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    "A study on An Electronic Auction"

    During last decade, the Internet has rapidly spread, and thus it has quickened the growth of the trading on the Internet. The Internet allows a business to reach a large number of potential customers and suppliers in a shorter time and a lower cost. As a result, an auction business also expands rapidly on Internet (e.g. Yahoo auction). An electronic auction has become a large system to trade any good. However, this rapid growth of electronic auction can cause different troubles. In realizing an electronic auction scheme, we need to consider from three points: bidder privacy, correctness of system, and efficiency.
    In an electronic auction, it is important to satisfy anonymity for an authority in order to protect the information of who wants a good and a bidder's history of bidding. Such information may be bought and sold through illegal channels. Therefore, nobody should be able to gather the useful trading information with personal data. In anonymous bidding anybody should be able to verify the validity of a winner, while in secret bidding anybody should be able to verify the correctness of a winning bid. Furthermore, each bidder should be able to place a bid efficiency on Internet.
    We realize the following three kinds of auction schemes. An English auction scheme satisfies the efficient bidding and anonymity of bidder. A first-price sealed-bid auction scheme has a single auction manager and satisfies a feature of entertainment as well as anonymity. A second-price sealed-bid auction scheme satisfies the secrecy of the highest bid with public verifiability. It also satisfies anonymity of bidder who places the second highest bid.

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