## 5 Conclusions  
In this paper, a novel asymmetric hyperchaotic image encryption scheme based on elliptic curve cryptography was proposed. To avoid public channel attacks, in accordance with good speed and security, ECC was used to encrypt sensitive data related with the initial parameters which generated the hyperchaotic sequence.  
For the enhancement of time efficiency, in permutation the plain image was firstly divided into five planes according to the amount of information contained in different bits: the combination of the low 4 bits, and the other four planes of high 4 bits. After that, the corresponding rules of block partition were adopted for different planes: smaller sized blocks for the plane contained more information than others. This was followed by the permutation in accordance with the hyperchaotic sequences, where these partied blocks were regarded as the basic units. In the process of diffusion, for the improvement of simplicity of the algorithm, the hyperchaotic sequence used in permutation was applied in diffusion. For the pixels in the two-dimensional plane, we started from the bottom right corner, right to left, bottom to top, and after this procedure, pixels were generally related to the pixels in the previous two directions, which results in more complexity for the correlation.  
The experimental results demonstrated that this scheme could resist public channel attacks, statistical analysis attacks, and chosen-plaintext attacks with advantages. According to the data from the analysis of encryption speed (throughput and the number of machine cycles consumed), the scheme performed better speed compared with some bit-level based scheme and showed more security than a various of block shuffling methods. The current version of the algorithm is implemented on the basis of the MATLAB platform, and to improve the time efficiency, the FPGA version will be considered soon for further progress.  
During the completion of this article, [PERSON] and [PERSON] guided the determination of the direction for the research and the revising of the whole article; [PERSON] offered the opportunity and the guidance of the knowledge that related with the hyperchaotic encryption; [PERSON] provided some advice and ideas for the implementation on the MATLAB during the experimental simulation; [PERSON] constructed the structure of the scheme, performed the experiments with the data mining and completed the whole paper; [PERSON] contributed to the composition with the use of texLive. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fundamental Research Funds for the Central Universities (Izujbky-2018-126).  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **256 \(\times\) 256** & **Platform** \\ \hline Ours & 0.4313 & MATLAB \\ [21] & 0.5612 & MATLAB \\ [33] & 0.7389 & MATLAB \\ [37] & 0.5358 & MATLAB \\ [38] & 0.3065 & MATLAB \\ \hline \hline \end{tabular}
\end{table}
Table 6: The encryption time for different algorithms (seconds).  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Encryption Throughput (MBps)** & **Cycles per Byte** \\ \hline Ours & **0.2029** & **10,394.31** \\ [21] & 0.1560 & 13,525.64 \\ [33] & 0.1184 & 17,807.46 \\ [37] & 0.1634 & 12,912.76 \\ [38] & 0.2856 & 7386.63 \\ \hline \hline \end{tabular}
\end{table}
Table 7: A comparison of the efficiency of different algorithms.  
**Acknowledgments:** In the whole process of accomplishing this paper, I really appreciate the support from my family and the help from colleagues of Lanzhou University, who also contributed a lot. Finally, I also sincerely thank the foundation for the research support.  
**Conflicts of Interest:** The authors declare no conflicts of interest.