# Cryptanalysis of Permutation-Diffusion-Based Lightweight Chaotic Image Encryption Scheme Using CPA
## 4 Conclusions  
This paper has proposed a novel means of attacking the recent proposed 2D chaotic encryption scheme. The original cryptosystem is based on permutation-diffusion structure, and its security merely relies on two permutation key matrices--**X** and **Y**--and an diffusion key \(R\). We found the cryptosystem has potential vulnerability for resistance against CPA attacks. In this paper, the total \(1+\left\lceil\log_{L}(M\times N)\right\rceil\) chosen-plaintext images can completely collapse the original cryptosystem: one full zero image was used for breaking the original diffusion phase and \(\left\lceil\log_{L}(M\times N)\right\rceil\) plaintext images used for cracking the original permutation phase. Experiments has verified the feasibility the proposed attack strategy, especially applicable for images with any sizes.  
Additionally, it is clear from the above discussion that the methods may be effective to improve the security of the original encryption scheme. (1) Associate the key with the plain image closely to reduce the possibility of violent attacks; the key is dynamic, and each plain image corresponds to a set of keys. (2) Add a substitute phase before the original diffusion phase to protect against chosen plaintext attacks to a certain extent. (3) Improve encryption structures, such as diffusion between row  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Image Size**} & \multirow{2}{*}{**Image**} & \multicolumn{3}{c}{**Encrypted**} & \multicolumn{3}{c}{**Attack**} \\ \cline{3-8}  & & **Permutation** & **Diffusion** & **Total** & **Permutation** & **Diffusion** & **Total** \\ \hline \multirow{3}{*}{\(256\times 256\)} & Lena & 0.0654 & 0.1445 & 0.2099 & 0.4619 & 2.4130 & 2.8749 \\  & Peppers & 0.1285 & 0.1359 & 0.2644 & 0.3859 & 2.4044 & 2.7903 \\  & Chemical plant & 0.0691 & 0.1343 & 0.2034 & 0.4268 & 2.4500 & 2.8768 \\ \hline \multirow{3}{*}{\(512\times 512\)} & Average running time & 0.0877 & 0.1382 & 0.2259 & 0.4249 & 2.4225 & 2.8473 \\ \cline{2-8}  & Lena & 0.3460 & 0.5924 & 0.9384 & 1.8203 & 8.2682 & 10.0885 \\  & Peppers & 0.3620 & 0.5283 & 0.8903 & 1.6024 & 8.0715 & 9.6739 \\  & Chemical plant & 0.3739 & 0.6094 & 0.9833 & 1.4860 & 8.3940 & 9.8800 \\ \hline \multirow{3}{*}{\(1024\times 1024\)} & Average running time & 0.3606 & 0.5767 & 0.9373 & 1.6362 & 8.2446 & 9.8808 \\ \cline{2-8}  & Lena & 1.3516 & 2.3106 & 3.6622 & 0.4619 & 32.7784 & 33.2403 \\ \cline{1-1}  & Peppers & 1.2991 & 2.2230 & 3.5221 & 6.6447 & 34.2910 & 40.9357 \\ \cline{1-1}  & Chemical plant & 1.3232 & 2.3558 & 3.6790 & 6.0613 & 32.3943 & 38.4556 \\ \hline \multirow{3}{*}{\(1024\times 1024\)} & Average running time & 1.3246 & 2.2965 & 3.6211 & 4.3893 & 33.1546 & 37.5439 \\ \cline{1-1} \cline{2-8}  & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Execution time (seconds).  
circular shift and column circular shift, increasing the number of pixels for boundary substitution and so on. Actually, the complexity and security of encryption schemes mainly depends on the structure of the encryption scheme and the choice of the key, which are difficult to preserve at the same time. Therefore, sometimes there is a trade-off between the security and complexity of encryption schemes.  
Conceptualization, M.L.; Methodology, M.L.; Software, K.Z.; Validation, H.R.; Formal Analysis, H.F.; Investigation, H.R.; Writing--Original Draft Preparation, K.Z. and H.R.; Writing--Review and Editing, H.F.; Visualization, K.Z.; Supervision, H.F.; Funding Acquisition, M.L. and H.F.  
This research was funded by the National Natural Science Foundation of China (Grant nos., 61602158, U1604154), the Science and Technology Research Project of Henan Province (Grant no., 182102210374), the Science Foundation for the Excellent Youth Scholars of Henan Normal University (Grant no., YQ201607), and the PhD Scientific Research Foundation of Henan Normal University (Grant no., 5101119170143).  
The authors declare no conflicts of interest.