Device-to-Device (D2D) communication enables devices in proximity to establish a wireless direct link. However, these devices may be severely constrained in terms of memory, CPU, and processing resources. Hence, a D2D communication with a constrained device implies new challenges as it does not have the resources required to be secured with standard cryptography. We propose lwAKE for class 0 devices (RFC 7228), which uses one-way cryptographic functions and zero-knowledge proofs to provide mutual authentication and a secure key establishment. We specify the protocol using the High Level Protocol Specification Language and then verify the security properties using the model checkers OFMC and CL-AtSe. The significance of the protocol stands in a key reuse for any successive authentication. Experimental results show that this shortened authentication mode reduces the computational load greatly.