A Quantum Group Signature Based on Quantum Walk in d Dimensions

In this paper, a group signature scheme based on quantum walk for quantum messages is proposed. Our scheme uses long step quantum walk-based teleportation and modified quantum one-time pad to authenticate the quantum messages respectively. In our scheme, the signer in a group signs the quantum messages by quantum walk-based teleportation and modified quantum one-time pad. The verifier can verify the signature via quantum walk-based teleportation while the group manager verifies the signature and identifies the signer via modified quantum one-time pad. The security analysis shows that the scheme can reach the properties of group signature. Compared to the teleportation via EPR pairs or Bell-like states, quantum walks are more flexible and use less measurement resources. Quantum teleportation via long-step quantum walk is more secure than that via one-step quantum walk in previous related works. The scheme can apply to arbitrary finite dimensional quantum systems and can also be possible to realize in practice.