With the ever-increasing demands on multimedia applications, cloud computing, due to its economical but powerful resources, is becoming a natural platform to process, store, and share multimedia contents. However, the employment of cloud computing also brings new security and privacy issues as few public cloud servers can be fully trusted by users. In this paper, they focus on how to securely share video contents to a certain group of people during a particular time period in cloud-based multimedia systems, and propose a cryptographic approach, a provably secure time-domain attribute-based access control (TAAC) scheme, to secure the cloud-based video content sharing. Specifically, they first propose a provably secure time-domain attribute-based encryption scheme by embedding the time into both the cipher texts and the keys, such that only users who hold sufficient attributes in a specific time slot can decrypt the video contents. They also propose an efficient attribute updating method to achieve the dynamic change of users' attributes, including granting new attributes, revoking previous attributes, and regranting previously revoked attributes. They further discuss on how to control those video contents that can be commonly accessed in multiple time slots and how to make special queries on video contents generated in previous time slots. The security analysis and performance evaluation show that TAAC is provably secure in generic group model and efficient in practice.