Multi-party Quantum Key Agreement Protocol Research Articles

Quantum Key Agreement Protocol Based on Quantum Search Algorithm

Quantum key agreement (QKA) and quantum search algorithm (QSA) are two important branches in quantum topic. The former asks all participants to negotiate the agreement key equally, and none of them can fully determine the agreement key. The latter is used to provide an acceleration in searching the marked item in an unsorted database. To date, several QKA schemes based on either BB84 or entangled states have been proposed, the QKA protocol based on QSA is rare, only exists one multi-party QKA (MQKA) protocol based on QSA. In this paper, on the basis of the properties of Grover’s QSA, the first two-party quantum key agreement protocol based on quantum search algorithm known as Grover’s algorithm is proposed. The participants transmit a two-particle quantum state sequence directly by inserting decoy photons randomly. The initial-prepared two-particle quantum states are easy to be prepared with current technology. Moreover, there is no swapping entanglement technology used in this protocol, it only needs unitary operations and single-particle measurements. Compared with the existing two-party QKA protocol, the proposed QKA protocol is more efficient. In addition, the security analysis shows that the proposed protocol is secure against both external attacks and internal ones. Finally, the proposed protocol is generated to MQKA protocol based on quantum search algorithm.

Novel multi-party quantum key agreement protocols under collective noise

Based on the logic Bell states, we present two novel multi-party quantum key agreement (QKA) protocols under collective noise. The proposed protocols make full use of four-qubit logic Bell states as quantum resources and perform the novel encoding operation to generate the shared key. The security analysis shows that these two protocols can resist against both participant and outsider attacks. Furthermore, compared with the other existing multi-party QKA protocols over collective noise, our protocols have higher qubit efficiency. Finally, we perform the simulation of the relationship between efficiency and security, which is completely consistent with the conclusion of the security analysis of the protocols.

Collusion Attack and Counterattack on the Quantum Key Agreement Via Non-maximally Entangled Cluster States

Recently, Li et al. (Int J Theor Phys: DOI: 10.1007/s10773-020-04588-w, 2020) proposed a multiparty quantum key agreement protocol via non-maximally entangled cluster states. They claimed that the proposed protocol can help all the involved participants have equal influence on the final shared key. However, this study points out a loophole that makes Li et al.'s protocol suffer from a collusion attack, i.e. several dishonest participants can conspire to manipulate the final shared key without being detected by others. To avoid this loophole, an improvement is proposed here.

An efficient circle-type multiparty quantum key agreement protocol with single particles

An efficient circle-type multiparty quantum key agreement protocol utilizing two non-orthogonal bases single particles is proposed. In our protocol, each participant performs one of two simple unitary operations to encode and additional unitary operations to protect his privacy. Both outside attacks and participant attacks can be perfectly resisted. Moreover, our protocol has a high efficiency up to [Formula: see text], where [Formula: see text] is the number of the participants, and it can be easily implemented with current quantum technologies as it needs only single particle measurements.

Improvements on “Multi-party Quantum Key Agreement Protocol with Bell States and Single Particles”

Liu et al. (Int. J. Theor. Phys. 58(5), 1659–1666 2019) proposed a multi-party quantum key agreement protocol with Bell states and single particles. They claimed that their protocol can resist the participant and outside attacks. However, we found that their protocol does not provide the fairness property and cannot resist collusion attacks. The last involved participant in Part P can conspire with anyone of the participants in Part Q to manipulate the final shared key without being detected. Moreover, two improved protocols depending on different strategies are proposed, in which the security and the fairness are both enhanced.

Multi-party quantum key agreement based on <i>d</i>-level GHZ states

A multi-party quantum key agreement protocol based on <i>d</i>-level multi-particle GHZ states is proposed. The “<i>d</i>-level” is common in other quantum cryptographic protocols, but there are few researches in the field of quantum key agreement. In our scheme, we introduce two indistinguishable orthogonal bases, i.e. the quantum Fourier transform and shift operation, into a <i>d</i>-level quantum system. In addition, we make full use of shift operation to encode the key into the sequence of quantum states, and the key can be measured by the <i>d</i>-level <i>Z</i>-basis. By decoding and calculating, each participant can equally extract other participants’ key and obtain the final shared key <inline-formula><tex-math id="M1">\begin{document}$ K = {K_0} \oplus {K_1} \oplus \cdots \oplus {K_{k - 1}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20200799_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20200799_M1.png"/></alternatives></inline-formula>. The protocol resists external eavesdropping by inserting decoy states and conducting two security checks. Furthermore, we present an example by assigning certain values to parameters for illustrative purpose. Finally, QKA protocol mainly involves two types of attacks: participant attack and external attack. The external attack can be divided into Trojan attack, intercept-resend attack, and entangle-measure attack. To demonstrate the security of the scheme, we analyze the two types of attacks. The results show that the scheme can effectively resist the attack from internal participants and external eavesdroppers. However, the premise of our protocol is based on the ideal quantum channel. In practical applications, particles are usually affected by noise in the process of quantum channel transmission. Therefore, how the agreement adapts itself to a more complicated environment is our main work in the future.

New quantum key agreement protocol with five-qubit Brown states

We propose a new two-party quantum key agreement (QKA) protocol using five-qubit Brown states. One-way quantum transmission can be realized by merging Brown states and decoy photons randomly. The security of this protocol is shown to resist the outsider attack and participant attack over the ideal channel. Some methods are also proposed to ensure its security in noisy and lossy quantum channel. Finally, we generalize it and propose a multi-party QKA protocol based on Brown states.

New Fair Multiparty Quantum Key Agreement Secure against Collusive Attacks

Fairness is an important standard needed to be considered in a secure quantum key agreement (QKA) protocol. However, it found that most of the quantum key agreement protocols in the travelling model are not fair, i.e., some of the dishonest participants can collaborate to predetermine the final key without being detected. Thus, how to construct a fair and secure key agreement protocol has obtained much attention. In this paper, a new fair multiparty QKA protocol that can resist the collusive attack is proposed. More specifically, we show that in a client-server scenario, it is possible for the clients to share a key and reveal nothing about what key has been agreed upon to the server. The server prepares quantum states for clients to encode messages to avoid the participants’ collusive attack. This construction improves on previous work, which requires either preparing multiple quantum resources by clients or two-way quantum communication. It is proven that the protocol does not reveal to any eavesdropper, including the server, what key has been agreed upon, and the dishonest participants can be prevented from collaborating to predetermine the final key.

Efficient travelling-mode quantum key agreement against participant\u2019s attacks

Quantum key agreement (QKA) is to negotiate a final key among several participants fairly and securely. In this paper, we show that some existing travelling-mode multiparty QKA protocols are vulnerable to internal participant’s attacks. Dishonest participants can exploit a favorable geographical location or collude with other participants to predetermine the final keys without being discovered. To resist such attacks, we propose a new travelling-mode multiparty QKA protocol based on non-orthogonal Bell states. Theoretical analysis shows that the proposed protocol is secure against both external and internal attacks, and can achieve higher efficiency compared with existing travelling-mode multiparty QKA protocols. Finally we design an optical platform for each participant, and show that our proposed protocol is feasible with current technologies.

Multi-party quantum key agreement with four-qubit cluster states

Based on four-qubit cluster states, we present a new multi-party quantum key agreement (QKA) protocol. The proposed protocol makes full use of four-qubit cluster states as quantum resources and performs the X operation to generate a shared key. In addition, our multi-party QKA protocol ensures each participant to contribute equally to the final key. Compared with other existed multi-party QKA protocols, our protocol has high efficiency. Furthermore, the security analysis shows that our protocol can resist the outsider and participant attacks.

Multi-Party Quantum Key Agreement Protocol with Bell States and Single Particles

Liu et al. [Quantum Inf. Process. 12, 1797–1805 (2013)] proposed a multi-party quantum key agreement (QKA) protocol based on single particles. Their protocol can resist outsider and participant attacks. However, its qubit efficiency is low. Min et al. [Int. J. Theor. Phys. 57, 1811–1822 (2018)] put forward a multi-party QKA protocol by using G-Like states and Bell states, which has high qubit efficiency, but it cannot resist the participant attack. In this paper, combining the advantages of the two protocols, we present a multi-party QKA protocol with Bell states and single particles. The protocol can guarantee that each party has an equal opportunity to influence the final shared key and no one can determine the final key alone. Furthermore, the efficiency analysis shows that our multi-party QKA protocol is very efficient.

Efficient Multiparty Quantum Key Agreement With a Single $d$ -Level Quantum System Secure Against Collusive Attack

Recently, multiparty quantum key agreement (MQKA) protocols have gained increasing attention. Several MQKA protocols in the traveling mode have been proposed for higher key generation rates, which, however, are vulnerable to a collusive attack presented by Liu. In this paper, an analysis of Liu's collusive attacks on Cao et al.'s protocol is given, based on which an efficient MQKA protocol that requires only sequential communication of a single d-level quantum system is put forward. Because of the single d-level quantum system, our protocol has huge advantages in scalability and can be realized with the state-of-the-art technology. The scalability means that each additional participant is only required to perform a unitary operator that is comparatively simple, and the complexity of measurements remains independent of the number of participants. Our protocol can also resist Liu's collusive attacks due to the encrypted quantum channel and has an efficiency rate of 1/2N(N is the number of participants) that is much better than those of other quantum key agreement protocols. In addition, by using the proposed encoding method, a wide class of problems for which quantum information protocols based on multisystem entanglement can be mapped into much simpler ones involving only one system.

Multiparty Quantum Key Agreement Based on Three-Photon Entanglement with Unidirectional Qubit Transmission

A multiparty quantum key agreement protocol based on three-photon entangled states is proposed. In this scheme, the quantum channel between all parties is that of a closed loop, in which the qubit transmission is one-way. Each party can obtain the sum of the other parties’ secret key values through the coding rules instead of extracting their private keys. The shared secret key cannot be determined by any subset of all the participants except the universal set and each party makes an equal contribution to the final key. Moreover, the security analysis shows our protocol can resist both outside attacks and inside attacks.

Multiparty Quantum Key Agreement Protocol with Entanglement Swapping

Secure and fair multiparty quantum key agreement protocols demand all participants influence and negotiate the shared secret key with equal right and nobody can determine the shared secret key only by himself. To ensure the security and high efficiency, a novel multiparty quantum key agreement protocol based on entanglement swapping between Bell states and G-like states is proposed. This protocol makes full use of Bell states and G-like states as quantum resources and utilizes Bell measurement, Z-basis measurement and unitary operations to generate the shared secret key. It demonstrates that this proposed multiparty quantum key agreement protocol is secure and fair, and simpler with higher efficiency than some other protocols, especially when the number of participants in the protocol is big enough. Furthermore, the proposed protocol can be implemented with existing physical technologies.

Improving the security of quantum key agreement protocols with single photon in both polarization and spatial-mode degrees of freedom

Quantum key agreement enables remote users to fairly establish a secure shared key based on their private inputs. In the circular-type multiparty quantum key agreement protocol, two or more malicious participants can collude together to steal the private inputs of honest participants or to generate the final key alone. In this paper, we focus on a powerful collusive attack strategy in which two malicious participants in particular positions, can learn sensitive information or generate the final key alone without revealing their malicious behavior. Most of the proposed circular-type multiparty quantum key agreement protocols are not secure against this particular collusive attack strategy. As an example, we analyze the security of a recently proposed multiparty key agreement protocol to show the vulnerability of existing circular-type multiparty quantum key agreement protocols against this collusive attack. We then design a general secure multiparty key agreement model that would remove this vulnerability from such circular-type key agreement protocols and describe the necessary steps to implement this model. Our model is general and does not depend on the specific physical implementation of quantum key agreement.

Multiparty Quantum Key Agreement with Four-Qubit Symmetric W State

Based on four-qubit symmetric W state, the delayed measurement, decoy photos method, block transmission technique and the dense coding method, a multi-party quantum key agreement protocol is proposed. By utilizing the delayed measurement and decoy photos method, the fairness and security of the protocol are ensured. That is, the final generation key can be got fairly by m participants and the outside eavesdropper (includes Trojan-horse attacks, Measure-resend attack, Intercept-resend attack and Entangle-measure attack) and the dishonest participants attacks can be resisted in this protocol. By utilizing block transmission technique and the dense coding method, the efficiency of the protocol is improved. The efficiency analysis shows that the proposed protocol is more efficient than other multi-party QKA protocols.

Multi-party traveling-mode quantum key agreement protocols immune to collusive attack

Owing to the disadvantages of susceptible to collusive attack in the existed multi-party quantum key agreement (MQKA) protocols with traveling mode, two secure MQKA protocols with traveling mode were proposed. In order to resist collusive attack, a trust party was introduced in the first protocol and additional random 0–1 sequence was added to the private key sequence of each participant in the second protocol. Compared to existed MQKA protocols with traveling mode, the proposed protocols have three considerable advantages. Firstly, due to the fact that only Bell state measurements and simple single-particle unitary transformation are used, the processions of the proposed protocols are simple and can be easily realized. Secondly, the proposed protocols can resist internal attack, especially collusive attack. Furthermore, the proposed protocols are superior to the existing traveling-mode MQKA protocols in efficiency. Hence, the proposed protocols have great significance both on theory and on practical application.

Efficient multi-party quantum key agreement protocol based on nonorthogonal quantum entangled pairs

Multi-party quantum key agreement protocols with traveling mode have attracted much attention due to their higher efficiency than protocols with distributing mode. Nevertheless, the structures with traveling mode are generally vulnerable to internal participants, i.e. collusive attack. In order to resist collusive attack, a multi-party quantum key agreement protocol based on nonorthogonal quantum pairs, bell states and their dualities, is proposed. In this paper, we propose the idea of mixed dense encoding on the Pauli operations and the Hadamard operation. The private key sequence of each participant is encoded into a sequence consisting of those single-particle unitary operations which will be performed on the nonorthogonal quantum pairs. In the end, all participants can extract the target common key by comparing the initial states with the final states of the nonorthogonal quantum pairs. The proposed structure has three considerable advantages. Firstly, thanks to the use of nonorthogonal quantum pairs and mixed encoding, the proposed protocol can resist collusive attack from internal participants efficiently. Secondly, the efficiency has been greatly improved. Furthermore, due to the fact that only quantum pairs and simple single-particle unitary transformations are used, the processions of the proposed protocols are simple and can be easily realized in current technology.

Multiparty quantum key agreement protocol based on locally indistinguishable orthogonal product states

Based on locally indistinguishable orthogonal product states, we propose a novel multiparty quantum key agreement (QKA) protocol. In this protocol, the private key information of each party is encoded as some orthogonal product states that cannot be perfectly distinguished by local operations and classical communications. To ensure the security of the protocol with small amount of decoy particles, the different particles of each product state are transmitted separately. This protocol not only can make each participant fairly negotiate a shared key, but also can avoid information leakage in the maximum extent. We give a detailed security proof of this protocol. From comparison result with the existing QKA protocols, we can know that the new protocol is more efficient.

Multi-party quantum key agreement with five-qubit brown states

In this paper, we propose a multi-party quantum key agreement protocol with five-qubit brown states and single-qubit measurements. Our multi-party protocol ensures each participant to contribute equally to the agreement key. Each party performs three single-qubit unitary operations on three qubits of each brown state. Finally, by measuring brown states and decoding the measurement results, all participants can negotiate a shared secret key without classical bits exchange between them. With the analysis of security, our protocol demonstrates that it can resist against both outsider and participant attacks. Compared with other schemes, it also possesses a higher information efficiency. In terms of physical operation, it requires single-qubit measurements only which weakens the hardware requirements of participant and has a better operating flexibility.