Pseudo-Chaotic Sequences Generated by the Discrete Arnold’s Map Over Z2m: Period Analysis and FPGA Implementation

In this work, we propose a method to generate 1-D pseudo-chaotic sequences based on the discrete Arnold’s map defined over the integer ring $\mathbb {Z}_{2^{m}}$ . The period of the generated sequences is investigated using properties of the Fibonacci sequence over $\mathbb {Z}_{2^{m}}$ . The pseudo-chaotic sequences are employed to design a pseudorandom number generator (PRNG), and the statistical properties of this PRNG are analyzed by the NIST statistical test suite. We implement the proposed PRNG in a field-programmable gate array (FPGA) and investigate its hardware requirements. We show that for the same bit generation rate, the sequences defined over $\mathbb {Z}_{2^{m}}$ require fewer hardware units than recently proposed sequences defined over $\mathbb {Z}_{3^{m}}$ . The proposed PRNG has higher throughput and competitive hardware consumption when compared to other architectures in the literature.