Multi-party semi-quantum private comparison protocol of size relation based on two-dimensional Bell states

Currently,all quantum private comparison protocols based on two-dimensional quantum states can only compare equality,via using high-dimensional quantum states that it is possible to compare the size relation in existing work.In addition,it is difficult to manipulate high-dimensional quantum states under the existing conditions of quantum information processing,leading to low practicality and engineering feasibility of protocols for comparing size relation.Considering this situation,we propose an innovative protocol.The proposed protocol can make size comparison by exploiting more manageable two-dimensional Bell states,which significantly enhances its feasibility with current quantum technologies.Simultaneously,the proposed protocol enables multiple participants to compare their privacies with the semi-quantum model.The communication process of the protocol is simulated on the IBM Quantum Experience platform to verify its effectiveness.Security analysis shows that the proposed protocol can withstand common attacks while preserving the privacies of all participants.Thus,the devised protocol may provide an important reference for implementation of quantum private size comparison protocols.

Efficient quantum private comparison protocol based on one direction discrete quantum walks on the circle

We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks.With the help of one direction quantum walk,we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result,which improves the qubit efficiency and the maximum quantity of the participants’secret messages.Besides,our protocol can judge the size of the secret messages,not only equality.Furthermore,the quantum walks particle is disentangled in the initial state.It only requires a quantum walks operator to move,making our proposed protocol easy to implement and reducing the quantum resources.Through security analysis,we prove that our protocol can withstand well-known attacks and brute-force attacks.Analyses also reveal that our protocol is correct and practical.

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.

Measure-Resend Semi-Quantum Private Comparison Scheme Using GHZ Class States

Quantum private comparison is an important topic in quantum cryptography.Recently,the idea of semi-quantumness has been often used in designing private comparison protocol,which allows some of the participants to remain classical.In this paper,we propose a semi quantum private comparison scheme based on Greenberge-Horne-Zeilinger(GHZ)class states,which allows two classical participants to compare the equality of their private secret with the help of a quantum third party(server).In the proposed protocol,server is semi-honest who will follow the protocol honestly,but he may try to learn additional information from the protocol execution.The classical participants’activities are restricted to either measuring a quantum state or reflecting it in the classical basis{0,1}.In addition,security and efficiency of the proposed schemes have been discussed.

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.

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.

A Novel Semi-Quantum Private Comparison Scheme Using Bell Entangle States

Private comparison is the basis of many encryption technologies,and several related Quantum Private Comparison(QPC)protocols have been published in recent years.In these existing protocols,secret information is encoded by using conjugate coding or orthogonal states,and all users are quantum participants.In this paper,a novel semi-quantum private comparison scheme is proposed,which employs Bell entangled states as quantum resources.Two semi-quantum participants compare the equivalence of their private information with the help of a semi-honest third party(TP).Compared with the previous classical protocols,these two semi-quantum users can only make some particular action,such as to measure,prepare and reflect quantum qubits only in the classical basis fj0i;j1ig,and TP needs to perform Bell basis measurement on reflecting qubits to obtain the results of the comparison.Further,analysis results show that this scheme can avoid outside and participant attacks and its’qubit efficiency is better than the other two protocols mentioned in the paper.

New Quantum Private Comparison Using Hyperentangled GHZ State

In this paper,we propose a new protocol designed for quantum private comparison(QPC).This new protocol utilizes the hyperentanglement as the quantum resource and introduces a semi-honest third party(TP)to achieve the objective.This protocol’s quantum carrier is a hyperentangled three-photon GHZ state in 2 degrees of freedom(DOF),which could have 64 combinations.The TP can decide which combination to use based on the shared key information provided from a quantum key distribution(QKD)protocol.By doing so,the security of the protocol can be improved further.Decoy photon technology is also used as another means of security and checks if the transmission in the quantum channel is secure or not before sending the quantum carrier.The proposed protocol is proved to be able to fend off various kinds of eavesdropping attacks.In addition,the new QPC protocol also can compare secret inputs securely and efficiently.

Robust and efficient quantum private comparison of equality with collective detection over collective-noise channels

We present a protocol for quantum private comparison of equality(QPCE) with the help of a semi-honest third party(TP).Instead of employing the entanglement,we use single photons to achieve the comparison in this protocol.By utilizing collective eavesdropping detection strategy,our protocol has the advantage of higher qubit efficiency and lower cost of implementation.In addition to this protocol,we further introduce three robust versions which can be immune to collective dephasing noise,collective-rotation noise and all types of unitary collective noise,respectively.Finally,we show that our protocols can be secure against the attacks from both the outside eavesdroppers and the inside participants by using the theorems on quantum operation discrimination.

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-Zeitinger （GHZ） states and error-correcting code （ECC） lint. J. Theor. Phys. 52, 2818 （2013）], claiming it is fault-tolerant and could be performed in a non-ideal scenario. However, there ex- ists 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.

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.

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 amongK 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.

Cryptanalysis and improvement of several quantum private comparison protocols

Recently, Wu et al(2019 Int. J. Theor. Phys. 58 1854) found a serious information leakage problem in Ye and Ji’s quantum private comparison protocol(2017 Int. J. Theor. Phys. 561517), that is, a malicious participant can steal another’s secret data without being detected through an active attack means. In this paper, we show that Wu et al’s active attack is also effective for several other existing protocols, including the ones proposed by Ji et al and Zha et al(2016 Commun. Theor. Phys. 65 711;2018 Int. J. Theor. Phys. 57 3874). In addition,we propose what a passive attack means, which is different from Wu et al’s active attack in that the malicious participant can easily steal another’s secret data only by using his own secret data after finishing the protocol, instead of stealing the data by forging identities when executing the protocol. Furthermore, we find that several other existing quantum private comparison protocols also have such an information leakage problem. In response to the problem, we propose a simple solution, which is more efficient than the ones proposed by Wu et al, because it does not consume additional classical and quantum resources.

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.

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 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.

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.

Cryptanalysis and Improvement of Quantum Private Comparison Protocol Based on Bell Entangled States

Recently, Liu et al. [Commun. Theor. Phys. 57(2012) 583] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party(TP). However, the present study points out there is a fatal loophole in Liu et al.'s protocol, and TP can make Bell-basis measurement to know all the participants' secret inputs without being detected. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol,it not only reduces the Bell states consumption but also simplifies the protocol steps.

Full-Blind Delegating Private Quantum Computation

The delegating private quantum computation(DQC)protocol with the universal quantum gate set{X,Z,H,P,R,CNOT}was firstly proposed by Broadbent et al.[Broadbent(2015)],and then Tan et al.[Tan and Zhou(2017)]tried to put forward a half-blind DQC protocol(HDQC)with another universal set{H,P,CNOT,T}.However,the decryption circuit of Toffoli gate(i.e.T)is a little redundant,and Tan et al.’s protocol[Tan and Zhou(2017)]exists the information leak.In addition,both of these two protocols just focus on the blindness of data(i.e.the client’s input and output),but do not consider the blindness of computation(i.e.the delegated quantum operation).For solving these problems,we propose a full-blind DQC protocol(FDQC)with quantum gate set{H,P,CNOT,T},where the desirable delegated quantum operation,one of{H,P,CNOT,T},is replaced by a fixed sequence(H,P,CZ,CNOT,T)to make the computation blind,and the decryption circuit of Toffoli gate is also optimized.Analysis shows that our protocol can not only correctly perform any delegated quantum computation,but also holds the characteristics of data blindness and computation blindness.

Approximate Quantum State Sharings via Pair of Private Quantum Channels

We investigate a quantum communication protocol, of so-called approximate quantum state sharing (AQSS), that protocol is basically based on pair of private quantum channels. In this paper, we prove that the scheme is secure against any external and internal attacks of wiretapping in principle. Although the protocol leaks small amount of information corresponding to a security parameter , the scheme still preserves its information-theoretic security.