Analysis of the digital implementation of a chaotic deterministic-stochastic attractor

In this work the digital implementation of a chaotic system onto a Field Programmable Gate Array (FPGA), is analyzed. Any digital implementation requires the choice of an algorithm to discretize time and a representation standard to represent real numbers. Each choice modifies the stochasticity degree of the system and also defines a different amount of resources on the FPGA. The main contribution of this paper is to study this issue, by comparing different realizations of the same chaotic system. An optimum design methodology for applications in which the chaotic system is going to replace a stochastic system is also reported. This is the case with PRNGs. The stochasticity degree must be measured. In this paper we use the global indicator proposed by Marsaglia in his widely used DIEHARD tests-suite. Results are exemplified for the Lorenz chaotic oscillator but the same methodology may be used with other low dimensional chaotic systems.