A new chaos function development through the combination of Circle map and MS map

¹ Department of Information Technology, Universitas Gunadarma, Depok, 16424, Indonesia
² Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia

^* Corresponding author: yadi.mt@sci.ui.ac.id

Abstract

Digital data protection is very important to prevent manipulation of digital data by unauthorized parties. Reliable techniques for securing digital data are needed, safe and fast. One technique is to use cryptography. One of the cryptographic techniques that can be used to encode digital data is to use the chaos function. We propose in this paper a new chaos function which is a composition of Circle map and MS map functions. This function has chaotic nature and the result of which is named the MSI-Circle map. The sensitivity and randomness tests of the MSI-Circle map function are carried out using a bifurcation diagram, Lyapunov exponent, and NIST test suites. The analysis result of the bifurcation diagram shows that the MSI-Circle map has a good density at the value of r ∈ (−∞,−3] ∪ [3,−∞]. Lyapunov exponent has a non-negative value at x₀ = 0.4, r = 3.8, Ω = 0.5, λ = 2.1, K = 4 which is the domain x_n ∈ (0, 1) and parameter values r, Ω, λ and K are any real numbers. The results of the NIST randomness level test show that the MSI-Circle map function passed all the randomness test of 16 NIST tests.