System state estimation and control are important issues to ensure the stability and reliability of the smart grid system. In this paper, the problem of how to securely estimate the system state and control the smart grid is studied. In the setup studied, the sensor(s) and the controller communicate with each other through a wireless channel subjected to monitoring by an eavesdropper. The channel capacity requirement that ensures negligible information leakage to the eavesdropper about the system state and control messages is studied from the information theoretic perspective. Two scenarios with single sensor or multiple sensors are studied. Numerical simulations are used to evaluate the capacity requirement in typical configurations of the smart grid.