Secure time synchronization is a paramount service for wireless sensor networks (WSNs) constituted by multiple interconnected body area networks (BANs). We propose a novel approach to securely and efficiently synchronize nodes at BAN level and/or WSN level. Each BAN develops its own notion of time. To this effect, the nodes of a BAN synchronize with their BAN controller node. Moreover, controller nodes of different BANs cooperate to agree on a WSN global and/or to transfer UTC time. To reduce the number of exchanged synchronization messages, we use an environmental-aware time prediction algorithm. The performance analysis in this paper shows that our approach exhibits very advanced security, accuracy, precision, and low-energy trade-off. For comparable precision, our proposal outstands related clock synchronization protocols in energy efficiency and risk of attacks. These results are based on computations.