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Fully homomorphic encryption (FHE) enables direct computation on encrypted data without decryption, ensuring data privacy in cloud computing scenarios and preventing the leakage of sensitive information. However, the computational overhead of HE typically exceeds that of plaintext computation by 4 to 5 orders of magnitude, while energy consumption is 5 to 6 orders of magnitude higher. These substantial performance and energy overheads significantly hinder the widespread adoption of FHE. This paper proposed LP-HENN, a novel low-power and energy-efficient FHE accelerator architecture that leverages a RISC-V vector coprocessor and ReRAM crossbar arrays. LP-HENN targets power-constrained application scenarios such as edge devices, aiming to provide highly energy-efficient acceleration support for FHE applications. LP-HENN leverages the collaborative work of the vector processor and ReRAM crossbars, employing optimization strategies to achieve full pipelining and minimize memory access. Furthermore, this paper proposed a parameter selection model for early-stage architecture design, which achieves an optimal balance between performance and energy consumption through the collaborative optimization of multiple parameters. Experimental results show that, for an FHE-based convolutional neural network (HE-CNN) inference application, LP-HENN achieves a 31.82Ã- and 11920.56Ã- improvement in performance and energy efficiency, respectively, compared to CPU. Compared to FxHENN, the state-of-the-art FPGA-based FHE accelerator with high energy efficiency for edge devices, LP-HENN achieves a 2.36Ã- and 10.04Ã- improvement in performance and energy efficiency, respectively. The energy efficiency of LP-HENN is comparable to that of F1, the state-of-the-art ASIC FHE accelerator, while featuring a low power design suitable for edge computing.