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量子秘密共享是一种通过使用量子力学的基本原理,实现在多个参与者之间安全分配和重建秘密信息的密码学协议.本文提出了一种可验证的多方量子秘密共享协议,该协议中存在一个具有验证能力的秘密分发者和多个接收方.在协议执行过程中,秘密分发者会通过设定的编码规则将欲共享的信息用对应的正交乘积态表示,并将量子态进行分割发送给各个接收方,只有各接收方共同合作才能最终恢复初始秘密信息.同时,考虑到在协议过程中可能存在参与者人数变化的情况,加入了人员动态变化操作.通过对协议的安全性分析,证明了该协议可以抵抗常见的内部和外部攻击.我们希望该思想能够对量子秘密共享的进一步研究产生积极的影响.Quantum secret sharing (QSS) is a cryptographic protocol that realizes secure distribution and reconstruction of secret information among multiple participants by leveraging fundamental principles of quantum mechanics. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications, entangled state preparation is constrained by short quantum coherence time, low state fidelity, etc., making it difficult to implement entangled resource-dependent QSS protocols. This paper proposes a novel practical and verifiable multi-party QSS protocol based on orthogonal product states, which are easier to prepare than entangled states. In the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into corresponding orthogonal product states according to encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD) to hide initial quantum sequence information through subsequent particle transformation operations. After preparing orthogonal product states, the distributor reorganizes particles by position—extracting particles at the same position from each state to form new sequences, scrambling their order—then applies Hadamard transformations with the pre-shared key, inserts decoy particles, and sends sequences to participants. Upon receipt, participants conduct eavesdropping detection, use the same key for inverse transformations, retain one particle from each sequence, and pass remaining particles sequentially until the last participant receives a complete set, triggering state verification with the distributor as arbiter. If verified, particles are returned to the first participant for a return stage with similar procedures. Only after both transmission and return stage verifications pass will the distributor reveal initial particle positions, allowing participants to collaboratively reconstruct the secret.In the protocol, the secret distributor acts as an arbitrator to verify with participants at periodic nodes (the end of the transmission stage and the end of the return stage) to determine whether the particle state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering the possible change in the number of participants during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, it is proven that our protocol can safely resist the existing common attack methods. Using Qiskit simulation experiments, we have successfully modeled the core quantum procedures of the protocol. The experimental results provide significant computational validation for the theoretical feasibility of the protocol.
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Keywords:
- quantum secret sharing /
- verifiable /
- orthogonal product state /
- dynamic change
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[1] Hellman M, Diffie W 1976 IEEE Trans. Inf. Theory 22644
[2] Fujisaki E, Okamoto T 1999 Annual international cryptology conference Santa Barbara, California, USA, August 15-19, 1999 p537
[3] Bellare M, Desai A, Jokipii E, Rogaway P 1997 Proceedings 38th Annual Symposium on Foundations of Computer Science Miami Beach, FL, USA, October 20-22, 1997 p394
[4] Feistel H 1973 Sci. Amer. 22815
[5] Shor P W 1999 SIAM Rev. 41303
[6] Grover L K 1996 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing Philadelphia, Pennsylvania, May 22-24,1996 p212
[7] Bennett C H, Brassard G 1984 Proc. Workshop on the theory and application of cryptographic techniques Santa Barbara, California, USA, August 19-22, 1984 p475
[8] Feng F Y, Zhang Q 2007 Acta Phys. Sin. 041924(in Chinese) [冯发勇, 张强2007物理学报041924]
[9] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 43054
[10] Wang T Y, Wen Q Y 2011 Chin. Phys. B 20040307
[11] Jiang S X, Zhao B, Liang X Z 2021 Chin. Phys. B 30060303
[12] Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68042317
[13] Zhao N, Jiang Y H, Zhou X T 2022 Acta Phys. Sin. 7136(in Chinese) [赵宁, 江英华, 周贤韬2022物理学报7136]
[14] Deng F G, Zhou H Y, Long G L 2006 J. Phys. A: Math. Gen. 3914089
[15] Sun Y, Du J Z, Qin S J, Wen Q Y, Zhu F C 2008 Acta Phys. Sin. 084689(in Chinese) [孙莹, 杜建忠, 秦素娟, 温巧燕, 朱甫臣2008物理学报084689]
[16] Dai Y W, Qin H Y 2015 Chinese Phys. Lett. 32100301
[17] Hillery M, Buzek V, Berthiaume A 1999 Phys. Rev. A 591829
[18] Karlsson A, Koashi M, Imoto N 1999 Phys. Rev. A 59162
[19] Xiao L, Lu Long G, Deng F G, Pan J W 2004 Phys. Rev. A 69052307
[20] Yang Y, Wen Q, Zhu F 2007 Sci. China Ser. G-Phys. Mech. Astron. 50331
[21] Wang T Y, Wen Q Y, Chen X B, Guo F Z, Zhu F C 2008 Opt. Commun. 2816130
[22] Wang C, Zhang Y 2009 Chin. Phys. B 183238
[23] Jia H Y, Wen Q Y, Gao F, Qin S J, Guo F Z 2012 Phys. Lett. A 3761035
[24] Hsu J L, Chong S K, Hwang T, Tsai C W 2013 Quantum Inf. Process. 12331
[25] Du Y T, Bao W S 2018 Chin. Phys. B 27080304
[26] Yang C W, Tsai C W 2020 Quantum Inf. Process. 191
[27] Hu W, Zhou R G, Li X, Fan P, Tan C 2021 Quantum Inf. Process. 201
[28] Tian Y, Wang J, Bian G, Chang J, Li J 2024 Adv. Quantum Technol. 72400116
[29] Lin J, Chen C C, Huang C Y 2024 Physica A 638129615
[30] Yu S, Oh C H 2015 arXiv:1502.01274[quant-ph]
[31] Guo G P, Li C F, Shi B S, Li J, Guo G C 2001 Phys. Rev. A 64042301
[32] Jiang D H, Wang J, Liang X Q, Xu G B, Qi H F 2020 Int. J. Theor. Phys. 59436
[33] Jiang D H, Hu Q Z, Liang X Q, Xu G B 2020 Int. J. Theor. Phys. 591442
[34] Walgate J, Hardy L 2002 Phys. Rev. Lett. 89147901
[35] Xu G B, Wen Q Y, Qin S J, Yang Y H, Gao F 2016 Phys. Rev. A 93032341
[36] Feng Y, Shi Y 2009 IEEE Trans. Inf. Theory 552799
[37] Deng F G, Li X H, Zhou H Y, Zhang Z J 2005 Phys. Rev. A 72044302
[38] Li X H, Deng F G, Zhou H Y 2006 Phys. Rev. A 74054302
[39] Cabello A 2000 Phys. Rev. Lett. 855635
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