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.The firstly proposed multi-authority signature scheme was that many attributes were monitored by many different authorities respectively and its attributes were picked from the large universe.By using the methodology of reduction security argument,the security of this scheme was proved equal to the computational Diffie-Hellman problem.Two characteristics of the scheme are the existential unforgeability and the prevention of collusion attacks.