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Industrial Internet of Things (IIoT) has strict requirements on the performance and security of devices. Public-key cryptography, as a kind of computing resource-consuming algorithm, is widely used in the digital signature, key exchange, and so on. The embedded graphics processing units (GPUs) are now rapidly achieving extraordinary computing power, such as NVIDIA Tegra K1/X1/X2/Xavier, which are also treated as edge computing devices. They are widely used in IIoT environments, such as intelligent manufacturing, smart cities, and vehicle-mounted systems. The performance advantages endow embedded GPUs with the possibility of accelerating cryptography that also requires high-density computing. This article implements an efficient Tegra-based embedded GPU RSA acceleration server-oriented IIoT, named TEGRAS. Various optimization methods are employed to promote efficiency, including multithreaded Montgomery multiplication and Chinese Remainder Theorem implementation on the resource-constricted embedded GPUs. With about 40-50 W of power consumption, TEGRAS can deliver 34 kops/s of RSA2048 signature generation and 1007 kops/s of RSA signature verification, which outperforms implementations in the desktop GPUs and embedded CPUs in the perspective of performance-to-power ratio. To evaluate TEGRAS in real-world scenarios, we additionally build a network stack to deliver digital signature services, which can provide more than 34 and 978 kops of signature generation and signature verification, respectively. In a word, based on the embedded GPU, we provide a high-throughput, low-latency, and ready-to-use RSA accelerator-oriented IIoT.