Cryptanalysis of an Image Encryption Algorithm Based on a 2D Hyperchaotic Map

. 2022 Oct 28;24(11):1551. doi: 10.3390/e24111551

Algorithm 1 The proposed chosen-plaintext attack

Output:
The plaintext P of C
Input:
The ciphertext C of size H × D
1:
// step1: construct an all-zero matrix and obtain the equivalent key T of diffusion stage
2:
$P 0$ = zeros $(H, W)$ ;
3:
$C 0$ = encrypt $(P 0)$ ;
4:
$T = C 0$ ;
5:
// step2: initialize $⌈ \log_{L} (H W) ⌉$ matrices and get the corresponding ciphertexts
6:
for $i = 1$ to $⌈ \log_{L} (H W) ⌉$ do
7:
$P i$ = JolfaeiAlgorithmGeneration(i);
8:
$C i$ = encrypt $(P i)$ ;
9:
end for
10:
// step3: obtain $⌈ \log_{L} (H W) ⌉$ middle results with the diffusion matrix T and the ciphertexts which are obtained in the step2
11:
for $i = 1$ to $⌈ \log_{L} (H W) ⌉$ do
12:
$S i =$ inverseDiffusionAttack $(C i - T)$ ;
13:
end for
14:
// step4: obtain the equivalent permutation matrix by the input plaintexts and the middle results
15:
for $i = 1$ to $⌈ \log_{L} (H W) ⌉$ do
16:
JolfaeiAlgorithmAdd $(P i, S i)$ ;
17:
end for
18:
$p e r m u t a t i o n M a t r i x$ = JolfaeiAlgorithm();
19:
// step5: recover the the plaintext of the target ciphertext with the equivalent key stream elements which are obtained in previous steps
20:
$S C$ = inverseDiffusionAttack $(C - T)$ ;
21:
P = inversePermute( $S C, p e r m u t a t i o n M a t r i x$ );