A novel multi-layer image encryption algorithm based on 2D drop-wave function

Image encryption is an effective method for protecting the security of image information, and chaotic maps are generally applied to realize some random operations. Inspired by the nonlinear characteristic of optimization test functions, a chaotic map called drop-wave map developed from the two-dimensional (2D) drop-wave function is proposed in this paper. The drop-wave map has a wide range of parameters and uniform phase trajectories. Utilizing the generated pseudo-random sequences with the proposed drop-wave map, a novel multi-layer image encryption algorithm is presented through processing bit-planes using bit circle-shift, bit-plane permutation using Baker map, intra-layer permutation, and multi-direction diffusion. First, the bit circle-shift operation is performed on each pixel to change values initially, where the shifted digits are determined with one pseudo-random sequence. Second, the Baker map is used to scramble the bit positions in each bit-plane and the timestamp is regarded as an extra key. Furthermore, the intra-layer permutation operation with another pseudo-random sequence is performed to permutate the bit positions completely. Finally, the ciphertext image is obtained by using multi-direction diffusion to change pixel values. The main contributions of this work lie in the design of a 2D drop-wave map and a combination of multi-layer operations to enhance the security of image encryption. Simulation results and security analysis verify the validity and feasibility of the proposed algorithm through statistical analysis and robustness analysis.