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EPJ Quantum Technology

Multiparty quantum key agreement based on GHZ states

Ya‐Xi Shu, Chen‐Ming Bai, Sujuan Zhang

Published Apr 22, 2025• 12 citations
Publisher

Abstract

This paper introduces the design process of a multiparty quantum key agreement protocol based on the Greenberger-Horne-Zeilinger state in detail. Building on the traditional circle-type quantum key agreement protocol, we introduce a star structure, which significantly improves the speed and efficiency of key agreement. To facilitate the reader’s understanding, we provide an example of a four participants quantum key agreement protocol. In the process of quantum state transmission, we perform operations using the Pauli matrix and the Hadamard matrix to ensure that the quantum state remains in one of the four basis states. This significantly enhances the security of the protocol. After rigorous security analysis, we find that the protocol can effectively resist intercept-resend attack, entangle-measure attack, collective attack, and dishonest participant attack. Under a collective attack, if the first particle is subjected to bit-flipping noise, then $p<0.2430$ only guarantees $r>0.2$ when $a=1$ . Additionally, we conduct a fairness analysis and evaluate the practical performance of the proposed protocol. In an ideal depolarization noise-free environment, the protocol can achieve a positive key rate only when the global detection efficiency exceeds 0.9636. Finally, we conduct a comprehensive comparative analysis of the protocols. The results show that our proposed protocol is superior to other existing schemes in terms of efficiency and running time.

DOI
10.1140/epjqt/s40507-025-00353-2

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This paper introduces the design process of a multiparty quantum key agreement protocol based on the Greenberger-Horne-Zeilinger state in detail. Building on the traditional circle-type quantum key agreement protocol, we introduce a star structure, which significantly improves the speed and efficiency of key agreement. To facilitate the reader’s understanding, we provide an example of a four participants quantum key agreement protocol. In the process of quantum state transmission, we perform operations using the Pauli matrix and the Hadamard matrix to ensure that the quantum state remains in one of the four basis states. This significantly enhances the security of the protocol. After rigorous security analysis, we find that the protocol can effectively resist intercept-resend attack, entangle-measure attack, collective attack, and dishonest participant attack. Under a collective attack, if the first particle is subjected to bit-flipping noise, then p<0.2430p<0.2430p<0.2430 only guarantees r>0.2r>0.2r>0.2 when a=1a=1a=1 . Additionally, we conduct a fairness analysis and evaluate the practical performance of the proposed protocol. In an ideal depolarization noise-free environment, the protocol can achieve a positive key rate only when the global detection efficiency exceeds 0.9636. Finally, we conduct a comprehensive comparative analysis of the protocols. The results show that our proposed protocol is superior to other existing schemes in terms of efficiency and running time.
Abstract In this paper, on the design process of a multiparty quantum key agreement protocol within a ‐dimensional Hilbert space is elaborated upon. A circular‐type multiparty quantum key agreement protocol based on the generalized Bell state is introduced. To enhance security against external attacks, decoy states into the transmission process is incorporated. Transmission sequences of the generalized Bell state and decoy states are passed between participants. The participants then encode their secret information into the corresponding particles. Ultimately, all participants are able to derive the same key. In addition, a combination of ‐dimensional Pauli operators is utilized, making the proposed protocol feasible with current technology. Analysis and protection against intercept‐resend attack, entangle‐measure attack and dishonest participants attacks, demonstrating the feasibility of the protocol in a ‐dimensional Hilbert space. The protocol has certain advantages over other protocols in terms of a comprehensive consideration of security and efficiency.
As a burgeoning branch of quantum cryptography, quantum key agreement is a kind of key establishing processes where the security and fairness of the established common key should be guaranteed simultaneously. However, the difficulty on designing a qualified quantum key agreement protocol increases significantly with the increase of the number of the involved participants. Thus far, only few of the existing multiparty quantum key agreement (MQKA) protocols can really achieve security and fairness. Nevertheless, these qualified MQKA protocols are either too inefficient or too impractical. In this paper, an MQKA protocol is proposed with single photons in travelling mode. Since only one eavesdropping detection is needed in the proposed protocol, the qubit efficiency and measurement efficiency of it are higher than those of the existing ones in theory. Compared with the protocols which make use of the entangled states or multi-particle measurements, the proposed protocol is more feasible with the current technologies. Security and fairness analysis shows that the proposed protocol is not only immune to the attacks from external eavesdroppers, but also free from the attacks from internal betrayers.
Recently, Chen et al. (DOI 10.1109/SMC.2015. 281) proposed a multiparty quantum key agreement protocol based on Greenberger-Horne-Zeilinger (GHZ) state. They claimed that their protocol can achieve both the security property and the fairness property. However, this study points out that Chen et al.'s protocol cannot achieve the fairness property by an Internal Attack. That is, one of the involved participant (Alice) can determine the final key alone without being detected by other participants.
In this paper, we discuss in some detail how multiparty quantum key agreement protocols must be carefully designed and present a collusion attack to illustrate this point. Then, a secure circle-type multiparty quantum key agreement with Bell states is proposed. Bell states are used as the information carriers and transmitted among the participants, who embed their secrets into the traveling particles via certain encoding operations. In this way, all participants simultaneously obtain the same agreement key, i.e., the sum of their secret inputs, at the end of the protocol. Here, quantum state discrimination is utilized to design the encoding operations, which ensures that the proposed protocol is correct and secure against the presented collusion attack. Furthermore, it is shown that the proposed protocol satisfies three conditions of a secure quantum key agreement protocol in theory. In addition, these encoding operations consist of some common single-qubit gates, the Hadamard operator and four Pauli operators, which makes the proposed protocol feasible using current technology.
Abstract:In order to solve the problem that the multi-particle joint measurements are difficult to implement with the existing technology in the quantum key agreement protocols based on multi-particle entangled states , a new two-party quantum key agreement protocol was proposed based on three-particle GHZ states. Two participants in the protocol could fairly establish a shared secret key by using the measurement correlation property of three-particle GHZ states and the delayed measurement technique. Since the new protocol only used Bell measurements and single particle measurements, it was easy to achieve on the basis of the existing technology. The security analysis showed that the protocol could not only resist against participant attacks and outsider attacks, but also resist against two kinds of Trojan horse attacks. The protocol was secure not only in the noise-free quantum channel but also in the quantum noise channel. Finally, the comparison with the existed secure two-party protocols showed that the protocol also achieved higher qubit efficiency.
Abstract In this paper, we study the properties of a set of quantum states. Based on these properties, we propose a multiparty semi-quantum key agreement (MSQKA) protocol. For the sake of clarity, we provide a three-party example to illustrate the protocol. Through rigorous security analysis, it is demonstrated that the proposed protocol can resist both inside attacks and outside attacks, which include Trojan horse attacks, measure-resend attacks, entangle-measure attacks and collective attacks. Besides, the proposed protocol achieves fairness among participants. Finally, we compare our protocol with other SQKA protocols. Compared to previous three-party and MSQKA protocols, our proposed protocol involves more classical parties, needs no external assistance and achieves relatively high key generation efficiency.