Weakness of two ID-based remote mutual authentication with key agreement protocols for mobile devices

Recently, Yoon et al. and Wu proposed two improved remote mutual authentication and key agreement schemes for mobile devices on elliptic curve cryptosystem. In this paper, we show that Yoon et al.’s protocol fails to provide explicit key perfect forward secrecy and fails to achieve explicit key confirmation. We also point out Wu’s scheme decreases efficiency by using the double secret keys and private/public pair, and is vulnerable to the password guessing attack and the forgery attack.