With rapid growth of mobile wireless networks, handheld devices are popularly used by people and many mobile applications have been rapidly developed. Considering the limited computing capability of smart cards or mobile devices, the security scheme design suitable for these mobile devices is a nontrivial challenge. A user authentication scheme is a mechanism to authenticate a remote user over an open network. In 2006, Das et al. proposed an identity (ID)based remote user authentication scheme with smart cards using bilinear pairings. Unfortunately, their scheme is insecure against forgery attack. Recently, Giri and Srivastava proposed an improved scheme to overcome the forgery attack. The computational cost required by the Giri