Newchaos function from the composition of DTM and Gauss iterated map for digital image encryption

This manuscript introduces a novel chaotic discrete function, formulated through the composition of the dyadic transformation map (DTM) and the Gauss iterated map (GIM), and designated as DTGIM. The National Institute of Science and Technology (NIST) randomness test suite, bifurcation diagrams, and Lyapunov exponents are used to examine the chaotic characteristics of DTGIM. With ini tial condition x0 = 0.12345 and parameters α = −15 and β = 0.3, the func tion shows chaotic behavior in the bifurcation diagram and produces a positive Lyapunov exponent. Strong randomness is further confirmed by NIST tests, which achieve 100% for 32-bit binary sequences and 63.75% for 8-bit binary sequences. Additionally, we compare a number other chaotic discrete functions that also employ the composition method. These findings show that DTGIM is a viable option for applications involving chaos-based cryptography.