The Internet of Things is a major development in information technology that increasingly dominates and reigns in the computer systems market. However, due to the threat of cyber attacks, the security of IoT is still one of the major issues holding back the evolution of this technology. For this, the authentication of objects is very important in IoT. In this paper, we propose a lightweight authentication protocol for the IoT Based Wireless Sensor Networks, called AuthenIoT. The objective is to provide mutual authentication services for connected objects. This protocol must take into account the constraints of the objects and the used communication technologies. To achieve such protocol, we opted for WSNs as an IoT use case. Furthermore, we demonstrate that the proposed scheme provides an efficient security for connected devices and that its computation and communication costs are suitable for extremely low-cost IoT devices.