A certificateless (t,n) threshold signature (CLTS) scheme allows at least t members to cooperatively sign a message on behalf of an n-member group,which is a good way to share the responsibility and authority.Many researchers have focused on CLTS schemes in the literature.However,these schemes numerously employ a single key generation center (KGC) and thus inevitably suffer from single point of failure and abuse of single key generator center.To settle these problems,Xiong et al.[1] introduced the concept of fully distributed CLTS,in which multiple distributed KGCs take the responsibility of generating and allocating the entity partial private key to distributed signers.Nevertheless,in their definition,each of the distributed KGCs directly generates and sends an entity partial private key share to a signer,which implicates two assumed conditions.One is that the number of KGCs and signers is the same,which results in poor scalability.The other one is that the collusion between KGCs and signers is forbidden,which weakens their security model.