Threshold Signatures in Dynamic Groups

In this paper we present the efficient solution for the dynamical groups with the variable threshold bound. In fact we consider the more general situation, when there is a family of dynamical groups instead of one group. We were able to handle this more general situation by joining the secret sharing idea together with the certification system device that enabled the system to distinguish the members of distinct groups of the family. The system proposed here is provably secure. The security is proved in the random oracle model, provided the number of corrupted players in the family of groups satisfies the suitable estimates and the "chosen target CDH problem" is computationally hard.