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Secure multi-unit sealed first-price auction mechanisms

Due to the popularity of auction mechanisms in real-world applications and the increasing awareness of securing private information, auctions are in dire need of bid-privacy protection. In this paper, we design three secure, multi-unit, sealed-bid, first-price auction schemes. The first is a secure auction using homomorphic encryption and is denoted by SAHE; the second is a secure action using masking values and is denoted by SAMV; and the third has an improved masked noise algorithm, denoted by ISAMV. In the first, SAHE, the auction is processed on encrypted bids by a server, and the final output is only known by the auctioneer. Neither the auctioneer nor the server can obtain the full information of the bidders. The second and third auctions, SAMV and ISAMV, decrease computational complexity. Instead of homomorphic encryption, they use random noise to mask the bid values. By using a masking method, the server only knows the noise, and the auctioneer only knows the auction results; neither will see the private information of the bidders. All three schemes enable the auctioneer to verify that the winners have paid the correct amounts. A thorough theoretical analysis is performed to evaluate the security properties, computational complexity, and communication complexity of the auctions. Copyright © 2016 John Wiley & Sons, Ltd.