Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (5): 89-95.DOI: 10.3778/j.issn.1002-8331.1712-0182

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(t,n) Threshold Quantum Secret Sharing Based on d-Dimensional Multi-Particle Entanglement State

SONG Xiuli1,2, XU Jiankun1,2   

  1. 1.College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
    2.Chongqing Key Laboratory of Network Information Security Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
  • Online:2019-03-01 Published:2019-03-06



  1. 1.重庆邮电大学 计算机科学与技术学院,重庆 400065
    2.重庆邮电大学 网络信息安全技术重庆市重点工程实验室,重庆 400065

Abstract: In order to overcome the limitation on 2-dimension of Hilbert space, and solve the problem that some participants cannot attend reconstructing process of the shared secret, a (t, n) threshold quantum secret sharing scheme is proposed by using maximally d-dimensional multi-particle entanglement state. The dealer prepares n d-dimensional 2-particle entangled pairs and distributes the 2nd particle to n participants respectively. When the dealer chooses t particles in his hand for joint projection measurement, the entanglement swapping causes the corresponding t particles in participants’ hands to collapse into a t-particle entangled state. These t participants add their share to the t-particle entangled state through QFT transformation and Pauli operation. Eventually, the shared secret is recovered by these t participants. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack.

Key words: threshold quantum secret sharing, d-dimensional multi-particle entanglement state, entanglement swapping, joint projection measurement

摘要: 为了突破Hilbert空间2维度的局限性,解决秘密重建过程中部分参与者缺席的问题,使用[d]维多粒子纠缠态,提出了一个[(t,n)]门限量子秘密共享方案。秘密分发者制备[n]个[d]维2粒子纠缠对,将第2个粒子分别分发给[n]个参与者。当秘密分发者选择自己手中[t]个粒子进行联合投影测量时,纠缠交换使得参与者手中的对应[t]个粒子坍塌成一个[t]粒子纠缠态。这[t]个参与者通过QFT变换和Pauli运算将份额加入[t]粒子纠缠态。最终,共享的秘密由这[t]个参与者一起合作恢复。安全性分析表明,该方案能抵抗截获-测量-重发攻击、纠缠-测量攻击、合谋攻击和伪造攻击。

关键词: 门限量子秘密共享, [d]维多粒子纠缠态, 纠缠交换, 联合投影测量