Information authentication in automated control systems based on finite groups with multidimensional cyclicity

The paper deals with information authentication for real time automatic control systems. Our approach differs from known ones in using finite groups of vectors over a finite field. We show that these groups of vectors are multidimensionally cyclic. This allows developing secure digital signature algorithms based on groups with the maximal prime factor of length $160/m$ bits where $m$ is the vectors' dimension. We list formulas describing this multidimensional cyclicity of vector groups.