The cloud-assisted Body Sensor Networks (BSN) often has an architecture of Multi-hop Wireless Networks (MWN) model, in which both the body sensors and the users must be secure to protect the whole infrastructure. Unfortunately, both the information providers and the users are movable and resource-constrained in communication and computation. Thus some new security problems are proposed, such as the light weight-secure au-thentication caused by limited resource, re-authentication in foreign zone caused by mobility, and composablilty security caused by heterogeneity between the transmission subnet, many BSN subnets. We propose a Random Roaming Authentication Protocol (RanRAP) for BSNs with these cloud-assisted infrastructure. We test the com-posable security at an AP/cluster head/gateway node by using strand spaces theory, and analyze the performance of RanRAP protocol in both the theoretical analysis and experiment simulations. It was shown that RanRAP has some advantages of composable security, computation and communication overheads over some related protocols.