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An Implementation of Parallel Number-Theoretic Transform Using Intel AVX-512 Instructions

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Computer Algebra in Scientific Computing (CASC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13366))

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Abstract

In this paper, we propose an implementation of the parallel number-theoretic transform (NTT) using Intel Advanced Vector Extensions 512 (AVX-512) instructions. The butterfly operation of the NTT can be performed using modular addition, subtraction, and multiplication. We show that a method known as the six-step fast Fourier transform algorithm can be applied to the NTT. We vectorized NTT kernels using the Intel AVX-512 instructions and parallelized the six-step NTT using OpenMP. We successfully achieved a performance of over 83 giga-operations per second on an Intel Xeon Platinum 8368 (2.4 GHz, 38 cores) for a \(2^{20}\)-point NTT with a modulus of 51 bits.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Number JP19K11989.

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Authors and Affiliations

  1. Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan

    Daisuke Takahashi

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  1. Daisuke Takahashi
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Correspondence to Daisuke Takahashi .

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Editors and Affiliations

  1. Université de Lille, Villeneuve d'Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Takahashi, D. (2022). An Implementation of Parallel Number-Theoretic Transform Using Intel AVX-512 Instructions. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2022. Lecture Notes in Computer Science, vol 13366. Springer, Cham. https://doi.org/10.1007/978-3-031-14788-3_18

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  • DOI: https://doi.org/10.1007/978-3-031-14788-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-14787-6

  • Online ISBN: 978-3-031-14788-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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