Perfect forward secrecy is considered as the most important standard to evaluate a strong authentication scheme. There are many results researched to achieve this property without using hard problems. Recently, the result of Chang et al has some advances such as, the correctness of schemes mutual authentication and session key agreement demonstrated in BAN-logic or the overheads reduction of system implementation. However, in this paper, we prove that their scheme is still vulnerable to impersonation attacks and session key leakage. To overcome those limitations and be practical, we use different notion to propose time efficient scheme conducted in experiment. Our proposed method can be applied for remote user authentication in various scenarios, including systems with user authentication using mobile or wearable devices.