Solution of Large Sparse System of Linear Equations over GF(2) on a Multi Node Multi GPU Platform

We provide an efficient multi-node, multi-GPU implementation of the Block Wiedemann Algorithm (BWA)to find solution a large sparse system linear equations over GF(2). One important applications ofsolving such systems arises in most integer factorization algorithms like Number Field Sieve. In this paper, wedescribe how hybrid parallelization can be adapted to speed up time-consuming sequence generation stage BWA. This involves generating matrix-matrix products and matrix transpose-matrix where matrices are very large, highly sparse, have entries describe GPU-accelerated parallel method for computation these using techniques row-wise distribution first multi-node platform MPI CUDA word-wise XORing rows second matrix. also product computation, we divide both into equal-sized blocks MPI. Then after generation, combine all those MPI_BXOR operation MPI_Reduce obtain result. The performance step on cluster multiple GPUs has been compared with only processors. used tool benchmarking HPC cluster. Detailed timings complete number field sieve RSA-130, RSA-140, RSA-170 paper 4 NVidia V100 DGX station. got speedup 2.8 that 1 GPU.