A Chaotic Image Encryption Scheme Based on Hénon–Chebyshev Modulation Map and Genetic Operations

Abstract

Thanks to the complex characteristics of ergodicity, pseudo-randomness and sensitivity in initial conditions, chaotic systems have been widely applied in the field of cryptography. By cascading the Hénon map and the Chebyshev map, a new two-dimensional Hénon–Chebyshev modulation map (2D-HCMM) is proposed in this paper. Several methods of objective assessment, including phase diagrams, bifurcation diagrams, Lyapunov exponents and information entropy, are utilized to analyze the dynamics of the 2D-HCMM. The results show that the 2D-HCMM possesses better ergodicity and unpredictability, with larger chaotic ranges, compared with the original chaotic maps. By using the proposed map and the essential principles of genetic recombination and genetic mutation, a new image encryption scheme is proposed. In this scheme, the bit planes of image are substituted by genetic recombination operation, and the pixel values are scrambled randomly by genetic mutation operation. The simulation results and security analysis demonstrate that the proposed scheme not only can resist various conventional attacks, but also possesses a fast speed, achieving a good trade-off between security and efficiency.