Multi-party Quantum Private Comparison Research Articles

A Multiparty Quantum Private Equality Comparison Scheme Relying on |GHZ3⟩ States

In this work, we present a new protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled |GHZ3⟩ triplets. Our intention was to develop a protocol that can be readily executed by contemporary quantum computers. This is possible because the protocol uses only |GHZ3⟩ triplets, irrespective of the number n of millionaires. Although it is feasible to prepare multiparticle entangled states of high complexity, this is overly demanding on a contemporary quantum apparatus, especially in situations involving multiple entities. By relying exclusively on |GHZ3⟩ states, we avoid these drawbacks and take a decisive step toward the practical implementation of the protocol. An important quantitative characteristic of the protocol is that the required quantum resources are linear both in the number of millionaires and the amount of information to be compared. Additionally, our protocol is suitable for both parallel and sequential execution. Ideally, its execution is envisioned to take place in parallel. Nonetheless, it is also possible to be implemented sequentially if the quantum resources are insufficient. Notably, our protocol involves two third parties, as opposed to a single third party in the majority of similar protocols. Trent, commonly featured in previous multiparty protocols, is now accompanied by Sophia. This dual setup allows for the simultaneous processing of all n millionaires’ fortunes. The new protocol does not rely on a quantum signature scheme or pre-shared keys, reducing complexity and cost. Implementation wise, uniformity is ensured as all millionaires use similar private circuits composed of Hadamard and CNOT gates. Lastly, the protocol is information-theoretically secure, preventing outside parties from learning about fortunes or inside players from knowing each other’s secret numbers.

Multi-Party Quantum Private Comparison Based on Bell States.

Multi-party quantum private comparison (MQPC) assumes responsibility for overseeing the flow of data and communication among diverse entities, wherein it boasts powerful security capabilities that have garnered substantial attention. Most current MQPC protocols rely on difficult-to-prepare quantum states and are inefficient in their use of resources. In this paper, we propose a novel MQPC protocol without entanglement swapping, thereby building upon the assumption of an ideal channel. This protocol is based on Bell states, which simplifies implementation and addresses the challenges associated with using complex quantum states; it also enables the comparison of secret information by having a trusted party prepare and transmit encoded quantum sequences to participants, thereby facilitating efficient equality comparison among all parties. Our MQPC protocol showcased remarkable efficiency in comparison to existing protocols for quantum private comparison. Furthermore, the incorporation of decoy photon and shared key technologies made external and internal attacks ineffective, thereby ensuring the utmost security and integrity of the protocol.

Efficient multiparty quantum private comparison protocol based on single photons and rotation encryption

Efficient multiparty quantum private comparison protocol based on single photons and rotation encryption

Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states

In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting -dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply -dimensional single-particle measurements rather than -dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.

Multiparty quantum private comparison based on quantum walks

Multiparty quantum private comparison based on quantum walks

Improved multiparty quantum private comparison based on quantum homomorphic encryption

Quantum homomorphic encryption has obvious superiority in privacy protection. In this paper, we propose an improved multiparty quantum private comparison protocol based on quantum homomorphic encryption. Firstly, a trusted key center is introduced to securely assist the distribution of the encryption keys and update of decryption keys, while preventing a malicious server from launching an attack that announces a false result. It can significantly improve the security of the protocol while ensuring that all participants get the correct comparison results. Then, our protocol is different from the previous protocols that use the help of a semi-honest third-party. The third-party in our protocol can be almost dishonest and will faithfully perform the homomorphic evaluation on the encrypted data without decryption. Finally, by preparing single photons, multiple participants request homomorphic computations from an almost dishonest third-party in parallel and there is no need for detection of the decoy photon, which greatly reduces the consumption of quantum resources. In addition, the correctness of the protocol is verified by the IBM Q experimental platform.

Multi-party quantum private size comparison protocol with d-dimensional Bell states

A feasible multi-party quantum private comparison (MQPC) protocol based on d-dimensional Bell states was proposed. In the protocol, all participants can independently encrypt their privacies and send them to a semi-honest quantum third party (TP) through authenticated channels. Then, the TP can determine the size relationship among all participants’ privacies without gaining access to the private information. We verified correctness and effectiveness of the proposed protocol with some examples. In addition, compared with other similar protocols, it is not necessary to perform unitary operation on particles and only single-particle measurement is required. Furthermore, the relatively high qubit efficiency is promised. The security analysis verifies that the proposed protocol can counteract external and internal attacks in theory.

A new multi-party quantum private comparison based on n-dimensional n-particle GHZ state

With the help of a semi-honest third party Calvin, n parties [Formula: see text] can determine whether all of their private inputs [Formula: see text] are equal or not without leaking any information. In this paper, we present a novel protocol using special quantum unitary operations and n-dimensional n-particle GHZ states. The proposed protocol is correct. It can also resist various outside attacks and overcome the problem of information leakage.

Multi-Party Quantum Private Comparison Based on Entanglement Swapping of Bell Entangled States within d-Level Quantum System

In this paper, a multi-party quantum private comparison (MQPC) scheme is suggested based on entanglement swapping of Bell entangled states within d-level quantum system, which can accomplish the equality comparison of secret binary sequences from n users via one execution of scheme. Detailed security analysis shows that both the outside attack and the participant attack are ineffective. The suggested scheme needn't establish a private key among n users beforehand through the quantum key distribution (QKD) method to encrypt the secret binary sequences. Compared with previous MQPC scheme based on d-level Cat states and d-level Bell entangled states, the suggested scheme has distinct advantages on quantum resource, quantum measurement of third party (TP) and qubit efficiency.

A class of protocols for multi-party quantum private comparison based on traveling mode

Multi-party quantum private comparison (MQPC) enables $$n (n\ge 2)$$ parties to compare the equality of their private secrets without leaking them. In this paper, a class of MQPC protocols are proposed based on single-particle states and maximally entangled states. With the help of a semi-honest third party, our protocols can compare the equality of n parties’ private secrets. Our protocol uses single-particle states and a class of maximally entangled states as the information carriers, which means that our protocol has flexibility in the selection of quantum states compared with all previous protocols; after all, each of the previous protocols only uses a specific quantum state. In addition, our protocols adopt traveling mode, which can significantly reduce resource consumption. What is more, the qubit efficiency of each of our protocols can reach 100%, which is much higher than that of all previous MQPC protocols. We show that our protocols are secure against the outside and participant attacks.

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.

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.

Secure dynamic multiparty quantum private comparison

We propose a feasible and efficient dynamic multiparty quantum private comparison protocol that is fully secure against participant attacks. In the proposed scheme, two almost-dishonest third parties generate two random keys and send them to all participants. Every participant independently encrypts their private information with the encryption keys and sends it to the third parties. The third parties can analyze the equality of all or some participants’ secrets without gaining access to the secret information. New participants can dynamically join the protocol without the need for any additional conditions in the protocol. We provide detailed correctness and security analysis of the proposed protocol. Our security analysis of the proposed protocol against both inside and outside attacks proves that attackers cannot extract any secret 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.

Circular Multi-Party Quantum Private Comparison with n-Level Single-Particle States

In this paper, a novel multi-party quantum private comparison (MQPC) protocol for equality comparison with n-level single-particle states is constructed, where the encoded particles are transmitted in a circular way. Here, n parties employ the qudit shifting operation to encode their private secrets and can compare the equality of their private secrets within one time execution of protocol. The proposed MQPC protocol can overcome both the outside attack and the participant attack. Specially, each party's secret can be kept unknown to other parties and the third party (TP).

Improved Dynamic Multi-Party Quantum Private Comparison for Next-Generation Mobile Network

The advent of next-generation networks, such as fifth-generation cellular wireless (5G), has transformed every aspect of our lives and promised improvement for various real-life applications. Recently, Liu and Wang proposed a dynamic quantum private comparison protocol that utilizes the property of single photon, in both polarization and spatial-mode degrees of freedom. The protocol is intended to compare the private information of any two parties in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> parties with the support of the other <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -2 parties. However, we show that their protocol is not secure against a particular strategy of collusion attacks that leads to the problem of information leakage. Therefore, this paper suggests a security enhancement against the proposed attack strategy trying to overcome the security limitation of Liu and Wang’s work. The security analysis of the suggested improvement proved that the modified protocol is secure against both the internal and external attacks, which could be used to control the various auction models for 5G services as wireless network virtualization in a secure way.

Multiparty Quantum Private Comparison of Size Relation Based on Single-Particle States

In order to reduce resource consumption and improve transmission efficiency, in this paper, using single-particle states, a multiparty quantum privacy comparison size relationship (QPCSR) protocol is proposed. Without leaking the compared private message, the blinded secret integer is encoded into the relative phase of single-particle by performing unitary operation. After each of the transformed quantum states has been measured, respectively, the comparison result of n participants' secret integers is obtained. Security analysis shows that this protocol not only resists outside attack and participant attack, but also resists the semi-honest third-party (TP) attack. Compared with the other similar quantum privacy comparison equal relationship (QPCER) protocols, the proposed protocol has better flexibility and universality; compared with the other similar QPCSR protocols, it has lower resource consumption and higher communication efficiency.

Multi-party quantum private comparison of size relation with d-level single-particle states

In this paper, by using d-level single-particle states, two novel multi-party quantum private comparison protocols for size relation comparison with two semi-honest third parties and one semi-honest third party are constructed, respectively. Here, each protocol can compare the size relation of secret integers from n parties rather than just the equality within one time execution. In each protocol, every third party is assumed to be semi-honest in the sense that she may misbehave on her own but is not allowed to collude with anyone else; and each party employs the qudit shifting operation to encode her secret integer. Each protocol can resist both the outside attack and the participant attack. Specially, each party's secret integer can be kept unknown to other parties and the third parties. The proposed protocol with two third parties is workable in a stranger environment, as there are no communication and no pre-shared key between each pair of party. The proposed protocol with one third party is workable in an acquaintance environment, as all parties need to share a common private key beforehand.

Robust Multi-party Quantum Private Comparison Protocols Against the Collective Noise Based on Three-Qubit Entangled States

Recently, Ye and Ji constructed a multi-party quantum private comparison (MQPC) protocol with Bell entangled states (Sci. China Phys. Mech. Astron. 60(9), 090312, 2017). However, this protocol is only workable over an ideal quantum channel. In this paper, we take the collective noise channel into account and generalize Ye and Ji’s protocol into the ones against the collective-dephasing noise and the collective-rotation noise, respectively. Concretely, we use three-qubit entangled states instead of Bell states as the initial quantum states and employ the corresponding logical qubits immune to the collective noise instead of the physical qubits as the travelling particles. The output correctness and the security of the proposed robust MQPC protocols can be guaranteed.