BANZKP is the best to date Zero Knowledge Proof (ZKP) based secure lightweight and energy efficient authentication scheme designed for Wireless Area Network (WBAN). It is vulnerable to several security attacks such as the replay attack, Distributed Denial-of-Service (DDoS) attacks at sink and redundancy information crack. However, BANZKP needs an end-to-end authentication which is not compliant with the human body postural mobility. We propose a new scheme BAN-GZKP. Our scheme improves both the security and postural mobility resilience of BANZKP. Moreover, BAN-GZKP uses only a three-phase authentication which is optimal in the class of ZKP protocols. To fix the security vulnerabilities of BANZKP, BAN-GZKP uses a novel random key allocation and a Hop-by-Hop authentication definition. We further prove the reliability of our scheme to various attacks including those to which BANZKP is vulnerable. Furthermore, via extensive simulations we prove that our scheme, BAN-GZKP, outperforms BANZKP in terms of reliability to human body postural mobility for various network parameters (end-to-end delay, number of packets exchanged in the network, number of transmissions). We compared both schemes using representative convergecast strategies with various transmission rates and human postural mobility. Finally, it is important to mention that BAN-GZKP has no additional cost compared to BANZKP in terms memory, computational complexity or energy consumption.