Image Encryption Algorithm Using Multi-Level Permutation and Improved Logistic–Chebyshev Coupled Map

Abstract

To improve the randomness of the Chebyshev chaotic sequences by coupling the Logistic map and the Chebyshev map, a new one-dimensional Logistic–Chebyshev chaotic map (LCCM) is first presented in this paper. Several tests, including the bifurcation diagram, Lyapunov exponents, and information entropy, are employed to analyze the dynamics of the LCCM. The proposed LCCM has better ergodicity and unpredictability than the traditional Chebyshev map. Next, a new image encryption algorithm based on the LCCM and multi-level manipulation is proposed. The LCCM is used to control the pixel permutation, bit-level shuffling, and subsequent pixel diffusion based on the modulo and XOR operation. Extensive experiments, including histogram analysis, information entropy, adjacent pixel correlation, and key sensitivity, show that the image encryption algorithm has high security and can effectively resist malicious attacks.