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Physica Scripta

Star-network multi-party semi-quantum private comparison with delegated measurement-device independence

Cao Meng-yan, Ri‐Gui Zhou, Lin-Tao Du

Published Oct 8, 2026• 0 citations
Publisher

Abstract

Abstract Multi-party semi-quantum private comparison (MSQPC) aims to determine equivalence relations among private inputs while requiring only restricted quantum operations at the user side. Representative existing approaches mainly provide global multi-party equality testing or selected pairwise comparisons, whereas a direct all-pairs construction requires a quadratic number of pairwise quantum links. We propose a star-network delegated measurement-device-independent MSQPC protocol that establishes only N − 1 hub–branch quantum masking correlations and recovers all N ( N − 1 ) / 2 pairwise equivalence relations, together with the corresponding equivalence-class partition, through classical algebraic elimination without pre-shared comparison keys. State preparation and measurement are separated between a semi-honest third party (TP) and an untrusted UTP, while decoherence-free subspace encoding and partial logical Bell-state measurement improve robustness against collective phase noise and measurement-side abnormalities. Under TP–UTP non-collusion, authenticated classical channels, secure commitment, sufficient conditional input min-entropy, and the session-digest pseudorandomness assumption, the protocol provides explicit finite-sample security verification while reducing the network-wide quantum-link requirement from quadratic to linear.

DOI
10.1088/1402-4896/aeb203

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Abstract Multi-party semi-quantum private comparison (MSQPC) aims to determine equivalence relations among private inputs while requiring only restricted quantum operations at the user side. Representative existing approaches mainly provide global multi-party equality testing or selected pairwise comparisons, whereas a direct all-pairs construction requires a quadratic number of pairwise quantum links. We propose a star-network delegated measurement-device-independent MSQPC protocol that establishes only N − 1 hub–branch quantum masking correlations and recovers all N ( N − 1 ) / 2 pairwise equivalence relations, together with the corresponding equivalence-class partition, through classical algebraic elimination without pre-shared comparison keys. State preparation and measurement are separated between a semi-honest third party (TP) and an untrusted UTP, while decoherence-free subspace encoding and partial logical Bell-state measurement improve robustness against collective phase noise and measurement-side abnormalities. Under TP–UTP non-collusion, authenticated classical channels, secure commitment, sufficient conditional input min-entropy, and the session-digest pseudorandomness assumption, the protocol provides explicit finite-sample security verification while reducing the network-wide quantum-link requirement from quadratic to linear.
Abstract In this paper, we utilize d-dimensional Bell states to construct a multi-party semiquantum private comparison (MSQPC) protocol with two supervisors, which can determine the size relationship of more than two classical users’ private inputs under the control of two supervisors within one round implementation. The two supervisors, i.e., one quantum third party (TP) and one classical TP, are both semi-honest, which means that they can misbehave at their own wishes but are not permitted to conspire with anyone else. Neither quantum entanglement swapping nor unitary operations are required in the proposed MSQPC protocol. The security analysis certifies that the proposed MSQPC protocol can overcome both the outside attacks and the participant attacks.
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 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 In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d -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 d -dimensional single-particle measurements rather than d -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 n 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.
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.
Abstract Semi-quantum private comparison (SQPC) security depends not only on quantum resources, but also on how verification evidence is generated and trusted. We examine the single-particle SQPC protocol of Ye et al as a representative case. Its source-defined semi-honest third party (TP) may perform possible attacks subject to non-collusion, while the prescribed TP-honesty checks rely on measurement evidence produced by the TP itself. We therefore investigate a reporting-trust boundary: an active-TP interpretation in which a malicious TP may falsify its own authenticated measurement reports or checking decisions. Under this adversarial self-reporting model, causally valid fake-state and intercept–measure–resend attacks recover the Alice–Bob intermediate key K A B and hence both individual private inputs without using future Alice/Bob operation information, while preserving the intended comparison relation. The prescribed checking procedure does not reject these attacks under the stated self-reporting interpretation. A participant-side replacement attack provides a contrast: it can compromise confidentiality on surviving executions, but the original first check detects the full-replacement strategy with high probability. The analysis distinguishes confidentiality, detectability, and comparison correctness, identifies four structural screening factors, and uses secret separation as a reference enhancement illustrating the independent secret resource needed to protect individual inputs. Protocol-level Monte Carlo results agree with the analytical predictions. Under adversarial self-reporting, both TP-side attacks achieve unit per-bit private-input reconstruction rates while maintaining unit comparison-correctness rates and producing zero rejection by the prescribed checking procedure. In contrast, the participant-side full-replacement strategy is detected with probability approximately 0.984 at N = 16 . With secret separation, individual per-bit reconstruction returns to approximately the 0.5 random-guessing baseline while comparison correctness remains unchanged.