A Three-Party Lightweight Quantum Key Distribution Protocol in a Restricted Quantum Environment

Abstract: This study proposes a new lightweight quantum key distribution (LQKD) protocol based on the four-particle cluster state within a quantum-restricted environment. The protocol enables a quantum-capable user to simultaneously establish two separate secret keys with two "classical" users, who are limited to performing only the Hadamard operation and measurements in the $Z$ basis. By adopting a one-way qubit transmission approach, the proposed protocol addresses several limitations of existing semi-quantum key distribution (SQKD) schemes that rely on two-way or circular transmission methods: (1) it eliminates the need for classical participants to be equipped with costly quantum devices to defend against quantum Trojan horse attacks; (2) it reduces the qubit transmission distance; and (3) it achieves higher qubit efficiency. Consequently, the proposed three-party LQKD protocol is both more lightweight and practical than existing SQKD protocols. Furthermore, the security analysis shows that, in the ideal case, the protocol achieves the same level of security as fully quantum protocols. Finally, the study proves the unconditional security of the protocol in the non-ideal case, demonstrating a noise tolerance close to that of the BB84 protocol.