Central authority free multi-authority attribute based encryption scheme for short messages will be presented. Several multi-authority attribute based encryption schemes were recently proposed. We can divide these schemes into two groups, one of them are the ciphertext-policy attribute based encryption schemes (CP-ABE), the another one are the key-policy attribute based encryption schemes (KP-ABE). In our new multi-authority attribute based encryption scheme we combine them: the access structure will be given by authorities and the encryptor in conjunction. The authorities will be able to decide who is able to decrypt a ciphertext under their names, but the encryptor will choose the authorities whom he would involve in the encryption. In addition, our scheme is free of any central authority. The security of our new scheme relies on the decisional 3-party Diffie-Hellman assumption.