An Efficient Analyses of the Behavior of One Dimensional Chaotic Maps using 0-1 Test and Three State Test

TL;DR

This paper rigorously analyzes the chaotic behavior of various one-dimensional maps using 0-1 and three state tests, revealing non-uniform chaos strength and aiding better parameter selection for encryption.

Contribution

It introduces a comprehensive analysis of chaos strength in one-dimensional maps using 0-1 and three state tests, highlighting limitations of Lyapunov exponent.

Findings

Identified strong and weak chaotic regions in LTS, LSS, and TSS maps.

Demonstrated non-uniformity of chaos strength across parameter spaces.

Proposed improved testing practices for cryptosystem research.

Abstract

In this paper, a rigorous analysis of the behavior of the standard logistic map, Logistic Tent system (LTS), Logistic-Sine system (LSS) and Tent-Sine system (TSS) is performed using 0-1 test and three state test (3ST). In this work, it has been proved that the strength of the chaotic behavior is not uniform. Through extensive experiment and analysis, the strong and weak chaotic regions of LTS, LSS and TSS have been identified. This would enable researchers using these maps, to have better choices of control parameters as key values, for stronger encryption. In addition, this paper serves as a precursor to stronger testing practices in cryptosystem research, as Lyapunov exponent alone has been shown to fail as a true representation of the chaotic nature of a map.