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In this paper, we propose a parallel implementation of the number-theoretic transform (NTT) on GPU clusters. The butterfly operation of the NTT can be performed using modular addition, subtraction, and multiplication. We show that the four-step fast Fourier transform algorithm can be applied to the NTT. We parallelized the four-step NTT using MPI and OpenACC on GPU clusters. We achieved a performance of over 745 giga-operations per second on 32 nodes of a GPU cluster equipped with NVIDIA H100 PCIe GPUs for a \(2^{35}\) -point NTT with a modulus of 63 bits.

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Parallel Implementation of Number-Theoretic Transform on GPU Clusters

  • 会议论文

  • 发表日期：

    2025年

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  • Daisuke Takahashi

摘要

In this paper, we propose a parallel implementation of the number-theoretic transform (NTT) on GPU clusters. The butterfly operation of the NTT can be performed using modular addition, subtraction, and multiplication. We show that the four-step fast Fourier transform algorithm can be applied to the NTT. We parallelized the four-step NTT using MPI and OpenACC on GPU clusters. We achieved a performance of over 745 giga-operations per second on 32 nodes of a GPU cluster equipped with NVIDIA H100 PCIe GPUs for a \(2^{35}\) -point NTT with a modulus of 63 bits.