GPU Acceleration of Dense Matrix and Block Operations for Lanczos Method for Systems Over GF(2)
- Авторлар: Zamarashkin N.1, Zheltkov D.1
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Мекемелер:
- Marchuk Institute of Numerical Mathematics
- Шығарылым: Том 40, № 11 (2019)
- Беттер: 1881-1891
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/206109
- DOI: https://doi.org/10.1134/S1995080219110337
- ID: 206109
Дәйексөз келтіру
Аннотация
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.
Негізгі сөздер
Авторлар туралы
N. Zamarashkin
Marchuk Institute of Numerical Mathematics
Хат алмасуға жауапты Автор.
Email: nikolai.zamarashkin@gmail.com
Ресей, Moscow, 119333
D. Zheltkov
Marchuk Institute of Numerical Mathematics
Хат алмасуға жауапты Автор.
Email: dmitry.zheltkov@gmail.com
Ресей, Moscow, 119333
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