A new chaotic map development through the composition of the MS Map and the Dyadic Transformation Map

In this paper, a new chaotic map is proposed, that is obtained from the composition of two chaotic maps, that is, the MS Map and the Dyadic Transformation Map. The composition process starts from the MS Map, followed by the Dyadic Transformation Map. The resulting composition is a new chaotic function. This is shown by the bifurcation diagram analysis result, Lyapunov Exponents, and the NIST randomness test. The bifurcation diagram shows that the best densities occur at λ ∈ (0.3, 5) and r = 3.8. The Lyapunov Exponents has nonnegative values for r ∈ [1, 4]. The NIST randomness test with initial value and parameters x 0 = 0.6, r = 3.8, and λ = 3.5 shows that the new chaotic map passes 14 out of 16 NIST tests.