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A Body Area Network (BAN) can be used to monitor the elderly people or patients with chronic diseases. Securing broadcasted data and commands within BANs is essential for preserving the privacy of health data and for ensuring the safety of the patient. We show how a group key can be securely established between the different sensors within a BAN. The proposed mechanism uses the inherent secure environmental values. An implementation of the protocols is carried out on mica2 motes and performance is examined in detail. The time elapsed, complexity of the code and memory requirements are analysed. The results confirm the potential benefits in real-world application. We show that a key establishment protocol based on RSA has advantages over a protocol based on ECC for this application.