A New Chaos Function Developed through the Composition of the MS Map and the Circle Map

Abstract

The rise of digital data theft makes researchers try to find better methods for digital data protection. Confidential digital data can be secured by encryption methods, one of which is the chaos function. We propose in this paper a new chaos function which is a composition of MS Map and Circle Map functions. This function has chaotic nature and is named the MS Circle Map. The sensitivity and randomness tests of the MS Circle map function are carried out using a bifurcation diagram, Lyapunov Exponent, and NIST. The analysis result of the bifurcation diagram shows that the MS Circle map has a good density at the value of r E (0,4). Besides that, the Lyapunov Exponent has a non-negative value at r E [0.4, 4], X0 = 0.9, r = 3.8, W = 0.5 λ = 2.1 which is the domain Xn E (0, 1) and parameter values r, E, and Ω, K are any real numbers. The results of the NIST randomness level test show that the MSC Map function all passed the randomness test of 16 NIST tests.