Some remarks on security of receipt-free E-auction

Recently, a receipt-free scheme is rising for a secure e-auction. The goal of a receipt-free scheme in an e-auction is to prevent a bid-rigging. If the bid-rigging happens in the e-auction. the winner can get the bidding item with an unreasonably low price. The first receipt-free scheme tea: the e-auction was proposed by Abe and Suzuki. Chen, Lee and Kim also proposed the extended receipt-free scheme. In this paper, we point out that the proposed receipt-free schemes do nor prevent perfectly the bid-rigging attack. Moreover, we indicate that a bid-collision is a possible cause of an e-auction. In the strict sense, the bid-collusion is different fro m the bid-rigging. In this paper, we do not present the scheme which can prevent the bid-collision attack. We compare the bid-rigging attack with the bid-collusion attack, and analyze the security of the existed receipt-free schemes in a viewpoint of the bidrigging attack and the bid-collusion attack.