In this paper, a design schema of a security authentication system combined with fingerprint identification and public key cryptography is explored, and its specific security mechanism is discussed in detail. In our schema, fingerprint is added into user's private key and served as a security parameter, such that user's secret key is separated into secret key parameters and fingerprint, by secret splitting mechanism, which makes the secret key to be bounded with user's information. This will increase the security of secret key ultimately. In such an authentication system, the diplex authentication technologies --- fingerprint and smart card --- are adopted, and the user fingerprint needn?t to be transmitted during the authentication process, which can protect user's privacy effectively.