Multi-party quantum private size comparison protocol with d-dimensional Bell states

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.