Quantum Private Comparison of Equality with χ-Type Entangled States

In this paper, a quantum private comparison protocol with χ-type entangled states is proposed. In the protocol, two users can determine whether their secret inputs are equal, with the help of a semi-trusted third party. Here, the only constraint condition of this third party is that he could not collude with one user. Although the third party takes part in the whole process of the presented protocol, a feature of χ-type entangled state is utilized to design a eavesdropping check method to stand against his attack. Security analysis showed that the presented protocol is secure against some well-known attacks. Meanwhile, all the particles undergo only a one-way trip, which improves the efficiency and security of the presented protocol. Furthermore, only two-particle measurement is required in the implementation of the protocol, which make it more feasible in technique.     

Quantum Private Comparison Protocol with the Random Rotation

We proposed a quantum secret comparison protocol for two parties with the random rotation angle, which is under the help of a semi-honest third party. The random rotation angle made it possible for the protocol to be safer and the two parties cannot deduce each other’s information by means of their own possessions. The participants’ secrets are divided into groups and the third party announced the results by group, which made the protocol more safely and sometimes it can save lots of resources. Moreover, during our protocol process any information of the two parties will not be leaked, even the third party cannot get any participants’ secrets.     

Quantum private comparison of arbitrary single qubit states based on swap test

By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants' attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.     

Quantum Private Comparison Protocol Based on Bell Entangled States

In this paper,a quantum private comparison protocol is proposed based on bell entangled states.In our protocol,two parties can compare the equality of their information with the help of a semi-honest third party.The correctness and security of our protocol are discussed.One party cannot learn the other's private information and the third party also cannot learn any information about the private information.     

Secure Quantum Private Comparison of Equality Based on Asymmetric W State

Recently, Liu et al. (Opt. Commun. 284:3160, 2011) proposed a protocol for quantum private comparison of equality (QPCE) based on symmetric W state. However, Li et al. (Eur. Phys. J. D 66:110, 2012) pointed out that there is a flaw of information leak, and they proposed a new protocol based on EPR pairs. While examining these two protocols, we find that there exists a same flaw: the third party (TP) can know the comparison result. In this paper, through introducing and constructing a special class of asymmetric W state, a secure QPCE protocol based on this asymmetric W state is presented. Analysis shows the present protocol can not only effectively avoid the information leak found by Li et al., but also ensure TP would not get any information about the comparison result.     

Quantum Private Comparison Based on Quantum Search Algorithm

We propose two quantum private comparison protocols based on quantum search algorithm with the help of a semi-honest third party. Our protocols utilize the properties of quantum search algorithm, the unitary operations, and the single-particle measurements. The security of our protocols is discussed with respect to both the outsider attack and the participant attack. There is no information leaked about the private information and the comparison result, even the third party cannot know these information.     

基于三粒子GHZ态的双向量子可控隐形传态

提出基于三粒子GHZ态的双向量子可控隐形传态方案.方案中,使用两个三粒子GHZ态作为量子通道.而根据在量子通道中发送者,接收者和控制者所拥有的粒子的不同以及所采用的测量基的不同,设计出了三方参与的双向可控量子隐形传态方案和四方参与的双向可控量子隐形传态方案.在方案中,Alice和Bob对所拥有的粒子做合适的投影测量,并将其测量结果通知对方和控制者.若控制者同意此次传态,则会对自己所拥有的粒子做投影测量,并将结果告知接收者.接收者根据发送者和控制者的测量信息,做出相对应的幺正操作来重建发送者的量子态.同时三方参与和四方参与的量子可控隐形传态方案提高了通信的安全性.     

Multi-Party Quantum Private Comparison Protocol with an Almost-Dishonest Third Party using GHZ States

This article proposes an innovative quantum private comparison (QPC) protocol for n users using GHZ states, where an almost-dishonest third party (TP) is introduced to assist the participants for comparing their secrets. It is argued that as compared to the existing QPC protocols our proposed scheme has some considerable advantages. First, in the existing QPC protocols, the TP can only to determine whether all participants’ secrets are equal or not. Instead of that, in our proposed scheme a TP can even compare the secrets between any subsects of users. Second, since our proposed scheme is based on GHZ state; hence it can ensure higher efficiency as compared to other existing multi-party QPC protocols on d-dimension photons.     

Quantum Private Comparison Using Genuine Four-Particle Entangled States

In this paper, a quantum private comparison protocol is proposed based on χ-type state. According to the protocol, two parties can determine the equality of their information with the assistant of a semi-honest third party. Due to utilizing quantum superdense coding, this protocol provides a high efficiency and capacity. Moreover, its security is also discussed.     

Cryptanalysis and Improvement of Quantum Private Comparison without Classical Computation

Recently, Lang suggested a quantum private comparison (QPC) without classical computation (Int J Theor Phys, 59(2020)2984). Lang claimed that this QPC protocol is secure against both the participant attack and the outside attack. It is pointed out in this paper that the third party (TP) can totally obtain the private binary sequences of two communicants by launching a special measurement attack; and moreover, an outside attacker can make this protocol fail by launching the disturbance attack. The corresponding methods are further put forward to overcome these drawbacks.

     

A New Multi-Party Quantum Private Comparison Protocol Based on Circle Model

Recently multi-party quantum private comparison (MQPC) has attracted more and more attentions in the research of quantum cryptography. In our paper, a new MQPC protocol has been proposed by encoding the compared secrets on the phase of n-level single photons. From the proposed protocol, a generic model named circle model can be summarized. With the help of a semi-honest third party (TP), it can be proved that our protocol is immune to the outside attack and dishonest participants’ (including TP) attack.

     

Quantum Private Comparison Protocol with W States

We propose a secure quantum protocol for comparing the equality of information with the help of a semi-honest third party (Trent). Our protocol utilizes the triplet W states, and the single-particle measurement. The technique for preparing W state is mature, which ensures the utility of our protocol. The security of our protocol with respect to both outsider attack and participant attack is discussed. Any information about the private information, the comparison result will not be leaked out, even the third party cannot know these information.     

Information leak in Liu et al.’s quantum private comparison and a new protocol

In a recent paper [W. Liu, Y.B. Wang, Z.T. Jiang, Opt. Commun. 284, 3160 (2011)], a quantum private comparison (QPC) protocol based on W states was presented. Compared to the previous QPCs, the protocol is promising for that it can prevent the comparison result from revealing to the third party. However, this study point out that a flaw of information leak is existent in the protocol. And a new QPC which can avoid the flaw and has higher efficiency is proposed in this paper.     

Quantum Private Comparison of Equal Information Based on Highly Entangled Six-Qubit Genuine State

Using the highly entangled six-qubit genuine state we present a quantum private comparison (QPC) protocol, which enables two users to compare the equality of two bits of their secrets in every round comparison with the assistance of a semi-honest third party (TP). The proposed protocol needs neither unitary operations nor quantum entanglement swapping technology, both of which may consume expensive quantum devices. Single particle measurements and Bell-basis measurements, which are easy to implement with current technologies, are employed by two users and TP in the proposed protocol, respectively. The proposed protocol can withstand all kinds of outside attacks and participant attacks. Moreover, none of information about the two users’ private secrets and the comparison result is leaked out to TP.     

A Protocol for the Quantum Private Comparison of Equality with χ-Type State

We present a new quantum protocol for comparing the equal information with the help of a semi-honest third party (TP). Different from previous protocols, we utilize the four-particle χ-type states as the information carriers. Various kinds of outside attacks and participant attacks are discussed in detail. One party cannot learn the other’s private information. The TP cannot learn any information about the private information, even about the comparison result or the length of secret inputs.     

A Quantum Protocol for (t,n)-Threshold Identity Authentication Based on Greenberger-Horne-Zeilinger States

A quantum protocol for (t,n)-threshold identity authentication based on Greenberger-Horne-Zeilinger states is presented. A trusted third party (TTP) can authenticate the users simultaneously when and only when t or more users among n apply for authentication. Compared with the previous multiparty simultaneous quantum identity authentication (MSQIA) protocols, the proposed scheme is more flexible and suitable for practical applications.     

Twice-Hadamard-CNOT attack on Li et al.’s fault-tolerant quantum private comparison and the improved scheme

Recently, Li et al. presented a two-party quantum private comparison scheme using Greenberger–Horne–Zeilinger (GHZ) states and error-correcting code (ECC) [Int. J. Theor. Phys. 52, 2818 (2013)], claiming it is fault-tolerant and could be performed in a non-ideal scenario. However, there exists a fatal loophole in their private comparison scheme under a special attack, namely the twice-Hadamard-CNOT attack. Specifically, a malicious party may intercept the other party’s particles and execute Hadamard operations on the intercepted particles as well as on his or her own particles. Then, the malicious party could sequentially perform a controlled-NOT (CNOT) operation between intercepted particles and the auxiliary particles, as well as between his or her own particles and the auxiliary particles prepared in advance. By measuring the auxiliary particles, the secret input will be revealed to the malicious party without being detected. For resisting this special attack, a feasible improved scheme is proposed by introducing a permutation operator before the third party (TP) sends the particle sequences to each participant.     

Cryptanalysis and Improvement of the Multi-User QPCE Protocol with Semi-Honest Third Party

In a recent work[Quantum Inf.Process 12(2013) 1077],a multi-user protocol of quantum private comparison of equality(QPCE) is presented.Here we point out that if we relax the constraint of a semi-honest third party,the private information of the users will be totally leaked out to the third party.A special attack is demonstrated in detail.Furthermore,a possible improvement is proposed,which makes the protocol secure against this kind of attack.     

Two-Party Quantum Private Comparison with Five-Qubit Entangled States

In this paper, a two-party quantum private comparison (QPC) protocol is proposed by using five-qubit entangled states as the quantum resource. The proposed protocol needs the help from a semi-honest third party (TP), who is allowed to misbehave on his own but not allowed to conspire with the adversary including the dishonest user. The proposed protocol has the following distinct features: (1) One five-qubit entangled state can be used to achieve the equality comparison of two bits in each round of comparison; (2) Neither unitary operations nor quantum entanglement swapping technology is needed, both of which may consume expensive quantum devices; (3) Only Bell measurements and single-particle measurements are employed, both of which can be realized with current quantum technologies; (4) The security toward both the outside attack and the participant attack can be guaranteed; (5) The private information of two parties is not leaked out to TP.     

Analysis of Counterfactual Quantum Certificate Authorization

A counterfactual quantum certificate authorization protocol was proposed recently (Shenoy et al., Phys. Rev. A 89, 052307 (20)), in which a trusted third party, Alice, authenticates an entity Bob (e.g., a bank) that a client Charlie wishes to securely transact with. However, this protocol requires a classical authenticated channel between Bob and Charlie to prevent possible attacks from the third party Alice, which is in conflict with the task of certificate authorization in the sense that Bob and Charlie can establish an unconditionally-secure key by a quantum key distribution protocol if there is a classical authenticated channel between them and hence securely transact with each other even without the assistance of the third party Alice.