Future IoT services execution may benefit from combining resources at cloud and at the edge. To that end, new architectures should be proposed to handle IoT services in a coordinated way at either the edge of the network, the cloud, or both. Reacting to that need, the Fog-to-Cloud concept has been recently proposed. A key aspect in the F2C design refers to security, since F2C raises security issues besides those yet unsolved in fog and cloud. Thus, we envision the need for new security strategies to handle all components in the F2C architecture. In this paper we propose an SDN-based (mater/slave) security architecture leveraging a centralized controller on the cloud, and distributed controllers at the edge of the network. We argue that the proposed architecture brings more security and privacy to the cloud users by reducing the distance between them and, therefore, reducing the risks of the so called man-in-the-middle attacks. The proposed security architecture is analyzed in some critical infrastructure scenarios in order to illustrate their potential benefits.