The loophole of the improved secure quantum sealed-bid auction with post-confirmation and solution

In the literature He et al. (Quantum Inf Process, 2011 ) performed the cryptanalysis about the protocol of secure quantum auction with post-confirmation, and proposed the melioration algorithm in order to defeat the collusion among some malicious bidders in Zhao et al.’s protocol (Zhao et al. in Opt Commun 283:3194, 2010 ). But unfortunately, this protocol can’t defeat the collusion among some malicious bidders either. In this paper, we will analyze the security of He et al.’s protocol and point out the potential loophole. Furthermore, we propose an improved protocol which can defeat the collusion among malicious bidders effectively.