Cryptanalysis of a chaotic image cipher based on plaintext-related permutation and lookup table

Abstract

In 2017, an efficient chaotic image cipher with dynamic lookup table driven by bit-level permutation strategy (ICDLT) was proposed (Hu et al. Nonlinear Dyn 87:1359–1375). The chaotic cipher adopts a plaintext-related image encryption mechanism as an efficient measure against chosen-plaintext/ciphertext attack. ICDLT is composed of four basic parts: inter-pixel permutation, sequential addition, intra-pixel permutation and diffusion processes, where two kinds of permutation are both related to the plaintext. Although ICDLT is built on complex nonlinear dynamics, we found that it is still vulnerable against chosen-plaintext attack and its individual sub-keys can be recovered using a divide-and-conquer strategy. Benefiting from the essential structure of ICDLT and the intrinsic properties of Latin square, the proposed attack requires only $$ (8 \cdot N^2 +256 + n_c \cdot (2 \cdot N -1))$$ plain images, where $$N^2$$ is the size of the image and $$n_c$$ is the number of cipher images that need to be cracked. Furthermore, we summarize a more general framework which is beneficial for cryptanalyzing a class of plaintext-related image ciphers. Finally, we propose an improved scheme based on the designed plaintext-related XOR encryption (PR-XOR) module to enhance the security of ICDLT. Theoretical analysis and experiments prove that the improved scheme not only maintains the excellent statistical performances of the original one, but also can resist various attacks.