  Recently, Liu W et al. proposed a two-party quantum private comparison (QPC)
protocol using entanglement swapping of Bell entangled state (Commun. Theor.
Phys. 57(2012)583-588). Subsequently, Liu W J et al. pointed out that in Liu W
et al.'s protocol, the TP can extract the two users' secret inputs without
being detected by launching the Bell-basis measurement attack, and suggested
the corresponding improvement to mend this loophole (Commun. Theor. Phys.
62(2014)210-214). In this paper, we first point out the information leakage
problem toward TP existing in both of the above two protocols, and then suggest
the corresponding improvement by using the one-way hash function to encrypt the
two users' secret inputs. We further put forward the three-party QPC protocol
also based on entanglement swapping of Bell entangled state, and then validate
its output correctness and its security in detail. Finally, we generalize the
three-party QPC protocol into the multi-party case, which can accomplish
arbitrary pair's comparison of equality among users within one execution.
