We improve the Bellare-Miner (Crypto '99) construction of signature schemes with forward security in the random oracle model. Our scheme has significantly shorter keys and is, therefore, more practical. By using a direct proof technique not used for forward-secure schemes before, we are able to provide better security bounds for the original construction as well as for our scheme.
Bellare and Miner also presented a method for constructing such schemes without the use of the random oracle. We conclude by proposing an improvement to their method and an additional, new method for accomplishing this.