Cracking a hierarchical chaotic image encryption algorithm based on permutation
In year 2000, an efficient hierarchical chaotic image encryption (HCIE) algorithm was proposed, which divides a plain image of size M x N with T possible value levels into K blocks of the same size and then operates position permutation on two levels: intra block and inter block. As a typical position permutation only encryption algorithm, it has received intensive attention. The present paper analyzes specific security performance of HCIE against ciphertext only attack and known/chosen plaintext attack. It is found that only O log T M N K known/chosen plain images are sufficient to achieve a good performance, and the computational complexity is O M N log T M N K which effectively demonstrates that hierarchical permutation only image encryption algorithms are less secure than normal (i.e. non hierarchical) ones. Detailed experiment results are given to verify the feasibility of the known plaintext attack. In addition, it is pointed out that the security of HCIE against ciphertext only attack was much overestimated. HighlightsSecurity performance of an encryption algorithm called HCIE is analyzed in detail.Hierarchical permutation only encryption schemes are less secure than normal ones.Security of HCIE against ciphertext only attack was reported being overestimated.
Signal Process.