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Chinese Physics B

Efficient semi-quantum private comparison protocol of size relation based on high-dimensional Bell states

Jie‐Hui Huang, Mao-Long Li, Yanyan Liu, Li‐Guo Qin, Li‐Hua Gong

Published Dec 10, 2025• 11 citations
Publisher

Abstract

Abstract An efficient semi-quantum private comparison protocol is proposed with d -dimensional Bell states to assist two classical parties in comparing the size relation of their secret information. With the assistance of a third party (TP), Alice and Bob do not need to measure qubits or prepare new qubits, reducing the consumption of quantum resources. The presented protocol has a higher qubit efficiency than other similar protocols, since the legal participants can compare two bits of privacy (i.e., secret information unknown to others) each time with one qubit. Moreover, the proposed scheme offers a greater advantage when comparing larger private numbers, with the correctness of its outputs verified through analytical methods. Simulation experiments further verified the correctness of the proposed protocol, and security analyses demonstrated its robustness against external and internal attacks. Furthermore, the proposed semi-quantum private comparison protocol can be converted into an efficient semi-quantum key distribution protocol.

DOI
10.1088/1674-1056/ae2abd

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Abstract An efficient semi-quantum private comparison protocol is proposed with d -dimensional Bell states to assist two classical parties in comparing the size relation of their secret information. With the assistance of a third party (TP), Alice and Bob do not need to measure qubits or prepare new qubits, reducing the consumption of quantum resources. The presented protocol has a higher qubit efficiency than other similar protocols, since the legal participants can compare two bits of privacy (i.e., secret information unknown to others) each time with one qubit. Moreover, the proposed scheme offers a greater advantage when comparing larger private numbers, with the correctness of its outputs verified through analytical methods. Simulation experiments further verified the correctness of the proposed protocol, and security analyses demonstrated its robustness against external and internal attacks. Furthermore, the proposed semi-quantum private comparison protocol can be converted into an efficient semi-quantum key distribution protocol.
Many semi-quantum private comparison (SQPC) protocols have been proposed to compare the equality of participants, but they suffer from low qubit efficiency and require classical participants to perform quantum state measurement and preparation operations. We here propose a novel SQPC protocol based on d-dimensional Bell states. With the assistance of a semi-honest third party, classical participants can compare the sizes of their privacies merely through particle reflection and simple unitary operations, but they do not need to prepare and measure quantum states. Furthermore, participants can compare two bits of privacy just once with one qubit. By combining decoy state eavesdropping detection with pre-shared key encryption as dual security strategies, analysis shows that the proposed protocol is secure against internal and external attack in theory. The qubit efficiency of the protocol reaches 66.7 % , which is significantly superior to existing schemes.
Abstract Based on Bell states, a new semi-quantum private comparison protocol is proposed that enables two classical users to securely compare the equality of their private information with the aid of a semi-honest third party. Different from the existing semi-quantum private comparison protocols, the two classical participants in the presented protocol do not need to measure and prepare any quantum state, which not only reduces the consumption of quantum devices, but also greatly improves the feasibility of the protocol. Performing different unitary operations on the received particles, classical users can securely compare their secret information. Besides, the devised protocol has higher qubit efficiency than the other similar counterparts, since participants can compare a two-bit privacy each time with one qubit. Meanwhile, after completing the comparison process, all Bell states could be reused since they still retain the corresponding entanglement property, which greatly facilitates the recycle of quantum resources. Security analyses indicate that the designed scheme is secure against external attack and internal attack. Moreover, the operations involved in our scheme are simulated on the IBM Quantum Experience to demonstrate the effectiveness and security of our scheme.
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 secretswithout any information leakage. To reduce the consumption of quantum devices, the qubit efficiency of our protocol isimproved by introducing the semi-quantum conception via the existing semi-quantum privatecomparisons. 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.
Semi-Quantum Private Comparison and Hamming Distance Calculation Based on ddd–Dimensional Bell States
This paper presents a semi-quantum private comparison and Hamming distance computation protocol based onddd-dimensional Bell states. The proposed protocol enables two parties, with the assistance of a trusted third party (TP), to determine whether their private information is identical and compute the Hamming distance without disclosing their secrets. In this protocol, the TP preparesddd-dimensional Bell states and distributes the entangled particles to Alice and Bob. Alice and Bob predetermine specific positions where they will perform REFLECT or MEASURE operations. Based on their measurement results, both parties encode their secret information and transmit the results to the TP via a classical channel. The TP then compares the data by incorporating pre-recorded offsets to determine whether the secrets are equal and to compute the Hamming distance, while ensuring that no private information is directly exposed. Compared to existing protocols, the proposed method demonstrates broader applicability in scenarios with limited quantum resources. To validate the protocol, we provide concrete examples demonstrating its theoretical and practical feasibility. Furthermore, security and efficiency analyses confirm its robustness against various external attacks and potential internal threats, including dishonest TP behavior.
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.
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.