T Ciphertext policy attribute-based encryption (CP-ABE) is a promising cryptographic technique for fine-grained access control of outsourced data in the cloud. However, some drawbacks of key management hinder the popularity of its application. One drawback in urgent need of solution is the key escrow problem. We indicate that front-end devices of clients like smart phones generally have limited privacy protection, so if private keys are entirely held by them, clients risk key exposure that is hardly noticed but inherently existed in previous research. Furthermore, enormous client decryption overhead limits the practical use of ABE. In this paper, we propose a collaborative key management protocol in CP-ABE. Our construction realizes distributed generation, issue and storage of private keys without adding any extra infrastructure. A fine-grained and immediate attribute revocation is provided for key update. The proposed collaborative mechanism effectively solves not only key escrow problem but also key exposure. Meanwhile, it helps markedly reduce client decryption overhead. A comparison with other representative CP-ABE schemes demonstrates that our scheme has somewhat better performance in terms of cloud-based outsourced data sharing on mobile devices. Finally, we provide proof of security for the proposed protocol.