There is an increasing trend for businesses to migrate their systems towards the cloud. Security concerns that arise when outsourcing data and computation to the cloud include data confidentiality and privacy. Given that a tremendous amount of data is being generated everyday from plethora of devices equipped with sensing capabilities, we focus on the problem of access controls over live streams of data based on triggers or sliding windows, which is a distinct and more challenging problem than access control over archival data. Specifically, we investigate secure mechanisms for outsourcing access control enforcement for stream data to the cloud. We devise a system that allows data owners to specify fine-grained policies associated with their data streams, then to encrypt the streams and relay them to the cloud for live processing and storage for future use. The access control policies are enforced by the cloud, without the latter learning about the data, while ensuring that unauthorized access is not feasible. To realize these ends, we employ a novel cryptographic primitive, namely proxy-based attribute-based encryption, which not only provides security but also allows the cloud to perform expensive computations on behalf of the users. Our approach is holistic, in that these controls are integrated with an XML based framework (XACML) for high-level management of policies. Experiments with our prototype demonstrate the feasibility of such mechanisms, and early evaluations suggest graceful scalability with increasing numbers of policies, data streams and users.