In smart environments, pervasive computing contributes in improving daily life activities for dependent people by providing personalized services. Nevertheless, those environments do not guarantee a satisfactory level for protecting the user privacy and ensuring the trust between communicating entities. In this paper, we propose a trust evaluation model based on user past and present behavior. This model is associated to a lightweight authentication key agreement protocol (EC-SAKA). The aim is to enable the communicating entities to establish a level of trust and then succeed in a mutual authentication using a scheme suitable for low-resource devices in smart environments. Finally, we tested and implemented our scheme on Android mobile phones in a smart environment dedicated for handicapped people.