As a distributed extension of ciphertext-policy attribute-based encryption (CP-ABE), multi-authority ABE (MA-ABE) does not require the participation of a trusted central authority and has a wider application prospect in the decentralized background of the cloud computing environment. We propose the first MA-ABE scheme supporting multi-fan-in circuits and collusion-resistance on prime-order bilinear groups and prove the fully adaptive security based on the matrix decision Diffie-Hellman (MDDH) assumption. Compared with the only two fully adaptively secure MA-ABE schemes, our scheme enjoys shorter parameters, which has lower ciphertext and key size, and supports many-use of attribute.
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