Color image encryption based on 2D enhanced hyperchaotic logistic-sine map and two-way Josephus traversing

Abstract

To improve the chaotic behavior of the chaotic map, this paper proposes a new two-dimensional (2D) chaotic map, namely, 2D enhanced hyperchaotic Logistic-sine map (2D-EHLM), which is derived from the idea of the 2D Logistic map and the Sine map. The performance analyses demonstrate that the 2D-EHLM has significantly better hyperchaotic property, unpredictability characteristics in terms of their Lyapunov exponents, trajectories, and 0-1test in comparison to some existing 2D chaotic maps. Such as the 2D-EHLM performs chaotic behavior when their control parameter μ within (−3,4), which indicates a large chaotic range comparing with other 2D dynamical systems. To investigate its application, this paper proposes a new image confusion strategy based on the two-way Josephus traversing (TJT) to efficiently scramble the color image components and pixel positions. Combining 2D-EHLM and TJT operation, a new color image encryption scheme is proposed. The stimulation experiments and security analysis demonstrate that the proposed algorithm is able to protect the image information with a high security as well as to resist common types of attacks, which also verify the superior hyperchaotic behaviors of the 2D-EHLM from the aspect of encryption effect.