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 one-dimensional pseudo-chaotic sequences based on the discrete Arnold’s map defined over the integer ring Z2m. The period of the generated sequences is investigated using properties of the Fibonacci sequence over Z2m. The pseudo-chaotic sequences are employed to design a pseudo-random 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 Z2mrequire fewer hardware units than recently proposed sequences defined over Z3m. The proposed PRNG has higher throughput and competitive hard-ware consumption when compared to other architectures in the literature.