Cracking a hierarchical chaotic image encryption algorithm based on permutation

Abstract

In year 2000, an efficient hierarchical chaotic image encryption (HCIE) algorithm was proposed, which divides a plain-image of size $M\times N$ 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 $O(\lceil {\log }_T(M\cdot N/K)\rceil )$ known/chosen plain-images are sufficient to achieve a good performance, and the computational complexity is $O(M\cdot N\cdot \lceil {\log }_T(M\cdot N/K)\rceil )$, 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.

8 pages

References in corpus (1)

• Cryptanalyzing image encryption using chaotic logistic map

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