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arXiv:1312.5572 · IETE Technical Review

Quantum Private Comparison: A Review

Wenjie Liu, Chao Liu, Haibin Wang, Tingting Jia

Published Jan 1, 2013• 42 citations
arXivHTMLPDF

Abstract

As an important branch of quantum secure multiparty computation, quantum private comparison (QPC) has attracted more and more attention recently. In this paper, according to the quantum implementation mechanism that these protocols used, we divide these protocols into three categories: The quantum cryptography QPC, the superdense coding QPC, and the entanglement swapping QPC. And then, a more in-depth analysis on the research progress, design idea, and substantive characteristics of corresponding QPC categories is carried out, respectively. Finally, the applications of QPC and quantum secure multi-party computation issues are discussed and, in addition, three possible research mainstream directions are pointed out.

DOI
10.4103/0256-4602.123129

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Abstract 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.
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.
A new quantum private comparison(QPC) protocol using Bell states and Bell entanglement swapping was proposed and analyzed.In the proposed protocol,Bell states were used as the quantum resources,and further Bell measurements and entanglement swapping were performed as the main operations for dealing with the private comparison of equal information without revealing their information content.The third part(TP) prepares Bell states and decoy photons,then inserts the decoy photons to sequences which he want to send to users for security.Users don't need to carry out any local unitary operations and only need to perform Bell measurements,then they send their sequences after coding their private information respectively.TP can achieve the comparison of two bits of classical information by simple calculation.Finally,TP announced the result of the comparison.In addition,the correctness and security of our protocol were discussed.
Private comparison allows n(n ≥ 2) participants who do not trust each other to compare whether their secret data are the same, without leaking the secret data of their own. Quantum private comparison (QPC) uses quantum mechanics to accomplish the comparison. In this paper, we present a simple and effective method which can design QPC protocols based on multi-particle entangled states including the genuinely entangled five-qubit state, the generalized Brown state, the genuine six-qubit entangled state, etc. We take the Bell state and the genuinely entangled five-qubit state as examples, respectively, to present two QPC protocols, where a semi-honest third party who assists two participants in implementing the protocols is assumed. A key feature of our protocols is that quantum states are prepared by two participants rather than by the third party, which effectively prevents the third party from preparing fake quantum states, thus improving the security of the protocols. In addition, we use the entanglement properties of multi-particle entangled states and collaborative computing between participants for privacy protection, and we use QKD to ensure the security of the cooperative computing when two participants are in different locations. We show that the security of our protocols towards both outsider and insider attacks can be guaranteed.
Quantum private comparison (QPC) is a crucial component of quantum multiparty computing (QMPC), allowing parties to compare their private inputs while ensuring that no sensitive information is disclosed. Many existing QPC protocols that utilize Bell states encounter efficiency challenges. In this paper, we present a novel and efficient QPC protocol that capitalizes on the distinct characteristics of Bell states to enable secure comparisons. Our method transforms private inputs into unitary operations on shared Bell states, which are then returned to a third party to obtain the comparison results. This approach enhances efficiency and decreases the reliance on complex quantum resources. A single Bell state can compare two classical bits, achieving a qubit efficiency of 100%. We illustrate the feasibility of the protocol through a simulation on the IBM Quantum Cloud Platform. The security analysis confirms that our protocol is resistant to both eavesdropping and attacks from participants.