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Body sensor networks (BSN) have the potential to provide improved data collection and analysis, as well as enhanced security, particularly in a wide range of medical applications. One of the main challenges in these types of networks is scarce resources, in terms of both computational and communication capabilities. In this work, we present methods to efficiently allocate these limited resources, while maintaining good security performance. Two main strategies are explored: first, a key distribution system is presented that allows for trade-offs between computational complexity and spectral efficiency; second, a data scrambling method based on random sampling is proposed as a possible alternative to conventional encryption in providing security. The obtained simulation results demonstrate the feasibility and efficacy of these schemes in the context of BSN, when using electrocardiogram (ECG) signals as biometrics.