  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.
