可公開驗證出價合法性的彌封式拍賣系統

Abstract

我們提出了一個具有可公開驗證出價合法性的拍賣系統。我們的想法結合了可驗證的加密知識簽章系統及公開金鑰之重新加密的證明。我們在對管理者的設計上，使用了兩種不同的管理者，註冊管理者及拍賣管理者，避免僅用一種管理者而使得管理者的權限過大。註冊管理者確認出價者的身分及其公開金鑰之間的對應關係，拍賣管理者則是管理拍賣時的一切活動。在我們的系統中，出價合法性不只包括了對出價價格的合法性更包括了出價者身分的合法性。我們最主要的設計便是使任何第三者都可以公開的驗證出價者出價的合法性卻又得不到與出價者身分及出價價格相關的任何訊息。如果任何人發現有不合法的出價都可以向拍賣管理者檢舉進而要求拍賣管理者撤銷該筆出價。因此我們的系統可以抵抗惡意的出價者提出不合法的出價干擾拍賣。 除此之外，在我們的系統中，我們將出價者的簽章和出價價格結合當做出價內容。而我們系統中所使用的簽章簽名時需要出價者所記憶的密碼與儲存在出價者可攜式裝置中的部分私鑰一同配合使用，藉以增加安全性。

We proposed a sealed-bid auction with publicly verifiable bid validity, which is based on verifiable encryption of signature of knowledge and 1-out-of-P re-encryption proof of encryption keys. In our scheme, we have two semi-trusted managers, the registration manager RM and the auction manager AM. The registration manager RM guarantees the relationship between a bidder and his corresponding public key. The auction manager AM holds an auction and manages operations in an auction. Bid validity in our scheme contains the validity of both bidding price and the bidder. In our scheme, every one can verify the validity of the bid, but he can not get any information about the relation of the bidder’s identity and his bidding price. If there are invalid bids, anyone can ask the auction manager AM to revoke them. Hence, our scheme can prevent malicious bidders to disturb the auction. Besides, in our scheme, we combine the bidder’s signature and his bidding price as the bid. The signature we use here needs the bidder’s password memorized in his mind and the corresponding partial secret stored in his mobile device to increase the security.