An adaptive image compression-encryption scheme using 2D logarithm-exponent-squared-sine coupling map

This study presents a novel hyperchaotic system named the two-dimensional logarithm-exponent-squared-sine coupling map (2D-LESSCM). Its chaotic performance is compared to existing systems using various measurements such as the largest Lyapunov exponent, permutation entropy, sample entropy, Kolmogorov entropy, and the 0-1 test. The mean values of 2D-LESSCM for these metrics are 7.3056, 0.9996, 1.9369, 2.1011, and 0.9970, respectively, indicating enhanced complexity and a broader chaotic region. Moreover, an adaptive scheme for image compression and encryption based on compressed sensing and DNA encoding, utilizing the 2D-LESSCM, is proposed. To achieve better reconstruction results, a 2D-Arnold transform is employed to scramble the sparse coefficients of plaintext, and a key-controlled partial Hadamard measurement matrix is constructed using hyperchaotic sequences generated by 2D-LESSCM. During the encryption phase, a novel bitwise preprocessing method and an image diffusion algorithm that combines Chinese remainder theorem with DNA encoding are applied, aiming to strengthen the security of compressed images. Experimental verification reveals that the mean information entropy of encrypted images reaches 7.9966 at a sample ratio of 0.75. Additionally, the mean values of NPCR and UACI for the test images are 99.6093% and 33.4636%, respectively. These findings underscore the capability of the proposed cryptographic scheme to not only enhance the reconstruction effect but also demonstrate superior security and robustness.