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We develop a secure keyword auction mechanism in which winners and payments are calculated without making bidding prices and CTRs public. First, we show that even if we utilize cryptographic techniques, the auctioneer can learn most bidding prices in existing keyword auction mechanisms, such as the Generalized Second Price (GSP) and the Vickrey-Clarke-Groves (VCG) mechanism. Thus we propose a new auction mechanism by introducing a simple but sufficient payment rule to prevent the leakage of bidding prices. The existing GSP is not strategy-proof, and neither is our new mechanism. However, possible manipulations are limited. We also propose a secure keyword auction scheme that securely realizes our mechanism by utilizing cryptographic techniques.