Cryptanalysis and Improvement of the Multi-User QPCE Protocol with Semi-Honest Third Party

In a recent work Quantum Inf. Process 12 (2013) 1077, a multi-user protocol of quantum private comparison of equality (QPCE) is presented. Here we point out that if we relax the constraint of a semi-honest third party, the private information of the users will be totally leaked out to the third party. A special attack is demonstrated in detail. Furthermore, a possible improvement is proposed, which makes the protocol secure against this kind of attack.