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With an advancement of wireless communication technology, wireless sensor network (WSN) has emerged as one of the most powerful technologies which can be used in various applications, such as military surveillance, environment monitoring, industrial control, and medical monitoring. WSNs are vulnerable to large collection of attacks than traditional networks because they transmit data using a wireless channel and are deployed in unattended environments. So, in this environment, how to ensure secure communications between different communication parties becomes a challenging issue with respect to the constraints of energy consumption, and large overhead generated during various operations performed. In this direction, the mutual authentication and key agreement (MAAKA) scheme attracts much attention in recent years. In literature, MAAKA schemes were presented in last several years. However …