We consider a cloud-based control architecture for a linear plant with Gaussian process noise, where the state of the plant contains a client's sensitive information. We assume that the cloud tries to estimate the state while executing a designated control algorithm. The mutual information between the client's actual state and the cloud's estimate is adopted as a measure of privacy loss. We discuss the necessity of uplink and downlink privacy masks. After observing that privacy is not necessarily a monotone function of the noise levels of privacy masks, we discuss the joint design procedure for uplink and downlink privacy masks. Finally, the trade-off between privacy and control performance is explored.