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Only the trusted server can determine the real identity of a user during the authentication, and any other entities including other users of the system get nothing about the user\u2019s real identity. In addition, the shared key of encryption can be easily computed by the user and trusted server using the Chebyshev map without additional burdensome key management. Once the partnered two users are authenticated by the trusted server, they can easily proceed with the agreement of the session key. 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