Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states

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 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.

Efficient Quantum Private Comparison without Sharing a Key

“…According to Equation (7), when the state of the first particle of |GHZ 1 is |0 , the state of the other two particles of |GHZ 1 corresponds to the Bell state |Φ + . When the state of the first particle of |GHZ 1 is |1 , the state of the rest particles of |GHZ 1 corresponds to the Bell state |Ψ + .…”

“…QKD technology primarily relies on the fundamental principles of quantum mechanics to ensure that users generate secure and dependable keys during the communication progress [3,4]. Moreover, the goal of quantum private comparison is to enable both parties to compare their secret data without revealing any information about the data to each other or any potential eavesdropper [5][6][7]. QPC has potential applications in a variety of fields, including secure online voting, financial transactions, and data sharing between government agencies.…”

Novel semi-quantum private comparison protocol with Bell states

“…Besides, to compare both the size and the equality of privacies, Chen et al came up with a novel two-party QPC protocol via quantum walks on circle [8]. Other than that, there are considerable QPC protocols based on other quantum states that have been investigated [9][10][11][12].…”

Different Secure Semi-quantum Summation Models without Measurement

“…Subsequently, Ye et al presented a more practical protocol capable of resisting collective-dephasing noise, although it failed to achieve the participants' summation results if a trusted party is absent [30]. In 2024, Lian et al expanded from dimension 2 to dimension d, aiming to facilitate modulo d addition for more than three semi-quantum users' private integers [31]. However, ongoing research on SQS faces several challenges:…”