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