Algorithm 3. Hill Cipher with Orthogonal Matrix

Input: Permuted image array $L,$ $K_2$ Output: An array $E$ of order $M$.   1.$\mathrm{Use}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{of}\mathrm{a}\mathrm{plane}\mathrm{to}\mathrm{generate}\mathrm{the}\mathrm{key}\mathrm{orthogonal}\mathrm{matrix}.K_2$$\mathrm{will}\mathrm{be}\mathrm{the}\mathrm{orthogonal}\mathrm{key}\mathrm{matrix}\mathrm{under}\mathrm{mod}256\mathrm{of}\mathrm{order}3\times 3$.   2. $\mathrm{Making}\mathrm{blocks}{L}_r$ (i) $\mathrm{Transform}\mathrm{one}\text{-}\mathrm{dimensional}\mathrm{array}\mathrm{into}\mathrm{block}\mathrm{vectors}\mathrm{of}\mathrm{size}3\times 1$$.\mathrm{The}r\mathrm{th}$$\mathrm{block}\mathrm{is}{L}_r$, where $$r=1,2,3,\mathrm{\dots },\raisebox{1ex}{$M$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$$ (ii) Hill cipher is implemented by using the following formula $$A^r=K_2\times L_r\left(mod256\right).$$ (iii) $\mathrm{Write}\mathrm{all}{A}_r{}^{\prime }s$ in one-dimensional array again such that $$E=\left\{A^1,A^2,A^3, \dots ,A^{\raisebox{1ex}{$M$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right\}.$$