Despite the large amount of Byzantine fault-tolerant algorithms for message-passing systems designed through the years, only recently algorithms for the coordination of processes subject to Byzantine failures using shared memory have appeared. This paper presents a new computing model in which shared memory objects are protected by fine-grained access policies, and a new shared memory object, the policy-enforced augmented tuple space (PEATS). We show the benefits of this model by providing simple and efficient consensus algorithms. These algorithms are much simpler and use less memory bits than previous algorithms based on ACLs and sticky bits. We also prove that PEATSs are universal (they can be used to implement any shared memory object), and present a universal construction.