In the smart environments several smart devices are continuously working together to make individuals' lives more comfortable. Few of the examples are smart homes, smart buildings, smart airports, etc. These environments consist of many resource constrained heterogeneous entities which are interconnected, controlled, monitored and analyzed through the Internet. One of the most challenging tasks in a distributed smart environment is how to provide robust security to the resource constraint Internet-enabled devices. However, an authentication can play a major role ensuring that only authorized devices are being connected to the distributed smart environment applications. In this paper, we present a robust and lightweight mutual-authentication scheme (RLMA) for protecting distributed smart environments from unauthorized abuses. The proposed scheme uses implicit certificates and enables mutual authentication and key agreement between the smart devices in a smart environment. The RLMA not only resists to various attacks but it also achieves efficiency by reducing the computation and communication complexities. Moreover, both security analysis and performance evaluation prove the effectiveness of RLMA as compared to the state of the art schemes.