Role of Symmetry and Geometry in a chaotic Pseudo-Random Bit Generator

TL;DR

This paper investigates how symmetry and geometry influence chaotic pseudo-random bit generators, introduces a 'symmetry-swap' mechanism to enhance key space, and evaluates their statistical and computational performance for cryptographic use.

Contribution

It explores the impact of symmetry and geometry on chaotic PRBGs and introduces a novel 'symmetry-swap' method to improve key space without sacrificing performance.

Findings

PRBG sequences pass statistical tests

'symmetry-swap' increases key space

PRBG maintains speed and efficiency

Abstract

In this work, Pseudo-Random Bit Generation (PRBG) based on 2D chaotic mappings of logistic type is considered. The sequences generated with two Pseudorandom Bit Generators (PRBGs) of this type are statistically tested and the computational effectiveness of the generators is estimated. The role played by the symmetry and the geometrical properties of the underlying chaotic attractors is also explored. Considering these PRBGs valid for cryptography, the size of the available key spaces are calculated. Additionally, a novel mechanism called 'symmetry-swap' is introduced in order to enhance the PRBG algorithm. It is shown that it can increase the degrees of freedom of the key space, while maintaining the speed and performance in the PRBG.