Fast K System Generators of Pseudorandom Numbers

We suggest fast algorithm for the matrix generator of pseudorandom numbers based on Kolmogorov-Anosov K systems which has been earliar proposed in \cite{savvidy1,akopov1}. This algorithm reduces $N^{2}$ operation of the matrix generator to $NlnN$ and essentially reduces the generation time. It also clarifies the algebraic structure of this type of K system generators.