With the continuous development of quantum calculations, the classic cryptosystem that relies on mathematical difficulties and computational complexity to ensure security is constantly under threat. Therefore, in recent years, a large number of scholars have attracted attention from the quantum cryptography produced by the combination of cryptography and quantum mechanics. At present, quantum cryptography has many branches, such as quantum key distribution, quantum key agreement, quantum secure sharing, quantum secure direct communication, and deterministic secure quantum communication. Among them, quantum key agreement is an important branch of quantum cryptography. In real life, quantum key agreement is widely used in scenarios such as end-to-end communication and internet of things. Although, in the current quantum key agreement protocol, a secure shared key can be established between legal participants. However, participants in the quantum key agreement protocol are required to have high capabilities and equipment. But, the quantum equipment is still too expensive even in relatively rich future material conditions. In order to cope with this situation, the semi-quantum key agreement protocol is proposed by scholars. It allows one or more participants in the protocol to only have simple quantum capabilities, that is, to use the Z basis (|0〉, |1〉) for preparation and measurement. Therefore, the protocol reduces the requirements for participant capabilities and equipment. In addition, research on semi-quantum key agreement is relatively small. Therefore, the semi-quantum key agreement needs to be studied by scholars.

In this paper, a new two-party semi-quantum key agreement protocol is designed based on the G-like state. The securely shared key in the protocol is established by the two classical parties, Alice and Bob, through the measurement-resending operation and the entanglement characteristics of the G-like state with the assistance of a trusted third party with full quantum capabilities, Charlie, and the contributions of both parties are equal. The shared key cannot be determined by any participants alone. The G-like state is a special three-particle entangled state, and its entanglement properties are used in the key agreement and eavesdropping detection part of the protocol. For example, the measurement result of the counterpart can be inferred by the participant through the entanglement properties of his own initial quantum state and the G-like state. And the measurement-resending operation means that the particles are randomly executed the CTRL and SIFT operations. Among them, the CTRL operation means that the particles are only executed to reflection operations, and the SIFT operation means that the particles are executed to the Z basic measurement and a new particle is prepared. Finally, the newly prepared particles are resent. In this protocol, the measurement-resending operation is performed twice by us. Therefore, the CTRL particles usually discarded in the previous protocol can be reused and the waste of quantum resources is reduced. In terms of security, the security of the protocol is guaranteed by the entanglement characteristics of the G-like state. In addition, two optical devices, wavelength quantum filter (WQF) and photon number separator (PNS), have been introduced, so that the protocol can also resist two Trojan horse attacks. In terms of qubit efficiency, the performance of the protocol is measured by Cabello qubit efficiency.

Although most of the quantum key agreement protocols have been proposed to enable the secure keys to be established between participants. But all participants in these protocols are required to have full quantum capabilities. However, quantum devices are relatively expensive and difficult to carry. Therefore, the semi-quantum key agreement protocol is proposed to solve this problem. A trusted third party with full quantum capabilities is introduced, and thus the two-party semi-quantum key agreement protocol can be realized. The trusted third party can be used to prepare the G-like state required for this protocol. At the same time, it can also perform eavesdropping detection jointly with all participants. This ensures that the external attacks can be well resisted by the protocol, and in addition, the participant attacks can also be well resisted by the protocol. Since the quantum state in this protocol has been transmitted for many times, the attacker can eavesdrop on the information related to the shared key through a Trojan horse attack. Therefore, two optical devices, the wavelength quantum filter and the photon number separator, are introduced by us. Among them, the invisible photons can be filtered out by the wavelength quantum filter, and the delayed photons can be detected by the photon number separator. This ensures that the protocol can also resist two types of Trojan attacks. In terms of performance, Cabello qubit efficiency is used to measure the performance of the protocol. At present, this method is mainly used to evaluate the performance of the quantum key agreement protocol. The qubit efficiency of the semi-quantum key agreement protocol is generally low. But this kind of agreement has low requirements for participants. Therefore, the semi-quantum key agreement protocol is more suitable for our current situation.

In this paper, a two-party semi-quantum key agreement protocol based on G-like state is proposed. A securely shared key can be established by two semi-quantum parties with the assistance of a trusted third party. In terms of security, participant attacks and external attacks can be well resisted. In addition, the protocol also has an advantage in performance.