Cryptanalysis and melioration of secure quantum sealed-bid auction with post-confirmation

We investigate the quantum sealed-bid auction protocol proposed by Zhao et al. (Opt Commun 283:1394, 2010). It uses M groups n-particle GHZ states to represent bids and a post-confirmation mechanism to guarantee the honesty of the quantum sealed-bid auction. However, in our opinion the protocol still does not complete the task of a sealed-bid auction fairly. It is shown that a large group of dishonest bidders can collude to obtain all the other one’s secret bids before the opening phase of the auction with a probability polynomially close to one. Moreover, a simple feasible improvement of the protocol is proposed.