Technique for Enhancing the Chaotic Characteristics of Chaotic Maps Using Delayed Coupling and Its Application in Image Encryption

Abstract

Chaotic systems are widely used in many scientific fields for their dynamic characteristics. This study proposes a new delayed coupling method, which not only disturbs the control coefficient in chaotic maps but also affects their function structure, such that using this improved method will produce chaotic maps with better effect. The numerical simulation results prove that the delayed coupling method can greatly improve the chaotic characteristics of chaotic maps. Furthermore, an image encryption algorithm based on the delayed coupling Logistic map is proposed. Several numerical simulations indicate that the image encryption algorithm has a high level of security, and can compete with other encryption algorithms.

A two-dimensional chaotic model and its application in image encryption

“…In the following discussion, we only test x-dimensional complexity. For different precision, we iterate the model 2000 times and from figure 4(a) and figure 4(b), we can see that our model reaches a steady state at a very low precision, while other models [7,15,18] usually need to reach a higher precision to enter a steady state. It proves that the proposed model can suppress the dynamical degradation in a low computing precision.…”

“…It can be seen from equation (10) that the above requirements can be satisfied as long as we choose the values of the control parameters reasonably. Based on equation (15) and the pre-determined values of some of the above variables, we can get a 1, 2…”

“…In figure 2, we control the parameters a 3 = 0.1, a 1 grows from 1 to 2 in a step of 0.01, it can be seen that the proposed model has two positive LE values when a 1 is in a certain range, which has the super chaotic property. Of course, not all equation (10) that satisfy equation (15) have the super chaotic property, so we will not discuss it too much. As shown in figure 3, we take the x-dimension and make a 1 = 1.99, a 3 = 0.1, and test the LE of the model at different precision, the proposed model has a larger LE than other delayed chaotic models.…”

“…We iterate equation (9) to generate a sequence of length 100,000 and remove the first 90,000 data. In figures 6, (a), (b) are the Auto-correlation analyses of the proposed chaotic model at precision 5 and 12, respectively, and (c), (d) are the Auto-correlation analyses of the chaotic model of [15] at precision 5 and 12, respectively, we can see that the Auto-correlation of our proposed chaotic model is still very low even with very low precision, indicating that our proposed model has good chaotic properties.…”

“…In order to further improve the dynamics of multidimensional chaotic models, it is necessary to apply the anti-chaotic dynamics degradation method to multidimensional chaotic models. Ming et al composes the tent map with the analog anti-control into a coupled 2D delayed chaotic map [14], Huang et al composes two one-dimensional logistic chaotic maps into one two-dimensional chaotic map by interchanging the values of different dimensions, and at the same time introduces delays to increase the complexity of the system [15]. But the delayed states on which they are based are often empirical and not mathematically analyzed.…”