Some aggregate forward-secure signature schemes

Ordinary digital signatures have an inherent weakness: if the secret key is leaked, then all signatures, even the ones generated before the leak, are no longer trustworthy. Forward-secure digital signatures address this weakness, they ensure that the past signatures remain secure even if the current secret key is leaked. Following the notion of aggregate signatures introduced by Boneh et al, which provides compression of signatures, we have come up with aggregate signature schemes for ElGamal/DSA/Bellare-Miner forward-secure signatures. We describe two schemes of aggregation for the Bellare-Miner Scheme. The first is a aggregate signature scheme with aggregation done separately in different time periods.The second is a aggregate signature scheme with aggregation done for a set of time periods.