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In 2009, Yang and Chang proposed an ID-based remote mutual authentication with key agreement scheme on elliptic curve cryptosystem (ECC). Based upon ID-based concept, Yang and Chang scheme (YC scheme) does not require additional computations for certificate and is not constructed by bilinear-pairings, which is an expensive operation on elliptic curve. In addition, YC scheme not only provides mutual authentication but also supports a session key agreement between the user and the server. Therefore, YC scheme is more efficient and practical than the related works. However, we find YC scheme is vulnerable to an impersonation attack and does not provide perfect forward secrecy in spite of efforts to perform mutual authentication and session key agreement between the user and the remote server and reduce the computational costs than the related works. Therefore, this paper proposes an improved …