Routers are located at the core of communication networks such as the Internet and sensor networks. The routing algorithms deployed in routers have a profound impact on network security. The traditional shortest-path algorithm used in OSPF and other routing protocols has inherent vulnerability to certain types of attacks. These routing algorithms also influence the life span of the switches and routers with high sensitivity to energy consumption. In this paper, we address these challenges by developing a novel routing algorithm with a randomization process so that packets are sent through optimal yet less predictable paths. It is expected that this process will help increase the network defense against eavesdropping and jamming attacks. It is also expected to improve the energy consumption in sensor networks and similar ad hoc networks.