We propose a generic method to construct forward-secure signature schemes from standard signature schemes. The proposed construction is more computationally efficient than previously proposed schemes. In particular, the key updating operation in the proposed scheme is orders of magnitude more computationally efficient than previous schemes, making it attractive for a variety of applications, such as electronic checkbooks. Another advantage of our proposed scheme is the ability to be easily extended to proxy signature schemes. We define two notions of forward-security in the proxy signature setup, namely, strong forward-secure proxy signatures and weak forward-secure proxy signatures. We then describe a construction of a scheme that satisfies the strong forward-secure proxy signature property.