Pseudo-Chaotic Sequences Generated by the Discrete Arnold’s Map Over Z<sub>2<sup><i>m</i></sup></sub>: Period Analysis and FPGA Implementation
Carlos E. C. Souza, Davi Moreno, Daniel P. B. Chaves, Cecílio Pimentel
Abstract
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 Z<sub>2<sup><i>m</i></sup></sub>. The period of the generated sequences is investigated using properties of the Fibonacci sequence over Z<sub>2<sup><i>m</i></sup></sub>. 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 Z<sub>2<sup><i>m</i></sup></sub> require fewer hardware units than recently proposed sequences defined over Z<sub>3<sup><i>m</i></sup></sub>. The proposed PRNG has higher throughput and competitive hard-ware consumption when compared to other architectures in the literature.