A Dynamic (t,n) Threshold Quantum Secret Sharing Scheme with Cheating Identification

doi:10.3969/j.issn.1671-1122.2024.05.008

Abstract

Abstract:

Based on homogeneous linear feedback shift register(LFSR) sequences and d-dimensional single quantum states, this paper proposed a dynamical (t,n) threshold quantum secret sharing scheme with cheating identification. In this scheme, a trusted dealer determined the shared secret and distributed shared to the participants, and the participants recovered the secret by performing the corresponding unitary operation on the transmitted particles. In the secret reconstruction phase, by performing quantum state digital signatures, not only the existence of cheating behavior could be detected, but also the specific cheater could be identified and removed, and finally the participants could verify the correctness of the recovered secret. The scheme allowed dynamic updating of participants without changing the shares of old participants and without the help of other participants. Security analysis shows that the scheme is resistant to common external and internal attacks.

Key words: quantum secret sharing, dynamic updating, cheating identification, quantum state digital signature

CLC Number:

TP309

GUO Jiansheng, GUAN Feiting, LI Zhihui. A Dynamic (t,n) Threshold Quantum Secret Sharing Scheme with Cheating Identification[J]. Netinfo Security, 2024, 24(5): 745-755.

Figures/Tables 3

References 28

[1]	HILLERY M, BUZEK V, BERTHIAUME A. Quantum Secret Sharing[J]. Physical Review A, 1999, 59(3): 1829-1834.
[2]	YAN Fengli, GAO Ting. Quantum Secret Sharing between Multiparty and Multiparty without Entanglement[EB/OL]. (2005-07-07)[2023-10-01]. https://doi.org/10.1103/PhysRevA.72.012304.
[3]	DEHKORDI M, FATTAHI E. Threshold Quantum Secret Sharing Between Multiparty and Multiparty Using Greenberger-Horne-Zeilinger State[J]. Quantum Information Processing, 2013, 12(2): 1299-1306.
[4]	CLEVE R, GOTTESMAN D, LO H. How to Share a Quantum Secret[J]. Physical Review Letters, 1999, 83(3): 648-651.
[5]	LIU Lu, LI Zhihui, LU Dianjun, et al. Quantum Secret Sharing Scheme Based on Linear Codes[J]. Netinfo Security, 2021, 21(8): 62-69.
	刘璐, 李志慧, 芦殿军, 等. 基于线性码的量子秘密共享方案[J]. 信息网络安全, 2021, 21(8): 62-69.
[6]	YANG Yuguang, WANG Yuan, CHAI Haiping, et al. Member Expansion in Quantum (t, n) Threshold Secret Sharing Schemes[J]. Optics Communications, 2011, 284(13): 3479-3482.
[7]	JIA Hengyue, WEN Qiaoyan, GAO Fei, et al. Dynamic Quantum Secret Sharing[J]. Physics Letters A, 2012, 376(10-11): 1035-1041.
[8]	HSU J L, CHONG Songkong, HWANG T, et al. Dynamic Quantum Secret Sharing[J]. Quantum Information Processing, 2013, 12(1): 331-344.
[9]	YANG Yuguang, TENG Yiwei, CHAI Haiping, et al. Verifiable Quantum (k, n)- Threshold Secret Key Sharing[J]. International Journal of Theoretical Physics, 2011, 50(3): 792-798.
[10]	SONG Xiuli, LIU Yanbing. Cryptanalysis and Improvement of Verifiable Quantum (k, n) Secret Sharing[J]. Quantum Information Processing, 2016, 15(2): 851-868.
[11]	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.
	李志慧, 罗双双, 韦性佳. 基于一类受限存取结构上的量子秘密共享方案[J]. 信息网络安全, 2023, 23(8): 32-40.
[12]	QIN Huawang, DAI Yuewei. Verifiable (t, n) Threshold Quantum Secret Sharing Using d-Dimensional Bell State[J]. Information Processing Letters, 2016, 116(5): 351-355.
[13]	LU Changbin, MIAO Fuyou, HOU Junpeng, et al. A Verifiable Framework of Entanglement-Free Quantum Secret Sharing with Information-Theoretical Security[EB/OL]. (2019-11-29)[2023-10-01]. https://doi.org/10.1007/s11128-019-2509-x.
[14]	LIU Xiaofen, CHEN Xiaofeng, LIAN Guiren, et al. Authenticated Multiparty Quantum Secret Sharing Protocol with d-Level Single Particle[J]. Netinfo Security, 2020, 20(3): 51-55.
	刘晓芬, 陈晓峰, 连桂仁, 等. 基于d级单粒子的可认证多方量子秘密共享协议[J]. 信息网络安全, 2020, 20(3):51-55.
[15]	YAN Chenhong, LI Zhihui, LIU Lu, et al. Cheating Identifiable (k, n) Threshold Quantum Secret Sharing Scheme[EB/OL]. (2021-12-23)[2023-10-01]. https://doi.org/10.1007/s11128-021-03343-2.
[16]	RATHI D, KUMAR S. A d-Level Quantum Secret Sharing Scheme with Cheat-Detection (t, m) Threshold[EB/OL]. (2023-04-28)[2023-10-01]. https://doi.org/10.1007/s11128-023-03928-z.
[17]	SHAMIR A. How to Share a Secret[J]. Communications of the ACM, 1979, 22: 612-613.
[18]	WANG Tianyin, LI Yanping. Cryptanalysis of Dynamic Quantum Secret Sharing[J]. Quantum Information Processing, 2013, 12(5): 1991-1997.
[19]	LIAO Cihong, YANG Chunwei, HWANG T. Comment on “Dynamic Quantum Secret Sharing”[J]. Quantum Information Processing, 2013, 12(10): 3143-3147.
[20]	YUAN Jiangtao, LI Lixiang. A Fully Dynamic Secret Sharing Scheme[J]. Information Sciences, 2019, 496: 42-52. doi: 10.1016/j.ins.2019.04.061
[21]	DU Yutao, BAO Wansu. Dynamic Quantum Secret Sharing Protocol Based on Two-Particle Transform of Bell States[J]. Chinese Physics B, 2018, 27(8): 1-6.
[22]	HU Wenwen, ZHOU Rigui, LI Xin, et al. A Novel Dynamic Quantum Secret Sharing in High-Dimensional Quantum System[EB/OL]. (2021-05-03)[2023-10-01]. https://doi.org/10.1007/s11128-021-03103-2.
[23]	LI Fulin, HU Hang, ZHU Shixin, et al. A Verifiable (k, n)- Threshold Dynamic Quantum Secret Sharing Scheme[EB/OL]. (2022-07-26)[2023-10-01]. https://doi.org/10.1007/s11128-022-03617-3.
[24]	LI Fulin, CHEN Tingyan, ZHU Shixin. Dynamic (t, n) Threshold Quantum Secret Sharing Based on d-Dimensional Bell State[J]. Physica A, 2022, 606: 1-9.
[25]	YANG Yuguang, LU Jiayu. A Dynamic and Hierarchical Quantum Secret Sharing Protocol Based on Starlike Cluster States[J]. Netinfo Security, 2023, 23(6): 34-42.
	杨宇光, 卢嘉煜. 一种基于星型簇态的动态的分级的量子秘密共享协议[J]. 信息网络安全, 2023, 23(6): 34-42.
[26]	WOOTTERS W, FIELDS B. Optimal State-Determination by Mutually Unbiased Measurements[J]. Annals of Physics, 1989, 191(2): 363-381.
[27]	GAO Fei, QIN Sujuan, GUO Fenzhuo, et al. Cryptanalysis of the Arbitrated Quantum Signature Protocols[EB/OL]. (2011-08-29)[2023-10-01]. https://doi.org/10.1103/PhysRevA.84.022344.
[28]	SONG Xiuli, LIU Yanbing, XIAO Min, et al. A Verifiable (t, n) Threshold Quantum State Sharing against Denial Attack[J]. IEEE Access, 2019, 7: 98908-98920. doi: 10.1109/ACCESS.2019.2928855

	${{p}_{i}}$	${{r}_{i}}$	${{q}_{i}}$	酉操作	${{\alpha }_{i}}$	${{\beta }_{i}}$
Bob1	4	6	10	${{U}_{10,10}}$	8	6
Bob2	10	1	0	${{U}_{0,0}}$	7	5
Bob3	8	4	1	${{U}_{1,1}}$	7	5

	文献[12]方案	文献[16]方案	文献[23]方案	文献[24]方案	本文方案
所用量子态	d维 Bell态	d维 Bell态	d维 GHZ态	d维 Bell态	MUB
动态	否	否	是	是	是
作弊识别	否	是	否	否	是
抵抗伪造攻击	是	是	是	是	是
抵抗否认攻击	否	否	否	否	是
诱饵粒子数	$N(m+1)$	$N(m+1)$	$nN$	$N(m+1)$	0
所用的粒子总数	$N(m+1)+2$	$N(m+1)+n(m-1)+2$	$n(N+1)$	$N(m+1)+2$	$4m-2$
酉操作次数	$m+1$	$\frac{n}{2}(m+1)(m-1)+1$	0	$m+1$	$9m-4$
测量操作次数	$N(m+1)+1$	$N(m+1)+\frac{nm}{2}+1$	$n(N+1)$	$N(m+1)+1$	$4m-1$