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Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1881–1891 | Cite as

GPU Acceleration of Dense Matrix and Block Operations for Lanczos Method for Systems Over GF(2)

  • N. L. ZamarashkinEmail author
  • D. A. ZheltkovEmail author
Article
  • 9 Downloads

Abstract

The algebraic operations with the dense matrices and blocks are bounding the scalability of block Lanczos–Montgomery method, that is used for the linear part in the RSA decomposition problem. This paper explores the possibility of implementation of the following algebraic operations over field \(\mathbb{F}_2\) on GPU: (1) multiplication of two 64k × 64k matrices; (2) multiplication of two N × 64k blocks. For matrix multiplication, we consider two algorithms: (a) the “naive” algorithm; (b) the “fast” algorithm by 4 Russians. For block multiplication, we consider just the “naive” algorithm. It seems that by now this is the only work where BLAS acceleration over \(\mathbb{F}_2\) are relatively successful accelerated on GPU.

Keywords and phrases

GPGPU GF(2) “four Russians” method 

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Notes

Funding

This article contains the results of the project performed in the framework of the implementation of the programs of the Central Competences of the National Technological Database “Center for Big Data Storage and Analysis” (project “Tensor methods for processing and analysis of Big Data”) of MSU with the Project Support Funding of the National Technological Reporting dated December 11, 2018, no. 13/1251/2018.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Marchuk Institute of Numerical MathematicsMoscowRussia

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