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In this paper, we study the problem of traffic analysis attacks in wireless body area sensor networks. When these networks are used in health-care for remote patient monitoring, traffic analysis can reveal the type of medical sensors mounted on the patient, and this information may be used to infer the patient's health problems. We show that simple signal processing methods can be used effectively for performing traffic analysis attacks and identifying the sensor types in a rather weak adversary model. We then investigate possible traffic obfuscation mechanisms aiming at hiding the regular patterns in the observable wireless traffic. Among the investigated countermeasures, traffic shaping, a mechanism that introduces carefully chosen delays for message transmissions, appears to be the best choice, as it achieves close to optimal protection and incurs no overhead.