Abstract
Stencil computations with fully homomorphic encryption (FHE) is an emerging area with significant potential to address the challenges of protecting sensitive data of HPC applications in outsourcing computing environment. However, the computational overhead introduced by FHE can drastically reduce the performance of stencil computations compared to unencrypted implementations. This paper proposes two optimized algorithms for stencil computation with FHE tailored to GPU platforms: Matrix Overlap Processing (MOP) and Matrix Fixed-point Processing(MFP). MOP divides the input matrix into multiple slices, encrypts elements at the same positions across slices into a single ciphertext, and processes them with a uniform computing pattern. MFP directly encrypts neighbouring elements into ciphertexts, stores them in a table, and processes them in parallel on the GPU. The experimental results show that our proposed methods achieve significant speedups compared to the corresponding OpenMP implementations on CPU. Specifically, the MOP implementation achieves a speedup of 8.7\(\times \), while the MFP implementation achieves a speedup of 10.3\(\times \) on GPU.
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References
Cheon, J.H., Kim, A., Kim, M., Song, Y.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 409–437. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_15
Chillotti, I., Gama, N., Georgieva, M., Izabachène, M.: TFHE: fast fully homomorphic encryption over the torus. J. Cryptol. 33(1), 34–91 (2020)
Denzler, A., et al.: Casper: accelerating stencil computations using near-cache processing. IEEE Access 11, 22136–22154 (2023)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 169–178 (2009)
Han, K., Ki, D.: Better bootstrapping for approximate homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 364–390. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40186-3_16
Ikeda, K., Ino, F., Hagihara, K.: Efficient acceleration of mutual information computation for nonrigid registration using CUDA. IEEE J. Biomed. Health Inform. 18(3), 956–968 (2014)
Jin, H., Wu, W., Shi, X., He, L., Zhou, B.B.: TurboDL: improving the CNN training on GPU with fine-grained multi-streaming scheduling. IEEE Trans. Comput. 70(4), 552–565 (2020)
Jung, W., Kim, S., Ahn, J.H., Cheon, J.H., Lee, Y.: Over 100x faster bootstrapping in fully homomorphic encryption through memory-centric optimization with GPUs. In: IACR Transactions on Cryptographic Hardware and Embedded Systems, pp. 114–148 (2021)
Kim, S., et al.: BTS: an accelerator for bootstrappable fully homomorphic encryption. In: Proceedings of the 49th Annual International Symposium on Computer Architecture, pp. 711–725 (2022)
Kondratyuk, N., Nikolskiy, V., Pavlov, D., Stegailov, V.: GPU-accelerated molecular dynamics: state-of-art software performance and porting from Nvidia CUDA to AMD HIP. Int. J. High Perform. Comput. Appl. 35(4), 312–324 (2021)
Liu, X., et al.: Toward accelerated stencil computation by adapting tensor core unit on GPU. In: Proceedings of the 36th ACM International Conference on Supercomputing, pp. 1–12 (2022)
Mouchet, C., Troncoso-Pastoriza, J., Bossuat, J.P., Hubaux, J.P.: Multiparty homomorphic encryption from ring-learning-with-errors. Proc. Privacy Enhancing Technol. 2021(4), 291–311 (2021)
Niculescu, V.: On the impact of high performance computing in big data analytics for medicine. Appl. Med. Inform. 42(1), 9–18 (2020)
Okuyama, T., et al.: Accelerating ode-based simulation of general and heterogeneous biophysical models using a GPU. IEEE Trans. Parallel Distrib. Syst. 25(8), 1966–1975 (2013)
Shen, J., Shigeoka, K., Ino, F., Hagihara, K.: An out-of-core branch and bound method for solving the 0-1 knapsack problem on a GPU. In: Ibrahim, S., Choo, K.-K.R., Yan, Z., Pedrycz, W. (eds.) ICA3PP 2017. LNCS, vol. 10393, pp. 254–267. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65482-9_17
Shen, J., Shigeoka, K., Ino, F., Hagihara, K.: GPU-based branch-and-bound method to solve large 0–1 knapsack problems with data-centric strategies. Concurr. Comput. Pract. Exp. 31(4), e4954 (2019)
Shen, J., Wu, Y., Okita, M., Ino, F.: Accelerating GPU-based out-of-core stencil computation with on-the-fly compression. In: Shen, H., et al. (eds.) PDCAT 2021. LNCS, vol. 13148, pp. 3–14. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96772-7_1
Shi, X., Agrawal, T., Lin, C.A., Hwang, F.N., Chiu, T.H.: A parallel nonlinear multigrid solver for unsteady incompressible flow simulation on multi-GPU cluster. J. Comput. Phys. 414, 109447 (2020)
Yantır, H.E., Eltawil, A.M., Salama, K.N.: Efficient acceleration of stencil applications through in-memory computing. Micromachines 11(6), 622 (2020)
Zhu, Y., Wang, X., Ju, L., Guo, S.: FxHENN: FPGA-based acceleration framework for homomorphic encrypted CNN inference. In: 2023 IEEE International Symposium on High-Performance Computer Architecture (HPCA), pp. 896–907. IEEE (2023)
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This work has been supported by the Natural Science Foundation of Hubei Province of China [grant number 2023AFB394] and Knowledge Innovation Program of Wuhan-Shuguang Project [grant number 2022010801020283].
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Zhou, X., Li, P., Chen, J., Yao, S. (2024). Accelerating Stencil Computation with Fully Homomorphic Encryption Using GPU. In: Carretero, J., Shende, S., Garcia-Blas, J., Brandic, I., Olcoz, K., Schreiber, M. (eds) Euro-Par 2024: Parallel Processing. Euro-Par 2024. Lecture Notes in Computer Science, vol 14803. Springer, Cham. https://doi.org/10.1007/978-3-031-69583-4_15
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