Algorithm 1. Pixel Permutation

Input: Secret key $K_1=\left(a,X\left(0\right)\right)$ Henon map (1), Color image $I$. Output: Array L of permuted pixels of an image $I$.   1.Take the original image I, which is stored in an array Y with size M = P × Q × 3, where P indicates the number of rows and Q indicates the number of columns of the image matrix I.   2.$\mathrm{Use}\mathrm{the}\mathrm{key}{K}_1$$\mathrm{with}\mathrm{Henon}\mathrm{map}\left(1\right)\mathrm{to}\mathrm{produce}\mathrm{a}\mathrm{sequence}.\mathrm{Generate}\mathrm{the}\mathrm{chaotic}\mathrm{sequence}H=\left\{h_1,h_2,\mathrm{\dots },h_M\right\}$$\mathrm{and}\mathrm{sort}\mathrm{it}\mathrm{in}\mathrm{ascending}\mathrm{order},\mathrm{the}\mathrm{resulting}\mathrm{sequence}\mathrm{is}\underset{\_}{H}=\left\{{\underset{\_}{h}}_1,{\underset{\_}{h}}_2,\mathrm{\dots },{\underset{\_}{h}}_M\right\}$.   3.$\mathrm{Compute}\mathrm{the}\mathrm{permutation}\mathrm{vector}J$$\mathrm{by}\mathrm{noting}\mathrm{the}\mathrm{positions}\mathrm{of}\mathrm{sequence}\mathrm{terms}\mathrm{of}H$$\mathrm{in}\underset{\_}{H}$$\mathrm{and}\mathrm{write}\mathrm{down}\mathrm{the}\mathrm{transformed}\mathrm{positions}J=\left\{j_1,j_2,\mathrm{\dots },j_M\right\}.$   4.$\mathrm{Use}J$$\mathrm{to}\mathrm{permute}\mathrm{the}\mathrm{positions}\mathrm{of}\mathrm{elements}\mathrm{of}\mathrm{an}\mathrm{array}Y$$\mathrm{to}\mathrm{get}L$.