Efficient implementation of pseudochaotic piecewise linear maps with high digitization accuracies

In this paper we discuss the efficient implementation of pseudochaotic piecewise linear maps with high digitization accuracies, taking the Rényi chaotic map as a reference. The proposed digital architectures are based on a novel algorithmic approach, that uses carry save adders for the nonlinear arithmetic modular calculations arising when computing piecewise linear maps with a finite precision. As a result, the system can be implemented by digital circuits obtaining high throughputs, which are not dependent on the digital resolution, whereas involving a hardware complexity linearly proportional to the number of bits used for representing the discretized state. The proposed solutions result to be particularly suitable for the implementation of pseudo-random number generators based on pseudo-chaos, or for the definition of efficient digital blocks that can be integrated in most of the pseudo-chaotic cyphers proposed in the literature.