Today, with the development of blockchain and Internet of Things technologies, we need authentication protocols and key exchanges to communicate with these different technologies. Symmetric and asymmetric encryption methods are used to design authentication and key exchange protocols, each of which has different computation costs. In the Internet of Things systems, due to the limited memory and computation power, researchers are looking the lightweight design protocols so that the pressure caused by the computation of protocols can be minimized. Calculating protocols' computational and communication costs was done manually until now, which was associated with human error. In this paper, we proposed an E3C tool that can calculate the computation and communication costs of the authentication and key exchange protocols. E3C provides the ability to compare several protocols in terms of communication and processing costs and present them in separate charts. Comparing the processing and communication costs of classical and modern protocols manually and with the E3C indicate that the E3C can calculate the processing and communication costs of authentication and key exchange protocols with 99.99% accuracy.