User authentication scheme with privacy-preservation for multi-server environment

New user authentication schemes for multiple-servers environment were proposed by Liao-Wang and Tsai. In their schemes, application servers do not need to maintain a verification table and this admired merit is not addressed by previous scholarship. Besides, the privacy of users is also addressed in Liao-Wang's scheme. In this article, we show that their schemes are not secure against the server spoofing and the impersonation attacks. Then we propose a robust user authentication scheme to withstand these attacks and keep the same merits.