Exploiting ergodicity of the logistic map using deep-zoom to improve security of chaos-based cryptosystems

TL;DR

This paper leverages the deep-zoom properties of the k-logistic map to enhance the security and unpredictability of chaos-based cryptosystems by improving their pseudo-random number generation capabilities.

Contribution

It introduces an improved cryptosystem that exploits the ergodic properties of the k-logistic map for better security and randomness compared to previous chaos-based methods.

Findings

Enhanced randomness of the k-logistic map

Reduced predictability of chaotic orbits

Improved security of the cryptosystem

Abstract

This paper explores the deep-zoom properties of the chaotic k-logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem.