In this paper we propose a method for authenticating the application that is to be downloaded or updated in smart cards. Previous works have some drawbacks such as having a long verification delay or requiring a large amount of primary/secondary storage. We propose an efficient parameterized scheme by using the hash chain technique where the secondary storage requirement and verification delay of updating the application are O(k) and O(k＋n/k), respectively. Moreover, both the first storage requirement and verification delay of downloading the application are O(1).