SCIENCE CHINA Information Sciences, Volume 61, Issue 5: 058104(2018) https://doi.org/10.1007/s11432-017-9191-x

## Spatial image encryption algorithm based on chaotic map and pixel frequency

Guodong YE1,2,*,
• AcceptedJul 19, 2017
• PublishedNov 20, 2017
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### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61602124, 61702116), Natural Science Foundations of Guangdong Province of China (Grant Nos. 2016A030310333, 2015A030313614, 2015A030313620), Science and Technology Planning Project of Guangdong Province of China (Grant No. 2017A010101025), China Postdoctoral Science Foundation (Grant No. 2017M611991), Program for Scientific Research Start-up Funds of Guangdong Ocean University of China (Grant No. R17037), and Special Funding Program for Excellent Young Scholars of Guangdong Ocean University of China (Grant No. HDYQ2017006). The authors would like to thank Professor Guanrong Chen at City University of Hong Kong for correcting the expressions in this whole manuscript.

Appendix A–C.

### References

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• Figure 1

Cipher-image of Lena.

•
 Algorithm 1 (For encryption) Input: image $P$, keys $x_{0}$, $y_{0}$, $z_{0}$. Output: image $E$. Let $D=P$, $E=zeros(m,~n)$; for $i=1:m$ do D(1, :)=[~]; Compute $s$ using Eq. (2) for $D$; $s=floor(s\times10^{14})+i~\textrm{mod}~m$; $H=T((i-1)n+1+s:~in+s)$; $E(i,~:)=~P(i,~:)+H+E(i-1,~:)~\textrm{mod}~256$; end for
•
 Algorithm 2 (For encryption) Input: image $E$, keys $x_{0}$, $y_{0}$, $z_{0}$. Output: cipher-image $C$. Let $D=E$, $C=zeros(m,~n)$; for $j=1:n$ do D(:, 1)=[~]; Compute $s$ using Eq. (2) for $D$; $s=floor(s\times10^{14})+j~\textrm{mod}~n$; $L=T((j-1)m+1+s:~jm+s)$; $C(:,~j)=~E(:,~j)+L+C(:,~j-1)~\textrm{mod}~256$; end for
• #### 9

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