Dynamic hierarchical quantum secret sharing protocol based on high-dimensional GHZ state

Quantum secret sharing is an important research branch of quantum cryptography. A novel dynamic hierarchical quantum secret sharing protocol based on high-dimensional GHZ (Greenberger-Horne-Zeilinger) state was proposed. In the presented protocol, participants were divided into multiple layers, with the number of participants and the shared secret in each layer being allowed to differ. Based on the entanglement characteristics between particles in high-dimensional GHZ states, all participants at the same layer could cooperate to recover the secret of the current layer by performing local measurements. Moreover, each participant was able to obtain the shared secrets at lower layers, but not those at higher layers. In addition to the realization of the hierarchical structure, the proposed protocol also allowed each layer to dynamically add or delete multiple participants without changing the shares held by original participants, which provided better flexibility and generality. The correctness of the proposed protocol was verified through mathematical proof. In addition, security analysis results showed that the proposed protocol could resist intercept-and-resend attack, measure-and-resend attack, entangle-and-measure attack, Trojan horse attack, as well as collusion attacks from internal participants.