Block Lanczos-Montgomery Method over Large Prime Fields with GPU Accelerated Dense Operations

  • Nikolai ZamarashkinEmail author
  • Dmitry Zheltkov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


Solution of huge linear systems over large prime fields is a problem that arises in such applications as discrete logarithm computation. Lanczos-Montgomery method is one of the methods to solve such problems. Main parallel resource of the method us the size of the block. But computational cost of dense matrix operations is increasing with block size growth. Thus, parallel scaling is close to linear only while complexity of such operations are relatively small. In this paper block Lanczos-Montgomery method with dense matrix operations accelerated on GPU is implemented. Scalability tests are performed (including tests with multiple GPU per node) and compared to CPU only version.


Linear systems over prime fields Parallel computations GPGPU 



The work was supported by the RAS presidium program №1 “Fundamental Mathematics and its applications”.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.INM RASMoscowRussia

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