On the design of a family of CI pseudo-random number generators

TL;DR

This paper introduces a new family of chaos-based pseudo-random number generators using chaotic iterations, demonstrating how to modify iteration functions to maintain randomness and security properties, supported by simulations and security analysis.

Contribution

It proposes a method to modify iteration functions in chaos-based generators to enhance their randomness while preserving security features.

Findings

The new generators exhibit good statistical properties.

Simulation results confirm the randomness of the generators.

Basic security analysis supports their robustness.

Abstract

Chaos and its applications in the field of secure communications have attracted a lot of attention. Chaos-based pseudo-random number generators are critical to guarantee security over open networks as the Internet. We have previously demonstrated that it is possible to define such generators with good statistical properties by using a tool called "chaotic iterations", which depends on an iteration function. An approach to find update functions such that the associated generator presents a random-like and chaotic behavior is proposed in this research work. To do so, we use the vectorial Boolean negation as a prototype and explain how to modify this iteration function without deflating the good properties of the associated generator. Simulation results and basic security analysis are then presented to evaluate the randomness of this new family of generators.