Quantum Private Comparison Protocol Research Articles

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.

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.

Correction to: Fault-Tolerant Quantum Private Comparison Protocol

Correction to: Fault-Tolerant Quantum Private Comparison Protocol

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 entanglementswapping 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.

Novel Quantum Private Comparison Protocol Based on Locally Indistinguishable Product States

Novel Quantum Private Comparison Protocol Based on Locally Indistinguishable Product States

Novel two-party quantum private comparison via quantum walks on circle

The quantum private comparison aims to make the size comparison of two participants’ private information without leaking the private data of their own with quantum mechanism. In this paper, different from the current method of using single particle or entangled state as the information carrier, a novel two-party quantum private comparison protocol is firstly proposed via quantum walks on circle. In the protocol, a third party is assumed to be semi-honest and allowed to misbehave on his own, but cannot conspire with either of the two dishonest participants and obtain the participants’ private information. The protocol adopts the two-particle quantum walks state on circle rather than entangled state as the initial quantum resource and only needs measurement and quantum walks operator without the unitary operation and quantum entanglement swapping. The two-particle state is transferred as a whole among different parties, which reduces the protocol complexity and avoids the chance of being attacked. It can implement the equality comparison of private information, but also the size comparison. Security analyses show that this protocol is resistant to the external and internal malicious attacks, which can also determine the disputes over the judgment result of the third party. Compared with other quantum private comparison protocols, the proposed protocol has better flexibility and universality.

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.

Cryptanalysis and Improvement of Quantum Gate-Based Quantum Private Comparison

Recently, Lang put forward for the first time a quantum gate-based quantum private comparison (QPC) protocol (Int J Theor Phys, 59(2020)833) which uses the quantum controlled-not gates to implement comparison instead of classical exclusive-or computations. It was claimed that this quantum gate-based QPC protocol is secure against both the outside attack and the participant attack. However, in this paper, it is pointed out that this protocol cannot resist a special measurement attack from the third party (TP) and the disturbance attack from an outside attacker. The corresponding improvements are further suggested to remedy these security loopholes.

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 {|0⟩,|1⟩} , 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.

Greenberger-Horne-Zeilinger-based quantum private comparison protocol with bit-flipping

By introducing a semi-honest third party (TP), this paper proposes a novel quantum private comparison (QPC) protocol using (n + 1)-qubit (n ≥ 2) Greenberger-Horne-Zeilinger (GHZ) states as information carriers. The parameter n not only determines the number of qubits contained in a GHZ state, but also determines the probability that TP can successfully steal the participants’ data and the qubit efficiency. In the proposed protocol, any other quantum technologies (e.g., entanglement swapping and unitary operation) except necessary technologies such as preparing quantum states and quantum measurements are employed, which can reduce the need for quantum devices. The proposed protocol uses the keys generated by quantum key distribution and bit-flipping for privacy protection, and decoy photons for eavesdropping checking, making both external and internal attacks invalid. Specifically, for external attacks, several well-known attack means (e.g., the intercept-resend attack and the measurement-resend attack) are taken as examples to show that the attackers outside the protocol can not steal the participants’ data successfully, in which the security proof of the protocol against the entanglement-measurement attack is provided. For internal attacks, it is shown that TP cannot steal the participants’ data and the participants cannot steal each other’s data. It is also shown that the existing attack means against QPC protocols are invalid for our protocol.

Cryptanalysis and improvement of Wu–Cai–Wu–Zhang’s quantum private comparison protocol

In a recent paper [Int. J. Quantum Inf. 17 (2019) 1950026], the authors discussed the shortcomings in the security of a quantum private comparison protocol that we previously proposed [Int. J. Quantum Inf. 15 (2017) 1750014]. They also proposed a new protocol aimed to avoid these problems. Here, we analyze the information leaked in their protocol, and find that it is even less secure than our protocol in certain cases. We further propose an improved version which has the following advantages: (1) no entanglement needed, (2) quantum memory is no longer required, and (3) less information leaked. Therefore, better security and great feasibility are both achieved.

Multi-Party Quantum Private Comparison with Qudit Shifting Operation

In this paper, a multi-party quantum private comparison (MQPC) protocol is proposed based on the qudit shifting operation. The semi-honest third party (TP) prepares the initial particles and sends them to the first user. Then, each of n users encodes his private integers on the travelling particles with the qudit shifting operations and transmits them to the next user. Finally, the travelling particles are transmitted back to TP. The equality of the private integers from n users can be determined within one time execution of the protocol. It is verified that the proposed protocol is secure against both the outside attack and the participant attack. One user cannot obtain other users’ private integers except for the case that their private integers are same. TP cannot know the private integers from n users except their comparison result.

Quantum Private Comparison without Classical Computation

There are usually two kinds of signals i.e. quantum and classical to process in lots of existing protocols of quantum private comparison (QPC), for they employ quantum technology and classical computation to implement security and comparison, respectively. Classical operations and their information are prone to classical attacks with insufficient security. Therefore, a protocol of quantum gate-based QPC has been proposed without classical operations, but it is only applicable for qubits of computational basis. For its application to diagonal basis, this paper uses quantum gates and GHZ states to propose a new QPC protocol without classical data to process. There being no classical computation could lead to the improvement of security. The presented protocol is not only simple and efficient but also broadening applicable occasions. The analyses indicate its correctness and security.

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. 56 1517), 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.

Improvement of multi-party quantum private comparison protocol using d-dimensional basis states without entanglement swapping

Recently, Gu et al. (2019, arXiv:1907.02656) and Zhang et al. (Quantum Inf Process (2019)18:336) independently pointed out that in Yang et al.’s quantum summation protocol (Quantum Inf Process (2018) 17:129), the party in charge of preparing the initial quantum states is able to steal other parties’ private integer strings without being discovered by launching two special kinds of attack. In this paper, it is pointed out that in Liu et al.’s MQPC protocol, if the third party (TP) named Calvin launches the similar attacks, she can also steal the private secrets from n parties without being discovered. Then, two methods are put forward to avoid this drawback, i.e., the first one is to add the process of checking whether the quantum states shared among n parties are genuinely in the state of |W〉12⋯n while the second one is to encrypt the private secrets from n parties with a private key sequence shared among them beforehand.

Continuous variable controlled quantum dialogue and secure multiparty quantum computation

A continuous variable (CV) controlled quantum dialogue (QD) scheme is proposed. The scheme is further modified to obtain two other protocols of (CV) secure multiparty computation. The first one of these protocols provides a solution of two-party socialist millionaire problem, while the second protocol provides a solution for a special type of multi-party socialist millionaire problem which can be viewed as a protocol for multiparty quantum private comparison. It is shown that the proposed scheme of (CV) controlled (QD) can be performed using bipartite entanglement and can be reduced to obtain several other two- and three-party cryptographic schemes in the limiting cases. The security of the proposed scheme and its advantage over corresponding discrete variable (DV) counterpart are also discussed. Specifically, the ignorance of an eavesdropper, i.e., information encoded by Alice/Bob, in the proposed scheme is shown to be more than that in the corresponding (DV) scheme, and thus the present scheme is less prone to information leakage inherent with the (DV) (QD) based schemes. It is further established that the proposed scheme can be viewed as a (CV) counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.

New Quantum Private Comparison Protocol Without a Third Party

New Quantum Private Comparison Protocol Without a Third Party

Quantum Private Comparison Protocol without a Third Party

This paper presents a novel quantum private comparision (QPC) protocol based on the single-qubit rotations, quantum SWAP-test and quantum SWAP gates. The proposed QPC protocol can secretly compare information of the two participants without the help of a third party (TP). The security analysis of the presented QPC protocol shows that it is quantum indistinguishable and information theory security for all outside attackers and inside attackers. Finally, we compare some important features of the presented QPC protocol with other QPC protocols. The results show that the proposed protocol has some advantages different from previous protocols.

Quantum Private Comparison Protocol Based on Four-Particle GHZ States

A new quantum private comparison protocol with four-particle GHZ states is proposed. Unlike most previous quantum private comparison protocols, this quantum private comparison protocol can compare the equality of three information bits in each comparison, which could greatly reduce the times of comparisons. The private input of either party will not be leaked out to others, including participants. Besides, it’s simple to implement the protocol with current technologies since only single-particle measurements and Bell measurements are involved. Furthermore, our protocol has good performance of withstanding various outside attacks and participant attacks.

An attempt at universal quantum secure multi-party computation with graph state

Quantum secure multi-party computation (SMC) is a vital field in quantum cryptography. In this paper, we try to resolve SMC problems universally via graph states. Firstly, three kinds of quantum SMC protocols are investigated, which are quantum private comparison protocol, quantum millionaire protocol and quantum multi-party summation protocol. Secondly, three proposed protocols are reviewed, and then the core of them is summarized. We further find that the computation, deduced as modulo subtraction, can be resolved by using graph state. This implies that our protocols are universal in part and will be widely applicable. Thirdly, analyses show that the proposed protocols are correct and secure. Our research will promote the development of quantum secure multi-party computation.