Security researchers have stated that the core concept behind current implementations of access control predates the Internet. These assertions are made to pinpoint that there is a foundational gap in this field, and one should consider revisiting the concepts from the ground up. Moreover, Insider threats, which are an increasing threat vector against organizations are also associated with the failure of access control. Access control models derived from access control matrix encompass three sets of entities, Subjects, Objects and Operations. Typically, objects are considered to be files and operations are regarded as Read, Write, and Execute. This implies an `open sesame' approach when granting access to data, i.e. once access is granted, there is no restriction on command executions. Inspired by Functional Encryption, we propose applying access authorizations at a much finer granularity, but instead of an ad-hoc or computationally hard cryptographic approach, we postulate a foundational transformation to access control. From an abstract viewpoint, we suggest storing access authorizations as a three-dimensional tensor, which we call Access Control Tensor (ACT). In Function-based Access Control (FBAC), applications do not give blind folded execution right and can only invoke commands that have been authorized for data segments. In other words, one might be authorized to use a certain command on one object, while being forbidden to use exactly the same command on another object. The theoretical foundations of FBAC are presented along with Policy, Enforcement and Implementation (PEI) requirements of it. A critical analysis of the advantages of deploying FBAC, how it will result in developing a new generation of applications, and compatibility with existing models and systems is also included. Finally, a proof of concept implementation of FBAC is presented.