An Efficient Analyses of the Behavior of One Dimensional Chaotic Maps using 0-1 Test and Three State Test
This work provides cryptosystem researchers with better choices of control parameters for stronger encryption by identifying optimal chaotic regions in common maps, addressing a limitation of relying solely on Lyapunov exponents.
This paper analyzes the chaotic behavior of standard logistic, Logistic Tent, Logistic-Sine, and Tent-Sine maps using the 0-1 test and three-state test. It identifies strong and weak chaotic regions within these maps, demonstrating that chaotic strength is not uniform.
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.