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A three-factor authentication scheme combines biometrics with passwords and smart cards to provide high-security remote authentication. Most existing schemes, however, rely on smart cards to verify biometric characteristics. The advantage of this approach is that the user's biometric data is not shared with remote server. But the disadvantage is that the remote server must trust the smart card to perform proper authentication which leads to various vulnerabilities. To achieve truly secure three-factor authentication, a method must keep the user's biometrics secret while still allowing the server to perform its own authentication. Our method achieves this. The proposed scheme fully preserves the privacy of the biometric data of every user, that is, the scheme does not reveal the biometric data to anyone else, including the remote servers. We demonstrate the completeness of the proposed scheme through the GNY (Gong, Needham, and Yahalom) logic. Furthermore, the security of our proposed scheme is proven through Bellare and Rogaway's model. As a further benefit, we point out that our method reduces the computation cost for the smart card.