Consider a zero-dimensional ideal $I$ in $K[X_1,\dots,X_n]$. Inspired by Faug\`ere and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of $I$ in order to compute a description of its zero set by means of univariate polynomials. Using the block-Wiedemann techniques, we present an algorithm that is easily parallelizable.
