Denial-of-service (DoS) attacks against server resources exhaustion are a major security threat to the Internet. A number of defense mechanisms have been proposed against such attacks. Recently, Aura et al. proposed a solution to resist DoS attacks against an authentication protocol. However, their puzzle solution cannot guarantee that all of their clients have fair computation time to solve a puzzle. The solution may even render some clients unable to obtain the puzzle solution within the lifetime, resulting in a lack of service from the server. In this paper, a simple solution as well as an applied authentication protocol was proposed.