New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption

Abstract

Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α < 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests).