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Advanced Quantum Technologies

Efficient Multi‐Party Semi‐Quantum Private Comparison Protocol Based on Bell States

Yang‐Yang Zhou, Yun‐Ping Wang, Jing‐Yi Dai, Li‐Hua Gong

Published Aug 19, 2025• 9 citations
Publisher

Abstract

Abstract An efficient multiparty semi‐quantum private comparison protocol based on Bell states is proposed. The proposed protocol enables the comparison of private information equality among multiple classical participants with the assistance of two semi‐honest third parties. Unlike previous protocols, the proposed protocol can be further extended to resist the collective‐dephasing noise and the collective‐rotation noise, respectively. The proposed protocol and its extensions do not require the classical participants to generate and send new quantum states to the third party, and these participants can compare two privacies within one round of comparison. In addition, the protocol performs better with a qubit efficiency up to 25%. The security analysis indicates that the protocol is resilient to various known quantum attacks. Furthermore, the feasibility of this protocol is confirmed by simulation results on the IBM quantum platform.

DOI
10.1002/qute.202500439

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Abstract An efficient multiparty semi‐quantum private comparison protocol based on Bell states is proposed. The proposed protocol enables the comparison of private information equality among multiple classical participants with the assistance of two semi‐honest third parties. Unlike previous protocols, the proposed protocol can be further extended to resist the collective‐dephasing noise and the collective‐rotation noise, respectively. The proposed protocol and its extensions do not require the classical participants to generate and send new quantum states to the third party, and these participants can compare two privacies within one round of comparison. In addition, the protocol performs better with a qubit efficiency up to 25%. The security analysis indicates that the protocol is resilient to various known quantum attacks. Furthermore, the feasibility of this protocol is confirmed by simulation results on the IBM quantum platform.
Abstract Based on the decoherence‐free states, two multi‐party semi‐quantum private comparison protocols are proposed to counteract collective noises. One can resist the collective‐dephasing noise well, and the other can resist the collective‐rotation noise. With the assistance of a semi‐honest third party (TP), multiple classical participants with restricted quantum abilities can compare their secret information by performing the proposed protocols once. It is manifested that the proposed protocols can resist both external attacks and internal attacks. Additionally, the operations in the multi‐party semi‐quantum private comparison protocols are simulated on the IBM Quantum Experience.
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.
Abstract In this paper, we propose a novel semiquantum private comparison (SQPC) protocol based on Bell states, which enables one quantum user and one classical user to compare the equality of their private inputs with the help of a semi-honest quantum third party (TP). TP is assumed to be semi-honest in the sense that she may take all possible attacks to steal users’ private inputs except conspiring with anyone. The security analysis validates that our protocol can resist not only the attacks from internal participants but also the attacks from an external eavesdropper. Besides, our protocol only asks TP to perform Bell basis measurements but does not need quantum entanglement swapping; and it releases the classical user from conducting quantum measurements and having a quantum memory. Moreover, our protocol can take advantage over previous SQPC protocols based on Bell states in qubit efficiency. Finally, our protocol can be generalized into its counterpart of the collective-dephasing noise quantum channel.
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.
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.
Abstract 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.