Cryptanalyzing a bit-level image encryption algorithm based on chaotic maps

Recently, a bit-level image encryption algorithm based on chaotic maps (BCIEA) has been presented. BCIEA consists of diffusion and confusion, and its security performance mainly relies on the dynamic mechanisms introduced during diffusion and confusion, respectively. However, after a careful cryptanalysis, we found that BCIEA has fatal security issues. Although the bit-level diffusion formally employs complex chaining operations, there is a defect that the chaotic sequences can be used as an equivalent key. In addition, by analyzing its confusion, it is found that the dynamic mechanism adopted has obvious statistical characteristics, and it is especially difficult to resist all zero ciphertext attack. In addition, we also found that the BCIEA description is not rigorous, resulting in algorithm details that cannot be decrypted. On the basis of slightly reasonable modification, we propose a chosen-ciphertext attack method for cracking BCIEA. The method first uses the all-zero ciphertext to degrade it into a diffusion-only algorithm, and then chooses a cipher image with the same sum value as that of the target cipher image to break the confusion module possessing a dynamic mechanism. Theoretical analyses and experimental results verify the effectiveness and efficiency of the proposed attack method. This work can provide a reference for improving the security of image encryption schemes based on bit-level techniques.