A non-degenerate m-dimensional integer domain chaotic map model over GF(2ⁿ)

To solve the problem of dynamic degradation over finite precision platform of chaotic map, we proposed a non-degenerate m-dimensional (m ≥ 2) integer domain chaotic map (mD-IDCM) model over GF(2ⁿ), which can be applied to construct arbitrary non-degenerate m-dimensional integer domain chaotic map with m positive Lyapunov exponents. Then, we proved the strong connectivity of state transition graphs of mD-IDCM, and further proved that the mD-IDCM is chaotic in the sense of Devaney. In addition, we proved the boundedness of Lyapunov exponents. To verify the effectiveness of mD-IDCM, we instantiated it to construct two maps and analyzed their dynamical behavior. Experimental results indicated that the integer domain chaotic maps constructed by mD-IDCM have ergodicity within a sufficient larger chaotic range and exhibit complex dynamic behavior.