Algorithm 1 The permutation on a single eight-base DNA-level cube

Input: an eight-base DNA-level cube C, the prism length E of the cube, and three hyperchaotic subsequences $H_j^p$ (j = 1, 2, 3)

Output: the eight-base DNA-level cube C after the permutation

1: function CubePermutation($C,E,H_j^p$)

2:     for i = 1 : E do

3:         for j = 1 : 3 do

4:           $P_{i,1}\leftarrow C(i,:,:)$;

5:            $P_{i,2}\leftarrow C(:,i,:)$;

6:            $P_{i,3}\leftarrow C(:,:,i)$;

7:            for t = 1 : E do

8:                $Shifts\leftarrow H_j^p(2\times (i-1)\times E+t)$;

9:                Circular shift $P_{i,j}(t,:)$ to right by Shifts;

10:            end for

11:            for t = 1 : E do

12:                $Shifts\leftarrow H_j^p(2\times (i-1)\times E+E+t)$;

13:                Circular shift $P_{i,j}(:,t)$ to bottom by Shifts;

14:            end for

15:            $C(i,:,:)\leftarrow P_{i,1}$;

16:            $C(:,i,:)\leftarrow P_{i,2}$;

17:            $C(:,:,i)\leftarrow P_{i,3}$;

18:         end for

19:     end for

20:     return C;

21: end function