A Practical Electronic Auction with Bids Confidential

In most of the existing cryptographic auctions, the bidders' bids no longer remain confidential if the third parts collude. However, keeping the bids secret in any case is vital to the bidders because the bids are their true evaluations of the commodities and these evaluations may be their critical secrets. A Practical sealed electronic auction scheme of keeping bidders' bids confidential is proposed. No bid is revealed to anyone except the selling price even there exists serious collusion. Any one can verify that bidders follow the protocol to cast their bids and the winning price is correctly resolved according to opening rules. Also, the scheme is much more efficient than the recent publicly verifiable auctions by Brandt. In its typical implementation, the scheme requires at most O(log\-2v) rounds of communication, where v is the range of bidding space. Non-forgery, replay-attack resistance and non-repudiation are achieved by the signature with temporary public key after registration by bidders. And the robustness of the system is based on the zero knowledge proof.