This study focuses on semi-quantum private comparison (SQPC) protocols, where participants with limited quantum capabilities compare private information with the help of a quantum third party (TP). Yan et al. introduced an SQPC protocol in 2021, but Li et al. later found it vulnerable to double controlled NOT (CNOT) operation attacks and proposed improvements. However, this study identifies a different vulnerability in Yan et al.’s protocol — a reflecting attack that allows information leakage. Bob can intercept and reflect quantum states, avoiding detection and then use Alice’s measurement outcomes and pre-shared key to access her confidential information. The study also proposes an enhanced method to secure the protocol.
This study focuses on semi-quantum private comparison (SQPC) protocols, where participants with limited quantum capabilities compare private information with the help of a quantum third party (TP). Yan et al. introduced an SQPC protocol in 2021, but Li et al. later found it vulnerable to double controlled NOT (CNOT) operation attacks and proposed improvements. However, this study identifies a different vulnerability in Yan et al.’s protocol — a reflecting attack that allows information leakage. Bob can intercept and reflect quantum states, avoiding detection and then use Alice’s measurement outcomes and pre-shared key to access her confidential information. The study also proposes an enhanced method to secure the protocol.
This study identifies a participant attack vulnerability in Li et al.’s SQPC protocol. The participant attack allows a malicious participant, Bob, to obtain the participant Alice’s secret information by intercepting and measuring photons sent to Alice, and later decrypting Alice’s encrypted comparison result. An improved SQPC protocol is proposed to address this problem. The key enhancement is introducing a mutual eavesdropping check requiring the third party and participants to verify they obtain the same photon measurement results. This enables detecting participant attacks like the one identified. The SQPC protocol proposed in this study not only withstands attacks from internal participants but also achieves quantum efficiency almost equivalent to Li et al.’s SQPC protocol. Thus, this study presents a more secure SQPC protocol without compromising quantum efficiency.
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.
The goal of semi-quantum privacy comparison (SQPC) is to use a small amount of quantum capabilities to compare private information for equality. In recent years, research on semi-quantum privacy comparison protocol has made some achievements. However, most of SQPC protocols can merely compare the private information of two parties, and the research of multi-party SQPC protocols are still scarce. If the number of participants is more than two, the protocol needs to be executed multiple times. Therefore, we proposed a multi-party semi-quantum private comparison protocol based on the maximally entangled GHZ-type state, which has the capability to compare the equality of n parties by executing the protocol once. What is more, the transmission of participant’s encrypted information is not through the classical channel, which improves the security of the protocol. Finally, the security analysis shows that outsider attacks, dishonest participants attacks and semi-honest TP attacks are all invalid for this 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.
In this paper, a novel semiquantum private comparison (SQPC) protocol based on single kind of Bell entangled states is proposed, which allows two classical parties to judge the equality of their private inputs securely and correctly under the help of a semi-honest third party (TP) who possesses complete quantum capabilities. TP is allowed to misbehave on her own but cannot conspire with anyone else. Our protocol does not need to share secret keys among different participants in advance, and needs neither unitary operations nor quantum entanglement swapping. Moreover, our protocol only needs to prepare single kind of Bell entangled states as initial quantum resource. Detailed security analysis turns out that our protocol is secure against various outside and participant attacks. Compared with most of the existing SQPC protocols based on Bell entangled states, our protocol is more feasible in practice.
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.