Forward-secure threshold signature schemes

Abstract

We construct forward-secure threshold signature schemes. These schemes have the following property: even if more than the threshold number of players are compromised, it is not possible to forge signatures relating to the past. This property is achieved while keeping the public key fix ed and updating the secret keys at regular intervals. The schemes are reasonably efficient in that the amount of secure storage, the signature size and the key lengths do not vary proportionally to the number of time periods during the lifetime of the public key. Both proposed schemes are based on the Bellare-Miner forward-secure signature scheme. One scheme uses multiplicative secret sharing and tolerates mobile eavesdropping adversaries. The other scheme is based on polynomial secret sharing and tolerates mobile halting adversaries. We prove both schemes secure via reduction to the Bellare-Miner scheme, which is known to be secure in the random oracle model assuming that factoring is hard.