Exploiting Dynamic Vector-Level Operations and a 2D-Enhanced Logistic Modular Map for Efficient Chaotic Image Encryption

. 2023 Jul 31;25(8):1147. doi: 10.3390/e25081147

Algorithm 2 Dynamic binary diffusion algorithm

Input:
The input image $C^{(1)}$ , $v^{(x)}$ and $U^{(x)}$ obtained in hash value stacking, and the key streams $Q^{(3)}$ .

1:
Get the height M and width N of $C^{(1)}$ ;
2:
Reshape $Q^{(3)}$ into a matrix of size $M \times N$ ;
3:
Set $r^{(p)} = ((v^{(x)} + Q^{(3)} (1, 1)) mod ⌊N / 8⌋) + ⌊N / 2⌋$ ;
4:
Set $R^{(t)} = 1 : r^{(p)}$ ;
5:
Set $C^{(2)} \in N^{M \times N}$ ;
6:
$C^{(2)} (1, R^{(t)}) = C^{(1)} (1, R^{(t)}) \dot{+} Q^{(3)} (1, R^{(t)}) \otimes U^{(x)} (1, R^{(t)}) \dot{+} Q^{(3)} (M, R^{(t)}) \otimes U^{(x)} (2, R^{(t)})$ ;
7:
$C^{(2)} (2, R^{(t)}) = C^{(1)} (2, R^{(t)}) \dot{+} Q^{(3)} (2, R^{(t)}) \otimes C^{(2)} (1, R^{(t)}) \dot{+} Q^{(3)} (1, R^{(t)}) \otimes U^{(x)} (3, R^{(t)})$ ;
8:
for $i = 3$ to M do
9:
$C^{(2)} (i, R^{(t)}) = C^{(1)} (i, R^{(t)}) \dot{+} Q^{(3)} (i, R^{(t)}) \otimes C^{(2)} (i - 1, R^{(t)}) \dot{+} Q^{(3)} (i - 1, R^{(t)}) \otimes C^{(2)} (i - 2, R^{(t)})$ ;
10:
end for
11:
$R^{(t)} = (r^{(p)} + 1) : N$ ;
12:
$C^{(2)} (1, R^{(t)}) = C^{(1)} (1, R^{(t)}) \oplus Q^{(3)} (1, R^{(t)}) \oplus C^{(1)} (M, R^{(t)})$ ;
13:
for $i = 2$ to M do
14:
$C^{(2)} (i, R^{(t)}) = C^{(1)} (i, R^{(t)}) \oplus Q^{(3)} (i, R^{(t)}) \oplus C^{(2)} (i - 1, R^{(t)})$ ;
15:
end for