In year 2000, an efficient hierarchical chaotic image encryption (HCIE) algorithm was proposed, which divides a plain-image of size M×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 permutationonly 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.
Li REF has presented the performance analysis of the Hierarchical Chaotic Image Encryption (HCIE) algorithm.
Cracking a hierarchical chaotic image encryption algorithm based on permutation
Signal Processing, 2016, 118: 203-210
Mathematics Computer Science