Verifiable quantum secret sharing scheme based on orthogonal product states

doi:10.1088/1674-1056/ad342a

Abstract In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the $d$-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the $\mathbb{C}^d \otimes \mathbb{C}^d$ framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a $(t,n)$-threshold architecture, a strategic choice that augments the protocol's practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.

Keywords: quantum secret sharing quantum product state threshold scheme unitary operations

Received: 21 December 2023
Revised: 04 March 2024
Accepted manuscript online: 15 March 2024

PACS:	03.67.-a	(Quantum information)
	03.65.Ud	(Entanglement and quantum nonlocality)

Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 12301590) and the Natural Science Foundation of Hebei Province (Grant No. A2022210002).

Corresponding Authors: Chen-Ming Bai
E-mail: baichm@stdu.edu.cn

Cite this article:

Chen-Ming Bai(白晨明), Lu Liu(刘璐), and Sujuan Zhang(张素娟) Verifiable quantum secret sharing scheme based on orthogonal product states 2024 Chin. Phys. B 33 070302

[1] Shamir A 1979 Commun. ACM 22 612
[2] Blakley G R 1979 In Proceedings of the 1979 International Workshop on Managing Requirements Knowledge (MARK), New York, NY, USA, 4-7 June 1979; Volume 48, pp. 313-317
[3] Hillery M, Buzek V and Berthiaume A 1999 Phys. Rev. A 59 1829
[4] Cleve R, Gottesman D and Lo H K 1999 Phys. Rev. Lett. 83 648
[5] Gottesman D 2000 Phys. Rev. A 61 042311
[6] Xiao L, Long G L, Deng F G and Pan J W 2004 Phys. Rev. A 69 052307
[7] Grice W P and Qi B 2019 Phys. Rev. A 100 022339
[8] Qin H W, Zhu X H and Dai Y W 2015 Quantum Inf. Process 14 2997
[9] Lipinska V, Murta G, Ribeiro J and Wehner S 2020 Phys. Rev. A 101 032332
[10] Gu J, Cao X Y, Yin H L, et al. 2021 Opt. Express 29 9165
[11] Mashhadi S 2022 Journal of Applied Security Research 17 123
[12] Li F, Chen T and Zhu S 2022 Physica A 606 128122
[13] Li F, Luo M, Zhu H, et al. 2023 Physica A 612 128494
[14] Li L and Li Z 2023 Entropy 25 265
[15] Xu J, Li X, Han Y, et al 2023 Frontiers in Physics 11 1213153
[16] Wang J, Li L, Peng H and Yang Y 2017 Phys. Rev. A 95 022320
[17] Tavakoli A, Herbauts I, Zukowski M and Bourennane M 2015 Phys. Rev. A 92 030302
[18] Qin H and Dai Y 2016 Information Processing Letters 116 351
[19] Bai C M, Zhang S and Liu L 2021 International Journal of Theoretical Physics 60 3993
[20] Liu S, Lu Z, Wang P, et al. 2023 npj Quantum Information 9 92
[21] Shen A, Cao X Y, Wang Y, et al. 2023 Science China Physics, Mechanics & Astronomy 66 260311
[22] Li C L, Fu Y, Liu W B, et al. 2023 Phys. Rev. Research 5 033077
[23] Gu J, Xie Y M, Liu W B, et al. 2021 Opt. Express 29 32244
[24] Guo G P and Guo G C 2003 Phys. Lett. A 310 247
[25] Hsu L Y, Li C M 2005 Phys. Rev. A 71 022321
[26] Yang Y G, Wen Q Y and Zhu F C 2007 Sci. China Ser. G 50 331
[27] Hu W, Zhou R G and Luo J 2022 Chin. J. Phys. 77 1701
[28] Xu G B, Wen Q Y, Gao F, Qin S J and Zuo H J 2017 Quantum Inf. Process 16 1
[29] Feng Y and Shi Y 2009 IEEE transactions on information theory 55 2799
[30] Xu G B, Wen Q Y, Qin S J, Yang Y H and Gao F 2016 Phys. Rev. A 93 032341
[31] Zhen X F, Fei S M and Zuo H J 2022 Phys. Rev. A 106 062432
[32] Long G L and Liu X S 2002 Phys. Rev. A 65 032302
[33] Li C Y, Zhou H Y, Wang Y and Deng F G 2005 Chin. Phys. Lett. 22 1049
[34] Walgate J and Hardy L 2002 Phys. Rev. Lett. 89 147901
[35] Li C Y, Li X H, Deng F G, et al. 2006 Chin. Phys. Lett. 23 2896
[36] Karimipour V, Asoudeh M, Gheorghiu V, Looi S Y and Griffiths R B 2015 Phys. Rev. A 92 030301

[1]	Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme Huan-Yao Jiang(姜欢窈), Min Nie(聂敏), Guang Yang(杨光), Ai-Jing Sun(孙爱晶), Mei-Ling Zhang(张美玲), and Chang-Xing Pei(裴昌幸). Chin. Phys. B, 2024, 33(7): 070303.
[2]	Cryptanalysis of efficient semi-quantum secret sharing protocol using single particles Gan Gao(高甘). Chin. Phys. B, 2024, 33(4): 040301.
[3]	An efficient multiparty quantum secret sharing scheme using a single qudit Wenwen Hu(胡文文), Bangshu Xiong(熊邦书), and Rigui Zhou(周日贵). Chin. Phys. B, 2023, 32(8): 080303.
[4]	Efficient semi-quantum secret sharing protocol using single particles Ding Xing(邢丁), Yifei Wang(王艺霏), Zhao Dou(窦钊), Jian Li(李剑),Xiubo Chen(陈秀波), and Lixiang Li(李丽香). Chin. Phys. B, 2023, 32(7): 070308.
[5]	Measurement-device-independent quantum secret sharing with hyper-encoding Xing-Xing Ju(居星星), Wei Zhong(钟伟), Yu-Bo Sheng(盛宇波), and Lan Zhou(周澜). Chin. Phys. B, 2022, 31(10): 100302.
[6]	Dynamic quantum secret sharing protocol based on two-particle transform of Bell states Yu-Tao Du(杜宇韬), Wan-Su Bao(鲍皖苏). Chin. Phys. B, 2018, 27(8): 080304.
[7]	Controlled unknown quantum operations on hybrid systems Yong He(何勇), Ming-Xing Luo(罗明星). Chin. Phys. B, 2016, 25(12): 120304.
[8]	Cryptanalysis and improvement of a quantum secret sharing scheme based on $\chi$-type entangled states Zhu Zhen-Chao(朱珍超), Zhang Yu-Qing(张玉清), and Fu An-Min(付安民) . Chin. Phys. B, 2012, 21(1): 010307.
[9]	Quantum secret sharing based on quantum error-correcting codes Zhang Zu-Rong (张祖荣), Liu Wei-Tao (刘伟涛), Li Cheng-Zu (李承祖). Chin. Phys. B, 2011, 20(5): 050309.
[10]	Efficient quantum secret sharing scheme with two-particle entangled states Zhu Zhen-Chao(朱珍超), Zhang Yu-Qing(张玉清), and Fu An-Min(付安民) . Chin. Phys. B, 2011, 20(4): 040306.
[11]	Three-party quantum secret sharing of secure direct communication based on $\chi$-type entangled states Yang Yu-Guang(杨宇光), Cao Wei-Feng(曹卫锋), and Wen Qiao-Yan(温巧燕). Chin. Phys. B, 2010, 19(5): 050306.
[12]	Quantum secret sharing protocol using modulated doubly entangled photons Wang Chuan(王川) and Zhang Yong(张勇). Chin. Phys. B, 2009, 18(8): 3238-3242.
[13]	Enhancing the security of quantum secret sharing against multiphoton attack Zhang Bin-Bin(张彬彬), Wang Da-Qing(王大庆), Huang Shan-Shan(黄珊珊), and Liu Yu(刘玉). Chin. Phys. B, 2009, 18(6): 2149-2153.
[14]	Participant attack on quantum secret sharing based on entanglement swapping Song Ting-Ting(宋婷婷), Zhang Jie(张劼), Gao Fei(高飞), Wen Qiao-Yan(温巧燕), and Zhu Fu-Chen(朱甫臣). Chin. Phys. B, 2009, 18(4): 1333-1337.
[15]	Proof of the insecurity of quantum secret sharing based on the Smolin bound entangled states Yu Ya-Fei(於亚飞) and Zhang Zhi-Ming(张智明). Chin. Phys. B, 2009, 18(4): 1342-1345.

[1]	ZHOU HAI-JUN (周海军), XU XIANG-YUAN (许祥源), HUANG WEN (黄雯), LI LIANG-QUAN (李良权), CHEN DIE-YAN (陈瓞延). STUDY OF HIGH-LYING EXCITED STATES OF RARE-EARTH ELEMENT Dy BY LASER RESONANCE IONIZATION SPECTROSCOPY[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 19 -26 .
[2]	ZHAN LI (詹黎), TU JIN-HONG (屠锦洪), GUO JIA-RONG (郭嘉荣). ANALYSIS OF THE GENERAL EFFECTS IN DOUBLE-GRATING DIFFRACTION-INTERFERENCE SYSTEM[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 27 -44 .
[3]	FAN WEI-JUN (范卫军), XIA JIAN-BAI (顾宗权), GU ZONG-QUAN (夏建白), LI GUO-HUA (李国华). FIRST-PRINCIPLE SELF-CONSISTENT PSEUDOPOTENTIAL CALCULATION OF THE ELECTRONIC STRUCTURES OF SHORT-PERIOD (GaAs)_m(AlAs)_n SUPERLATT1CES[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 45 -50 .
[4]	YE HONG-JUAN (叶红娟), HU CAN-MING (胡灿明), HUANG YE-XIAO (黄叶肖), LU XIAO-FENG (陆晓峰), WANG ZHI-TAO (王志涛), ZENG WEN-SHENG (曾文生), ZHANG GUANG-YIN (张光寅), YAN SHAO-LIN (阎少林). FAR-INFRARED AND INFRARED REFLECTIONS OF Tl₂Ba₂Ca₂Cu₃O₁₀ FILM[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 51 -56 .
[5]	SHEN BAO-GEN (沈保根), YANG LIN-YUAN (杨林原), GUO HUI-QUN (郭慧群). MAGNETIC PROPERTIES AND CRYSTALLIZATION OF THE RAPIDLY QUENCHED (Fe_1-xNd_x) _81.5B_18.5 ALLOYS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 57 -62 .
[6]	LIN WEI-ZHU (林位株), PENG WEN-JI (彭文基), QIU ZHI-REN (丘志仁), ZHOU XUE-CONG (周学聪), MO DANG (莫党). DYNAMICS OF CARRIER CAPTURE IN AlGaAs/GaAs MULTIPLE QUANTUM WELLS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 63 -68 .
[7]	DENG WEN-JI (邓文基), LIU YOU-YAN (刘有延), HUANG XIU-QING (黄秀清). ON THE LOCALIZATION OF ELECTRONIC STATES IN ONE-DIMENSIONAL QUASILATTICES[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 113 -122 .
[8]	FAN HONG-CHANG (范宏昌), ZHANG YI-TONG (张贻瞳), JIN XIN (金新), TONG HONG-WU (童红武), YAO XI-XIAN (姚希贤). THERMALLY ACTIVATED FLUX MOTION IN HIGH-T_c SUPERCONDUCTORS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 123 -129 .
[9]	JIN YING (金鹰), ZHANG SHU-LIN (张树霖), QIN GUO-GANG (秦国刚), FAN YONG-LIANG (樊永良), ZHOU GOU-LIANG (周国良), YU MING-REN (俞鸣人). RAMAN SCATTERING INTENSITIES OF FOLDED LONGITUDINAL ACOUSTIC PHONONS IN Ge_xSi_1-x/Si SUPERLATTICES[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 130 -137 .
[10]	WANG DA-CHUN (王大椿), DING XUN-LIANG (丁训良), YANG HUA (杨华), LUO PING-AN (罗平安). MASS ATTENUATION COEFFICIENTS FOR ELEMENTS MEASURED WITH CHARACTERISTIC X-RAYS FROM TARGETS EXCITED BY ENERGETIC PROTON[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 138 -148 .

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Verifiable quantum secret sharing scheme based on orthogonal product states

Cite this article:

Online attention