Generating Even More Chaotic Instances in Hardware

Abstract

It is well known that multiplication inside a computer does not follow the associative property because of roundoff effects. It is possible to use this fact to generate other different chaotic instances of chaotic maps or oscillators when a multiplication of three terms appears. Chaos is very sensitive to small changes in the initial conditions and amplifies these small rounding effects. We use this condition to build different chaotic instances, which give different results, of the Lü oscillator and the 2D map, and we show one application to create new instances of a pseudo random number generator using the 2D map. Both chaotic systems are simulated in software and in hardware within an FPGA where another 144 different 2D map instances and 81 different Lü oscillators can be created. To best of our knowledge, it is the first paper that analyze the construction of new chaotic entities by using the roundoff effects.