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Wireless body area network (WBAN) has been recognized as one of the promising wireless sensor technologies for improving healthcare service, thanks to its capability of seamlessly and continuously exchanging medical information in real time. However, the lack of a clear in-depth defense line in such a new networking paradigm would make its potential users worry about the leakage of their private information, especially to those unauthenticated or even malicious adversaries. In this paper, we present a pair of efficient and light-weight authentication protocols to enable remote WBAN users to anonymously enjoy healthcare service. In particular, our authentication protocols are rooted with a novel certificateless signature (CLS) scheme, which is computational, efficient, and provably secure against existential forgery on adaptively chosen message attack in the random oracle model. Also, our designs ensure that application or service providers have no privilege to disclose the real identities of users. Even the network manager, which serves as private key generator in the authentication protocols, is prevented from impersonating legitimate users. The performance of our designs is evaluated through both theoretic analysis and experimental simulations, and the comparative studies demonstrate that they outperform the existing schemes in terms of better trade-off between desirable security properties and computational overhead, nicely meeting the needs of WBANs.