One-Dimensional Pseudo-Chaotic Sequences Based on the Discrete Arnold’s Cat Map Over ℤ₃ᵐ
Carlos E. C. Souza, Daniel P. B. Chaves, Cecilio Jose Lins Pimentel · IEEE Transactions on Circuits & Systems II Express Briefs · 2020
In this brief we employ the discrete Arnold’s cat map over the integer ring$\mathbb {Z}_{3^{m}}$to construct one-dimensional pseudo-chaotic sequences. We analyze their period properties using the properties of the Fibonacci sequence over$\mathbb {Z}_{3^{m}}$and show that they have twice the period of the sequences generated by the logistic map over$\mathbb {Z}_{3^{m}}$recently 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.