Cloud computing solutions enable Cyber-Physical Systems (CPSs) to utilize significant computational resources and implement sophisticated control algorithms even if limited computation capabilities are locally available for these systems. However, such a control architecture suffers from an important concern related to the privacy of sensor measurements and the computed control inputs within the cloud. This paper proposes a solution that allows implementing a set-theoretic model predictive controller on the cloud while preserving this privacy. This is achieved by exploiting the offline computations of the robust one-step controllable sets used by the controller and two affine transformations of the sensor measurements and control optimization problem. It is shown that the transformed and original control problems are equivalent (i.e., the optimal control input can be recovered from the transformed one) and that privacy is preserved if the control algorithm is executed on the cloud. Moreover, we show how the actuator can take advantage of the set-theoretic nature of the controller to verify, through simple set-membership tests, if the control input received from the cloud is admissible. The correctness of the proposed solution is verified by means of a simulation experiment involving a dual-tank water system.