One-Dimensional Pseudo-Chaotic Sequences Based on the Discrete Arnold’s Cat Map Over ℤ₃ᵐ

In this brief we employ the discrete Arnold’s cat map over the integer ringZ_3ᵐto construct one-dimensional pseudo-chaotic sequences. We analyze their period properties using the properties of the Fibonacci sequence overZ_3ᵐand show that they have twice the period of the sequences generated by the logistic map overZ_3ᵐrecently proposed. Moreover, we investigate the pseudo-chaotic properties of the proposed sequences in the context of pseudo-chaos. Finally, these sequences are employed to design a pseudo-random number generator and a statistical analysis with the NIST statistical test suite is performed.