum Key Distribution in Optical Fiber[J]. Physical Review Letters, 2007, 98(1): 1-4.
[6]	WANG Xiangbin, YU Zongwen, HU Xiaolong. Twin-Field Quantum Key Distribution with Large Misalignment Error[EB/OL]. (2018-12-18)[2023-05-10]. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.062323.
[7]	MA Xiongfeng, ZENG Pei, ZHOU Hongyi. Phase-Matching Quantum Key Distribution[EB/OL]. (2018-05-15)[2023-05-10]. https://doi.org/10.1103/PhysRevX.8.031043.
[8]	PHOENIX S J, BARNEET S M, TOWNSEND P D, et al. Multi-User Quantum Cryptography on Optical Networks[J]. Journal of Modern Optics, 1995, 42(6), 1155-1163. doi: 10.1080/09500349514551001 URL
[9]	ALLATI A E, BAZ M E, HASSOUNI Y. Quantum Key Distribution via Tripartite Coherent States[J]. Quantum Information Processing, 2010, 10: 589-602. doi: 10.1007/s11128-010-0213-y URL
[10]	HWANG W Y, YUEN H P. Quantum Key Distribution with High Loss: Toward Global Secure Communication[EB/OL]. (2003-05-19)[2023-05-10]. https://doi.org/10.48550/arXiv.quant-ph/0211153.
[11]	HILLERY M, BUZEK V, BERTHIAUME A. Quantum Secret Sharing[EB/OL]. (1999-03-01)[2023-05-10]. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.59.1829.
[12]	PIVOLUSKA M, HUBER M, MALIK M. Layered Quantum Key Distribution[EB/OL]. (2017-11-23)[2023-05-10]. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.032312.
[13]	YAN Chenhong, LI Zhihui, LIU Lu, et al. Cheating Identifiable (k, n) Threshold Quantum Secret Sharing Scheme[J]. Quantum Information Processing, 2022, 21(8): 1-24. doi: 10.1007/s11128-021-03349-w
[14]	CABELLO A. Quantum Key Distribution in the Holevo Limit[EB/OL]. (2000-12-18)[2023-05-10]. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.85.5635.
[15]	BENNETT C H. Quantum Cryptography Using Any Two Non-Orthogonal States[EB/OL]. (1992-05-25)[2023-05-10]. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.68.3121.
[16]	GOLDENBERG L, VAIDMAN L. Quantum Cryptography Based on Orthogonal States[EB/OL]. (1995-02-25)[2023-05-10]. https://doi.org/10.48550/arXiv.quant-ph/9502021.
[17]	KOASHI M, IMOTO N. Quantum Cryptography Based on Split Transmission of One-Bit Information in Two Steps[EB/OL]. (1997-09-22)[2023-05-10]. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.79.2383.
[18]	BAI Chenming, LI Zhihui, LI Yongming. Sequential Quantum Secret Sharing Using a Single Qubit[J]. Communications in Theoretical Physics, 2018, 69(5): 513-518. doi: 10.1088/0253-6102/69/5/513 URL
[19]	LI Lei, LI Zhi. A Verifiable Multiparty Quantum Key Agreement Based on Bivariate Polynomial[J]. Information Sciences, 2020, 521: 343-349. doi: 10.1016/j.ins.2020.02.057 URL
[20]	RAHAMAN R, PARKER M G. Quantum Scheme for Secret Sharing Based on Local Distinguishability[EB/OL]. (2015-02-20)[2023-05-10]. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.022330.
[21]	YANG Yinghui, GAO Fei, WU Xia, et al. Quantum Secret Sharing via Local Operations and Classical Communication[EB/OL]. (2015-11-20)[2023-05-10]. https://www.nature.com/articles/srep16967.
[22]	BAI Chenming, LI Zhihui, XU Tingting, et al. Quantum Secret Sharing Using the d-Dimensional GHZ State[J]. Quantum Information Processing, 2017, 16(3): 1-13. doi: 10.1007/s11128-016-1481-y URL
[23]	LU Changbin, MIAO Fuyou, HOU Junpeng, et al. A Verifiable Framework of Entanglement-Free Quantum Secret Sharing with Information-Theoretical Security[EB/OL]. (2019-12-03)[2023-05-10]. https://doi.org/10.1007/s11128-019-2509-x.
[24]	LI Fulin, HU Hang, ZHU Shixin, et al. A Verifiable (k, n)- Threshold Dynamic Quantum Secret Sharing Scheme[J]. Quantum Information Processing, 2022, 21(7), 259-268. doi: 10.1007/s11128-022-03617-3
[25]	KARTICK S, HARI O. Efficient Quantum Secret Sharing without a Trusted Player[J]. Quantum Information Processing, 2020, 19(2): 1-15. doi: 10.1007/s11128-019-2494-0
[26]	WEN Qiaoyan, GUO Fenzhuo, ZHU Fucheng. Design and Analysis of Quantum Confidential Communication Protocols[M]. Beijing: Science Press, 2009.
	温巧燕, 郭奋卓, 朱甫成. 量子保密通信方案的设计与分析[M]. 北京: 科学出版社, 2009.
[27]	LIU Chengji, LI Zhui, BAI Chenming, et al. Quantum Secret Sharing Scheme Based on Local Distinguishability of Orthogonal Seven-Qudit Entangled States[J]. International Journal of Theoretical Physics, 2018, 57(2): 428-442. doi: 10.1007/s10773-017-3574-5 URL
[28]	LI Zhihui, JIANG Xue, LIU Lu. Multi-Party Quantum Secret Sharing Based on GHZ State[EB/OL]. (2022-10-08)[2023-05-10]. https://doi.org/10.3390/e24101433.

	文献[20] 方案	文献[21] 方案	文献[27] 方案	文献[22] 方案	文献[28] 方案	本文方案
可实现门限	限制(2,$n$)	(2,$n$)	(6,7)	广义限制(2,$n$)	限制(2,$n$)	限制($t$,$n$)
所用信息量子态类型	$n$维 GHZ态	$n$维GHZ态	$7$维纠缠态	$n$维 GHZ态	$2$维GHZ态	$d$维 GHZ态
所用信息量子态个数	2	2	5	2	2	1
参与者分组	2组	—	—	2组	2组	2组
所用检测量子态类型	2维 GHZ态	$n$维GHZ态	单光子	单光子	单光子	单光子
所用检测量子态个数	$nL$	$nL$	$nu$	$nu$	$nL$	$\left( t+3 \right)u$
酉操作次数	0	0	0	0	0	$t+3$
测量次数	$n\left( v+L \right)$	$n\left( v+L \right)$	$n\left( v+u \right)$	$n\left( v+u \right)$	$n\left( v+L \right)$	1
信息效率	$\frac{v}{n\left( v+L \right)}$	$\frac{v}{n\left( v+L \right)}$	$\frac{v}{n\left( v+u \right)}$	$\frac{v}{n\left( v+u \right)}$	$\frac{v}{n\left( v+L \right)}$	$\frac{v}{\left( t+3 \right)\left( v+u \right)}$