2D Henon-Chebyshev Chaotic Map for Image Encryption

Abstract

Chaotic systems is widely employed in image encryption on account of its momentous properties including nonperiodicity, ergodicity, randomness and initial state sensitivity. However, some chaos-based cryptosystems still exhibit security problems due to the weak performance of their applied chaotic maps. To address those problems, a new two-dimensional HenonChebyshev map (2D-HCM) is first proposed in this paper. It is generated by connecting Henon map and Chebyshev map where the output of one map is used to adapt the input of the others. It results in a better chaotic performance in 2D-HCM, including better chaotic behaviors, higher chaotic index, wider chaotic range and finer ergodicity than other extant chaotic maps. Using the 2D-HCM, we further design an image encryption algorithm. The proposed algorithm disorganize the pixel positions of the input plain image with random sequence generated by 2D-HCM, and then convert it into DNA-planes using DNA operation rules. Finally, the cipher image is acquired by employing the newly defined DNA-level 2D cellular automata (DNA-CA) to update the DNA-planes in each iteration where 2D-HCM produces the rule number sequences applied in the update. Our scheme has proven to be highly efficient and secure by the experimental results and security analysis.