On the security of Wu-Lin's robust key authentication scheme

In 2004, Wu-Lin pointed out that Lee et al.'s key authentication scheme is vulnerable to public key substitution attacks. For enhancing the security, Wu-Lin proposed a simply improved key authentication scheme with better efficiency and a robust key authentication scheme resistant to public key substitution attacks. However, in this paper, we will show that Wu-Lin's robust key authentication scheme is still vulnerable to public key substitution attack. Also, we will show that Lee et al.'s scheme and Wu-Lin's efficiency improved key authentication scheme are vulnerable to simple public key substitution attack than Wu-Lin's attack method.