Hwang-Lo-Lin proposed a user identification scheme [3] based on the Maurer-Yacobi scheme [6] that is suitable for application to the mobile environment. Hwang-Lo-Lin argued that their scheme is secure against any attack. Against the Hwang-Lo-Lin argument, Liu-Horng-Liu showed that the Hwang-Lo-Lin scheme is insecure against a Liu-Horng-Liu attack mounted by an eavesdrop attacker. However, Liu-Horng-Liu did not propose any improved version of the original identification scheme which is still secure against the Liu-Horng-Liu attack. In this paper, we propose an identification scheme that can solve this problem and a non-interactive public key distribution scheme also.