Abstract: In attribute-based cryptosystem, many attributes of a user were monitored by a single authority, which would inevitably increase its workload and reduce its efficiency. In this paper, a multi-authority signature scheme without a central authority is proposed. In this scheme, many attributes of a user are monitored by many different authorities respectively, in stead of a trusted central authority. The scheme increases the system's applicability. The security of this scheme is proved equal to computational Diffie-Hellman (CDH) problem. So the scheme has two characteristics of existential unforgeability and security preventing collusion attack.