Solving homogeneous linear equations over 𝐺𝐹(2) via block Wiedemann algorithm

Abstract

We propose a method of solving large sparse systems of homogeneous linear equations over G F ( 2 ) GF(2) , the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requirements. It may be useful in the last stage of integer factorization.