基于d维多粒子纠缠态的(t,n)门限量子秘密共享

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

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。

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.