Non-linear Pseudo-Random Number Generators via Coupling DX Generators with the Logistic Map

Abstract

This brief proposes a class of nonlinear pseudo-random number generators (PRNGs) based on coupling linear generators (DX generators) with a nonlinear generator (digitized Logistic map). By breaking the linearity, the unpredictability of the proposed generators in the family of coupling PRNGs is enhanced while the nice properties of efficiency, long period, and excellent statistical properties are preserved. Furthermore, the hardware efficiencies are validated by hardware implementations using a TSMC 0.18 mu m CMOS process with a throughput rate greater than 8,000 Mbit/s. In addition to the extremely long period length, the proposed nonlinear PRNGs can generate random sequences that fulfill all the randomness requirements of NIST SP 800-22 test suite.