Image encryption algorithm based on 2D hyperchaotic map

Abstract It is well known that chaos is unpredictability and sensitivity to initial values and parameters. It is a best choice for cryptography application. However, the existing chaotic cryptography systems have many defects because of the chaotic maps that without complexity dynamic performances. To improve these weaknesses, we introduced a 2D hyperchaotic map through two 1D-chaotic maps, linear function and represents multiplier. The dynamic performances of the 2D hyperchaotic map are analyzed by attractor trajectory, 0–1 test, bifurcation diagram, Lyapunov exponents and Permutation entropy. The results illustrate that 2D hyperchaotic map has more complexity dynamic characteristics and randomness, which indicates that 2D hyperchaotic map is more suitable for image encryption algorithm. Therefore, an image encryption algorithm is introduced based on 2D hyperchaotic map. In encryption algorithm, based on 2D hyperchaotic map, the image is scrambled by row shift and column shift, then pixel values are diffused through forward and backward diffusion, finally, the ciphertext image is obtained. The simulation results show that the proposed image encryption algorithm is reliable. Moreover, the security analysis indicate that the introduced algorithm has a better security performances than several image encryption algorithms. This algorithm is not absolutely safe and efficient, and does not limit the improvement and optimization of the algorithm. However, this work provide a theoretical basis in chaotic theory and chaotic image encryption algorithm.