Algorithm 3 Diffusion algorithm

Input: The shuffled image, H, $q_{10},q_{20},a,b,c_1,c_2,{\mu }_1,{\mu }_2,{\nu }_1$, and ${\nu }_2$.  Output: D, the diffusion vector.  Step 1: Reshape H, $H=\{h_1,h_2,\dots ,h_{MN}\}$.  Step 2: Covert H to binary, $H_b$.  Step 3: Set $q_1\left(0\right)=q_{10},q_2\left(0\right)=q_{20}$.  Step 4: Perform initial iterations,           For $t=0$ to 999                   $q_1(t+1)=q_1\left(t\right)+{\nu }_1{q}_1\left(t\right)[(1-{\mu }_1)(a-2b{q}_1\left(t\right)-b{q}_2\left(t\right))-c_1]$                   $q_2(t+1)=q_2\left(t\right)+{\nu }_2{q}_2\left(t\right)[(1-{\mu }_2)(a-2b{q}_2\left(t\right)-b{q}_1\left(t\right))-c_2]$         End For  Step 5: Set $q_1\left(0\right)=q_1\left(1000\right),q_2\left(0\right)=q_2\left(1000\right)$.  Step 6: For $t=0$ to $MN-1$                   $q_1(t+1)=q_1\left(t\right)+{\nu }_1{q}_1\left(t\right)[(1-{\mu }_1)(a-1\left(t\right)-b{q}_2\left(t\right))-c_1]$                   $q_2(t+1)=q_2\left(t\right)+{\nu }_2{q}_2\left(t\right)[(1-{\mu }_2)(a-2b{q}_2\left(t\right)-b{q}_1\left(t\right))-c_2]$                   $q(t+1)=(q_1(t+1)+q_2(t+1))/2$         End For  Step 7: Preprocess the values of $Q=\left\{q\right(1),q(2),\dots ,q(MN\left)\right\}$ as follows:           $q\left(t\right)=mod(ceil(q\left(t\right)\ast {10}^{14}),256),t=1,2,\dots ,MN$.  Step 8: Covert Q to binary, $Q_b$.  Step 9: Perform $XOR$ between $H_b$ and $Q_b$, say $D=XOR(H_b,Q_b)$.