This paper introduces a simple and effective chaotic system using a combination of two existing one-dimension (1D) chaotic maps (seed maps). Simulations and performance evaluations show that the proposed system is able to produce many 1D chaotic maps with larger chaotic ranges and better chaotic behaviors compared with their seed maps. To investigate its applications in multimedia security, a novel image encryption algorithm is proposed. Using a same set of security keys, this algorithm is able to generate a completely different encrypted image each time when it is applied to the same original image. Experiments and security analysis demonstrate the algorithm’s excellent performance in image encryption and various attacks.
New chaotic system
Figure 1 shows the new chaotic system. It is a nonlinear combination of two different 1D chaotic maps which are considered as seed maps.
Figure 1. The new chaotic system
Figure 2. Bifurcation diagrams of three new chaotic maps.
Figure 3. shows the Lyapunov exponents of three new chaotic maps. The values have similar distributions and are close to $0.7$ in the entire parameter range r∈[0,4]. This indicates that they all have the similar properties and excellent chaotic performance.
Figure 3. Lyapunov exponent of three new chaotic maps.
New image encryption algorithm
Figure 4 shows the proposed encryption algorithm. It has a 4-round-encryption structure. Each encryption round includes five steps: the random pixel insertion, row separation, 1D substitution, row combination and image rotation. The algorithm first inserts a random pixel in the beginning of each row in the original image, separates each row into a 1D data matrix, applies a substitution process to change data values in each 1D matrix, combines all 1D matrices back into a 2D data matrix according to their row positions in the original image, and then rotates the 2D matrix 90 degrees counterclockwise. Repeating these processes four times obtains the final encrypted image. The proposed algorithm is able to transform original images randomly into different noise-like encrypted images with excellent confusion and diffusion properties.
Figure 4. The new image encryption algorithm