Quantum Private Comparison via Cavity QED

The first quantum private comparison(QPC) protocol via cavity quantum electrodynamics(QED) is proposed in this paper by making full use of the evolution law of atom via cavity QED, where the third party(TP) is allowed to misbehave on his own but cannot conspire with either of the two users. The proposed protocol adopts two-atom product states rather than entangled states as the initial quantum resource, and only needs single-atom measurements for two users. Both the unitary operations and the quantum entanglement swapping operation are not necessary for the proposed protocol. The proposed protocol can compare the equality of one bit from each user in each round comparison with one two-atom product state. The proposed protocol can resist both the outside attack and the participant attack.Particularly, it can prevent TP from knowing two users' secrets. Furthermore, the qubit efficiency of the proposed protocol is as high as 50%.     

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 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.     

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.     

Quantum Private Comparison Based on χ-Type Entangled States

A two-party quantum private comparison (QPC) protocol is constructed with χ-type entangled states in this paper. The proposed protocol employs a semi-honest third party (TP) that is allowed to misbehave on his own but cannot conspire with the adversary. The proposed protocol need perform Bell basis measurements and single-particle measurements but neither unitary operations nor quantum entanglement swapping technology. The proposed protocol possesses good security toward both the outside attack and the participant attack. TP only knows the comparison result of the private information from two parties in the proposed protocol.

     

Improvements of Quantum Private Comparison Protocol Based on Cluster States

Quantum private comparison aims to determine whether the secrets from two different users are equal or not by utilizing the laws of quantum mechanics. Recently, Sun and Long put forward a quantum private comparison (QPC) protocol by using four-particle cluster states (Int. J. Theor. Phys. 52, 212–218, 2013). In this paper, we investigate this protocol in depth, and suggest the corresponding improvements. Compared with the original protocol, the improved protocol has the following advantages: 1) it can release the requirements of authenticated classical channels and unitary operations; 2) it can prevent the malicious attack from the genuine semi-honest TP; 3) it can enhance the qubit efficiency.     

Quantum Private Comparison of Equality Based on Five-Particle Cluster State

A protocol for quantum private comparison of equality (QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party (TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information (each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups (each group has N private information) in one execution or just N private information.     

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 of Equality Based on Five-Particle Cluster State

A protocol for quantum private comparison of equality(QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party(TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information(each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups(each group has N private information)in one execution or just N private information.     

Secure Quantum Private Comparison Protocol Based on the Entanglement Swapping Between Three-Particle W-Class State and Bell State

We propose a new quantum private comparison protocol with the help of a semi-honest third party (TP), enabling two participants to compare the equality of their private inputs without exposing any information about their respective private inputs. Different from previous protocols, our protocol utilizes the properties of entanglement swapping between three-particle W-Class state and Bell state. The presented protocol can ensure correctness, fairness and security. Meanwhile, all the quantum particles undergo a one-way transmission, and all the participants including TP are just required having the ability to perform Bell-state measurement and exclusive-or operation which make our protocol more feasible and efficient. At last, the security of this protocol with respect to various kinds of attacks is analyzed in detail.     

Multi-user quantum private comparison with scattered preparation and one-way convergent transmission of quantum states

Quantum private comparison (QPC) aims to accomplish the equality comparison of the secrets from different users without disclosing their genuine contents by using the principles of quantum mechanics. In this paper, we summarize eight modes of quantum state preparation and transmission existing in current QPC protocols first. Then, by using the mode of scattered preparation and one-way convergent transmission, we construct a new multi-user quantum private comparison (MQPC) protocol with two-particle maximally entangled states, which can accomplish arbitrary pair’s comparison of equality among K users within one execution. Analysis turns out that its output correctness and its security against both the outside attack and the participant attack are guaranteed. The proposed MQPC protocol can be implemented with current technologies. It can be concluded that the mode of scattered preparation and one-way convergent transmission of quantum states is beneficial to designing the MQPC protocol which can accomplish arbitrary pair’s comparison of equality among K users within one execution.     

Quantum Private Comparison Protocol Based on Cluster States

We present a quantum private comparison (QPC) protocol, enabling two players to compare the equality of their information without revealing any information about their respective private inputs, in which the four-particle cluster states as the information carriers are used. The presented protocol can ensure correctness, privacy, and fairness with the assistance of a semi-trusted third party (TP). Meanwhile, the participants including the TP are just required having the ability to perform single-particle measurements, which make the presented protocol more feasible in technique. Furthermore, the photon transmission is a one-way distribution; the Trojan horse attacks can be automatically avoided. The security of this protocol is also analyzed.     

Intercept-Resend-Measure Attack Towards Quantum Private Comparison Protocol Using Genuine Four-Particle Entangled States and its Improvement

Recently, Jia et al. proposed the quantum private comparison protocol with the genuine four-particle entangled states (Jia et al., Int. J. Theor. Phys. 51(4), 1187–1194 (2012)). Jia et al. claimed that in this protocol, TP cannot obtain Alice and Bob’s secrets and only knows their comparison result. However, in this paper, we demonstrate that if TP is a genuine semi-honest third party, he can totally obtain Alice and Bob’s secrets by launching a particular intercept-resend-measure attack. After suggesting the intercept-resend-measure attack strategy from TP first, we put forward one corresponding improvement to prevent this attack.     

Semi-quantum private comparison protocol of size relation with d-dimensional GHZ states

A novel efficient semi-quantum private comparison protocol based on the d-dimensional GHZ states is proposed.With the assistance of semi-honest third party,two classical participants can compare the size relation of their secrets without any information leakage.To reduce the consumption of quantum devices,the qubit efficiency of our protocol is improved by introducing the semi-quantum conception via the existing semi-quantum private comparisons.Furthermore,it is unnecessary to prepare the secure classical authentication channel among participants in advance.It is shown that our protocol is not only correct and efficient,but also free from external and internal attacks.     

Efficient quantum private comparison protocol utilizing single photons and rotational encryption

As a branch of quantum secure multiparty computation, quantum private comparison is applied frequently in many fields, such as secret elections, private voting, and identification. A quantum private comparison protocol with higher efficiency and easier implementation is proposed in this paper. The private secrets are encoded as single polarized photons and then encrypted with a homomorphic rotational encryption method. Relying on this method and the circular transmission mode, we implement the multiplexing of photons, raising the efficiency of our protocol to 100%. Our protocol is easy to realize since only single photons, unitary operation, and single-particle measurement are introduced. Meanwhile, the analysis shows that our protocol is also correct and secure.     

Cryptanalysis and Improvement for the Quantum Private Comparison Protocol Based on Triplet Entangled State and Single-Particle Measurement

Quantum private comparison (QPC) aims to accomplish the equality comparison of secret inputs from two users on the basis of not leaking their contents out. Recently, Chen et al. proposed the QPC protocol based on triplet GHZ state and single-particle measurement (Optics Communications 283, 1561–1565 (2010)). In this paper, they suggested the standard model of a semi-honest third party (TP) for the first time, and declared that their protocol is secure. Subsequently, Lin et al. pointed out that in Chen et al.’s protocol, one user can extract the other user’s secret without being discovered by performing the intercept-resend attack, and suggested two corresponding improvements (Optics Communications 284, 2412–2414 (2011)). However, Yang et al. first pointed out that the model of TP adopted by both Chen et al.’s protocol and Lin et al.’s improved protocols is unreasonable, and thought that a practical TP may also try any possible means to steal the users’ secrets except being corrupted by the adversary including the dishonest user (Quantum Inf Process 12, 877–885 (2013). In this paper, after taking the possible attacks from TP into account, we propose the eavesdropping strategy of TP toward Lin et al.’s improved protocols and suggest two feasible solutions accordingly.     

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.     

Quantum Protocol for Millionaire Problem

A quantum protocol for millionaire problem based on commutative encryption is proposed. In our protocol, Alice and Bob don’t have to use the entangled character, joint measurement of quantum states. They encrypt their private information and privately get the result of their private information with the help of a third party (TP). Correctness analysis shows that the proposed protocol can be used to get the result of their private information correctly. The proposed protocol can also resist various attacks and overcomes the problem of information leakage with acceptable efficiency. In theory, our protocol can be used to build complex secure protocols for other multiparty computation problems and also have lots of other important applications in distributed networks.

     

An Efficient Quantum Private Comparison of Equality over Collective-Noise Channels

This article proposes a collective-noise resistant QPC protocol with the help of an almostdishonest third party (TP) who may try to perform any sort of attacks to derive participants’ private secrets except colluding with any participant. The proposed scheme has some considerable advantages over the state-of-the-art QPC protocols over collective-noise channels, where it does not require any pre-shared key between the participants (Alice and Bob). Nevertheless, the proposed scheme can resist Trojan horse attacks without consuming half of the transmitted qubits and any additional equipment (wavelength filter and PNS) support. As a consequence, the proposed QPC protocol can guarantee higher qubit efficiency as compared to the others over collective noise channels.     

Multi-Party Quantum Private Comparison Protocol Based on Entanglement Swapping of Bell Entangled States

Recently, Liu et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57 (2012) 583). Subsequently, Liu et al. pointed out that in Liu et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62 (2014) 210). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, and then suggest the corresponding improvement by using the one-way hash function to encrypt the two users' secret inputs. We further put forward the three-party QPC protocol also based on entanglement swapping of Bell entangled state, and then validate its output correctness and its security in detail. Finally, we generalize the three-party QPC protocol into the multi-party case, which can accomplish arbitrary pair's comparison of equality among K users within one execution.