Optimal resilient threshold GQ signatures

GQ signature scheme is widely used in many cryptographic protocols, such as forward-secure signature scheme, identity-based signature scheme, etc. However, there is no threshold version of this important signature scheme in the open literature. We proposed the first threshold GQ signature scheme. The scheme is proved unforgeable and robust against any adaptive adversary by assuming hardness of computing discrete logarithm modulo a safe prime and existence of fully synchronous broadcast channel. Furthermore, with some modifications, our scheme achieves optimal resilience such that the adversary can corrupt up to a half of the players. As an extension of our work, we provided a threshold identity-based signature scheme and a threshold forward-secure signature scheme, which is the threshold version of the most efficient forward-secure signature scheme up to now.