Algorithm 2 Row/Columns shuffling algorithm

Input: The plain image, O, the polynomial $p\left(x\right)$, ${\alpha }_1,{\alpha }_2,{\beta }_1$, and ${\beta }_2$.  Output: H, the shuffled image.  Step 1: Set $[M,N]=size\left(O\right)$  Step 2: Use Algorithm 1, with polynomial $p\left(x\right)$, and interval $[{\alpha }_1,{\beta }_1]$, to generate a random            permutation of size M for shuffling the rows, say $S_{Rows}$.  Step 3: Use Algorithm 1, with polynomial $p\left(x\right)$, and interval $[{\alpha }_2,{\beta }_2]$, to generate a random            permutation of size N for shuffling the columns, say $S_{Columns}$.  Step 4: For $i=1$ to M, compute                   For $j=1$ to N, compute                        $H(i,j)=O(S_{Rows}\left(i\right),S_{Columns}\left(j\right))$                    End For j             End For i  Step 5: H, the shuffled image.