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Due to the influence of external environment and internal factors, the security of quantum dialogue is facing huge challenges. In order to improve the security of quantum dialogue, we proposed the feasible and efficient quantum dialogue protocol with hyperentangled states in discrete-time quantum walk. In the proposed protocol, the trusted third party and both communicating parties entangle themselves via GHZ states and distribute their secret keys. The communicating party(Alice) prepares and signs her message and obtains an entangled quantum set of message and signature. And the other communicating party(Bob) verifies Alice's signature with the the trusted third party's help. Then, Alice and Bob perform a discrete-time quantum walk in the network until they meet at a node. Meanwhile, Alice and Bob have a quantum dialogue at the node where they meet. We provide detailed security analysis of the proposed protocol. Security analysis of the proposed protocol against both inside and outside attacks proves that attackers cannot extract any secret information. [ABSTRACT FROM AUTHOR]