Consider a process being controlled remotely by a controller. Let an attacker have access to the communication channel so that she is able to replace the signal transmitted by the controller with any signal she wishes. The attacker wishes to degrade the control performance maximally without being detected. The controller wishes to detect the presence of the attacker by watermarking signaling information in the control input without degrading the control performance. There are no other assumptions on the capabilities of the attacker and the controller. We present an information theoretic formulation of the problem. Our main result is to show that in the one step version of the problem, if the watermark is a Gaussian distributed random variable, then the maximal performance degradation for any given level of stealthiness for the attacker is achieved when the attacker replaces the control input with the realization of a Gaussian random variable. Conversely, we show the watermark signal that minimizes the stealthiness of a Gaussian attacker is also Gaussian.