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How to Make Lanczos-Montgomery Fast on Modern Supercomputers?

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Supercomputing (RuSCDays 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14388))

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Abstract

This paper deals with the performance analysis of the INM RAS implementation of the block Lanczos-Montgomery method that was used to accomplish the factorization of the RSA-232 number. Other steps of RSA-232 factorization carried out by CADO-NFS open source library are also mentioned. Further adaptation of parallel block Lanczos-Montgomery method for the modern supercomputers is discussed, including implementation of basic operations of the method on GPUs.

RSA-232 factorization was supported by the Moscow Center of Fundamental and Applied Mathematics at INM RAS (Agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2022-286), block Lanczos performance analysis and its improvements research was supported by the Russian Science Foundation project № 19-11-00338, https://rscf.ru/en/project/19-11-00338/.

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia

    Dmitry Zheltkov, Nikolai Zamarashkin & Sergey Matveev

  2. Lomonosov Moscow State University, Moscow, Russia

    Nikolai Zamarashkin & Sergey Matveev

Authors
  1. Dmitry Zheltkov
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  2. Nikolai Zamarashkin
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  3. Sergey Matveev
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Corresponding author

Correspondence to Dmitry Zheltkov .

Editor information

Editors and Affiliations

  1. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Vladimir Voevodin

  2. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Sergey Sobolev

  3. Russian Academy of Sciences (RAS), Keldysh Institute of Applied Mathematics, Moscow, Russia

    Mikhail Yakobovskiy

  4. Russian Federal Nuclear Center, Sarov, Russia

    Rashit Shagaliev

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Zheltkov, D., Zamarashkin, N., Matveev, S. (2023). How to Make Lanczos-Montgomery Fast on Modern Supercomputers?. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds) Supercomputing. RuSCDays 2023. Lecture Notes in Computer Science, vol 14388. Springer, Cham. https://doi.org/10.1007/978-3-031-49432-1_9

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  • DOI: https://doi.org/10.1007/978-3-031-49432-1_9

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