Quantum cryptography is a new research field emerging from the combination of cryptography and quantum mechanics. Furthermore, the basic principles of quantum mechanics guarantee its security, such as Heisenberg's inaccuracy principle and the unclonability principle which are different from classical ciphers. Therefore, quantum cryptography is theoretically capable of achieving unconditional security. Recently, with the continuous development of quantum cryptography, its related research has received wide attention. Meanwhile, the quantum key agreement is an important branch of quantum cryptography and a quantum channel-based security protocol that calls for a secure shared key able to be negotiated between participants and does not allow any part of the participants to control the generation of this key. Unlike classical key agreement protocols relying on mathematical hard problems to guarantee security, the security of quantum key agreement protocols is guaranteed by the basic principles of quantum mechanics and can achieve unconditional security, thus better meeting practical needs. However, general quantum key agreement protocols can only satisfy the cases where all participants have full quantum capabilities. Thus, semi-quantum key agreements have been proposed by scholars, which means that one participant in the protocol has full quantum capability while the other participants have only semi-quantum capability. In this case, some of the large institutions or companies are treated as entities with full quantum capabilities, while some ordinary users are treated as entities with semi-quantum capabilities who only need to employ the Z-base 0,1 for quantum state preparation or measurement. However, there are still few studies on multi-party semi-quantum key agreement protocols, with cases of reliance on trusted third parties or low efficiency of quantum bits. Therefore, the multi-party semi-quantum key agreement protocol is significant to be studied.

We design a new four-party semi-quantum key protocol based on a four-particle cluster state. Furthermore, the secure shared key in this protocol is established by one full-quantum party of Dave, and three semi-quantum parties including Alice, Bob, and Charlie through measurement-resend operations and the entanglement properties of the four-particle cluster state, without the assistance of a trusted third party. The four-particle cluster state is a particular sort of four-particle entangled state whose entanglement properties are adopted in the key agreement and eavesdropping detection parts of the protocol. In this protocol, the measurement-resend operation is performed several times. Finally, since CTRL particles that are normally discarded in a previous protocol can be employed again, the quantum resource waste is reduced. In terms of security, the protocol is proven to be effective against internal attacks and all external attacks. Additionally, two optical devices, the wavelength quantum filter (WQF), and the photon number separator (PNS) are introduced in the protocol, which allows both Trojan horse attacks to be effectively defended against. In terms of qubit efficiency, the protocol performance is measured by Cabello qubit efficiency.

Firstly, general quantum key agreement protocols can achieve the purpose of shared keys securely established between participants. However, in the existing quantum key agreement protocols, participants are required to have excessive capabilities and equipment. Therefore, we put forward a new four-party semi-quantum key negotiation protocol based on a four-particle cluster state. The three semi-quantum participants of Alice, Bob, and Charlie, and one participant Dave with full quantum capability in this protocol can perform key negotiation without any third party. As a consequence, the requirements for participant capacity and equipment in this protocol are reduced. The four-particle cluster state is utilized in the protocol for key agreement and eavesdropping detection. Secondly, the measurement-resend operation is leveraged in the protocol, which means that the particle is randomly executed with a CTRL or SIFT operation. In this case, the CTRL operation means that the particle is subjected to a reflection operation, the SIFT operation means that the particle is subjected to a Z-base measurement with the preparation of a new particle, and finally the newly prepared particle is resent. Furthermore, the measurement-resend operation is performed twice in the protocol to make the CTRL particles normally discarded in the previous protocol can be reused, Therefore, the quantum resource waste is reduced. Thirdly, the protocol is verified to be effective against both external and internal attacks through security analysis. Meanwhile, the protocol shows superior performance through performance analysis.

Our paper proposes a four-party semi-quantum key agreement protocol based on a four-particle cluster state. In this protocol, no assistance from trusted third parties is required to ensure that a secure shared key is established by negotiation between a full quantum party and three semi-quantum parties and that the contributions of each party to the shared key are equal. Analysis indicates that internal attacks and all external attacks can be effectively defended by the new semi-quantum key agreement protocol. The final comparison results show that the proposed semi-quantum key agreement protocol can improve performance and save quantum resources simultaneously.