Multi-party semiquantum private comparison of size relationship with d-dimensional Bell states

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.