Attribute-based signature (ABS),which could realize fine-grained access control,was considered to be an important method for anonymous authentication in cloud computing.However,normal ABS only provided simple access control through threshold structure and thus could not cope with the large-scale attribute sets of users in the cloud.Moreover,the attribute sets were supervised by only one attribute authority,which increased the cost of computation and storage.The whole system was in danger of collapsing once the attribute authority was breached.Aiming at tackling the problems above,a novel scheme,was proposed called multi-authority ABS supporting dendritic access structure which supported any AND,OR and threshold gates and affords more flexible access control.Meanwhile,the attribute sets of users were classified by diverse attribute authorities which reduced the overhead and the risk of systems.Besides,the scheme is proved to be selective predicate chosen message attack secure in the random oracle model.