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Wireless Sensor Network (WSN) technology is being increasingly adopted in a wide variety of applications ranging from home/building and industrial automation to more safety critical applications including e-health or infrastructure monitoring. Considering mobility in the above application scenarios actually introduces additional technological challenges, especially with respect to security. The resource constrained devices should be robust to diverse security attacks and communicate securely while they are moving in the considered environment. To this aim, proper authentication and key management schemes supporting node mobility should be used. This paper presents an effective mutual authentication and key establishment scheme for heterogeneous sensor networks consisting of numerous mobile sensor nodes and only a few more powerful fixed sensor nodes. Moreover, OMNET++ simulations are used to provide a comprehensive performance evaluation of the proposed scheme. The obtained results show that the proposed solution assures better network connectivity, consumes less memory, has low communication overhead during the authentication and key establishment phase and has better network resilience against mobile nodes attacks compared with existing approaches for authentication and key establishment.