The popularization and conveniences of Internet have changed traditional auction transactions into electronic auction via Internet. In 2006, Chang and Chang proposed an anonymous auction that enabled bidders to bid in anonymous cases without any bonds. However, in the initiation phase, the bidder is unable to be anonymous as there is no mechanism to protect his (her) identity. Therefore, the lawless person might take this chance to do something illegal. Once the latter, who participates in the

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... uction activity, knows the bidder's identity, he may threaten the honest bidder to become the bid winner. This situation may make bidders refuse to bid to avoid damages. To solve the above mentioned matter, in this paper, we propose an efficient anonymous auction protocol, to protect all bidders' identities in both initiation and auction phases with low levels of computation and communication: only 27% and 50% of Chang and Chang protocol, respectively. A problem in anonymous auction protocol is that bidder A impersonates bidder B to participate an auction. This may be harmful to bidder B. We prove the proposed auction protocol is secure against this attack as it is based on the Gap Diffie-Hellman (GDH) assumption.