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Multimedia data, ranging from text, audio, video to animation, undergoes intellectual property protection or has high sensitivity. To deal with privacy leakage during multimedia sharing and dissemination, it is crucial to trace the origin and transformation history of multimedia data, which is called multimedia provenance. In this paper, we construct a multimedia access control system with secure provenance in fog-cloud computing networks, which is designed based on attribute based encryption (ABE) and zero of knowledge technologies. The proposed scheme realizes confidentiality of multimedia big data that is outsourced to the cloud, anonymity of data provider, fine-grained access control of encrypted data, irrefutable of the provenance data, and traceability of data provider. We utilize the fog server to reduce user's decryption burden and transfer partial decryption tasks. The suggested system is formally proved indistinguishable against chosen plaintext attack (IND-CPA). The simulation and experimental results indicate that our system has low communication overhead and low computation cost. [ABSTRACT FROM AUTHOR]