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IEEE International Conference on Quantum Control, Computing and Learning (qCCL)

Semi-Quantum Private Comparison and Hamming Distance Calculation Based on $d$–Dimensional Bell States

Yi Yang, Min Jiang

Published Jun 25, 2025• 0 citations
Publisher

Abstract

This paper presents a semi-quantum private comparison and Hamming distance computation protocol based on$d$-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 prepares$d$-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.

DOI
10.1109/qccl65142.2025.11157968

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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.
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 In this paper, we propose two multi-party quantum private comparison protocols based on the properties of the d-dimensional GHZ state. Protocol 1 is designed to compare the equality of multiple participants’ secrets with the help of a semi-honest third party TP. The semi-honest TP will follow the protocol honestly, but he may attempt to learn additional information from the protocol execution. In this protocol, multiple participants encode their secret information into the corresponding particles in turn through unitary operations, thereby achieving the comparison of the equality of their multiple secrets in a single execution. This protocol has a wide range of applications. For example, by combining the basic model framework of this protocol with the Chinese Remainder Theorem, we propose Protocol 2. In this protocol, multiple participants compare the size relationships of their multiple secrets with the help of a semi-honest third party TP. Therefore, based on the same basic model framework, the two protocols proposed in this paper can be applied respectively to the comparison of the equality and the size relationships of multiple participants’ secrets. Importantly, the two protocols do not require pre-shared keys. Security analysis shows that the proposed protocols can resist various attacks, including entangle-measure attack, intercept-resend attack, third party attacks, and participant attacks.
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.
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.
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.