Wearable computing has garnered a lot of attention due to its various advantages, including automatic recognition and categorization of human actions from sensor data. However, wearable computing environments can be fragile to cyber security attacks since adversaries attempt to block, delete, or intercept the exchanged information via insecure communication channels. In addition to cyber security attacks, wearable sensor devices cannot resist physical threats since they are batched in unattended circumstances. Furthermore, existing schemes are not suited for resource-constrained wearable sensor devices with regard to communication and computational costs and are inefficient regarding the verification of multiple sensor devices simultaneously. Thus, we designed an efficient and robust authentication and group–proof scheme using physical unclonable functions (PUFs) for wearable computing, denoted as AGPS-PUFs, to provide high-security and cost-effective efficiency compared to the previous schemes. We evaluated the security of the AGPS-PUF using a formal security analysis, including the ROR Oracle model and AVISPA. We carried out the testbed experiments using MIRACL on Raspberry PI4 and then presented a comparative analysis of the performance between the AGPS-PUF scheme and the previous schemes. Consequently, the AGPS-PUF offers superior security and efficiency than existing schemes and can be applied to practical wearable computing environments.