Cross-plane colour image encryption using a two-dimensional logistic tent modular map

Chaotic systems are suitable for image encryption owing to their numerous intrinsic characteristics. However, chaotic maps and algorithmic structures employed in many existing chaos-based image encryption algorithms exhibit various shortcomings. To overcome these, in this study, we first construct a two-dimensional logistic tent modular map (2D-LTMM) and then develop a new colour image encryption algorithm (CIEA) using the 2D-LTMM, which is referred to as the LTMM-CIEA. Compared with the existing chaotic maps used for image encryption, the 2D-LTMM has a fairly wide and continuous chaotic range and more uniformly distributed trajectories. The LTMM-CIEA employs cross-plane permutation and non-sequential diffusion to obtain the diffusion and confusion properties. The cross-plane permutation concurrently shuffles the row and column positions of pixels within the three colour planes, and the non-sequential diffusion method processes the pixels in a secret and random order. The main contributions of this study are the construction of the 2D-LTMM to overcome the shortcomings of existing chaotic maps and the development of the LTMM-CIEA to concurrently encrypt the three colour planes of images. Simulation experiments and security evaluations show that the 2D-LTMM outperforms recently developed chaotic maps, and the LTMM-CIEA outperforms several state-of-the-art image encryption algorithms in terms of security.