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.

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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.

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