Wireless body area network(WBAN) has shown great potential in improving healthcare quality not only for patients but also for medical staff. However, security and privacy are still an important issue in WBANs especially in multi-hop architectures. In this paper, we propose and present the design and the evaluation of a secure lightweight and energy efficient authentication scheme BANZKP based on an efficient cryptographic protocol, Zero Knowledge Proof (ZKP) and a commitment scheme. ZKP is used to confirm the identify of the sensor nodes, with small computational requirement, which is favorable for body sensors given their limited resources, while the commitment scheme is used to deal with replay attacks and hence the injection attacks by committing a message and revealing the key later. Our scheme reduces the memory requirement by 56.13 % compared to TinyZKP [13], the comparable alternative so far for Body Area Networks, and uses 10 % less energy.