Attribute-based signature (ABS) is a new cryptographic primitive, in which a signer can sign a message with his attributes, and the verifier can only known whether the signer owns attributes satisfying his policy. Moreover, the signature cannot be forged by any user not having attributes satisfying the policy. ABS has many applications, such as anonymous authentication, and attribute-based messaging systems. But many applications may require a user obtaining attributes from different authorities, which calls for multi-authority ABS schemes.