Security Analysis of an Image Encryption Based on the Kronecker Xor
Product, the Hill Cipher and the Sigmoid Logistic Map
George Tes¸eleanu
1,2 a
1
Advanced Technologies Institute, 10 Dinu Vintil
˘
a, Bucharest, Romania
2
Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei, Bucharest, Romania
Keywords:
Image Encryption Scheme, Chaos Based Encryption, Cryptanalysis.
Abstract:
In 2023, Mfungo et al. introduce an image encryption scheme that employs the Kronecker xor product, the
Hill cipher and a chaotic map. Their proposal uses the chaotic map to dynamically generate two out of the
three secret keys employed by their scheme. Note that both keys are dependent on the size of the original
image, while the Hill key is static. Despite the authors’ assertion that their proposal offers sufficient security
(149 bits) for transmitting color images over unsecured channels, we found that this is not accurate. To support
our claim, we present a chosen plaintext attack that requires 2 oracle queries and has a worse case complexity
of O(2
32
). Note that in this case Mfungo et al.’s scheme has a complexity of O(2
33
), and thus our attack is two
times faster than an encryption. The reason why this attack is viable is that the two keys remain unchanged
for different plaintext images of the same size, while the Hill key remains unaltered for all images.
1 INTRODUCTION
The security risks associated with digital images,
particularly theft and unauthorized distribution, have
been amplified by the widespread use of social me-
dia. Consequently, researchers have devoted signif-
icant attention to this issue and have developed var-
ious techniques to encrypt images. Chaotic maps
have emerged as a popular choice due to their high
sensitivity to initial conditions and previous states,
which makes predicting their behavior difficult. As
a result, several novel cryptographic algorithms based
on chaos have been developed. However, many im-
age encryption schemes based on chaotic maps suf-
fer from critical security vulnerabilities due to inad-
equate security analysis and a lack of design guide-
lines. In fact, numerous compromised schemes ex-
ist, which are listed non-exhaustively in Table 1. For
further information, please refer to (Zolfaghari and
Koshiba, 2022; Muthu and Murali, 2021; Hosny,
2020;
¨
Ozkaynak, 2018).
In (Mfungo et al., 2023), the authors propose a
new image encryption scheme that combines the Kro-
necker xor product, Hill cipher and sigmoid logistic
map. More specifically, their algorithm starts by shift-
ing the values in each row of all 4 × 4 image blocks
a
https://orcid.org/0000-0003-3953-2744
using the AES shift row operation. Then, the algo-
rithm performs a bitwise xor between the top value of
each odd or even column and all other values in the
corresponding even or odd column, excluding the top
value. Next, the Hill Cipher encrypts each 4×4 block
of the result. The resulting image is then xor-ed with
a key generated using the sigmoid logistic map. To
further obscure the image’s pixels, the result is trans-
formed using the Kronecker xor product. Finally, an-
other key generated using the sigmoid logistic map
is xor-ed with the output to obtain the encrypted im-
age. Since the sigmoid logistic map is simply used as
a pseudorandom number generator (PRNG) and the
scheme’s weakness is independent of the employed
generator, we omit its description and simply consider
the two keys as being randomly generated.
The focus of this paper is to carry out a security
analysis of the Mfungo et al. scheme (Mfungo et al.,
2023). We describe a chosen plaintext attack, which
would allow an attacker to decrypt all images of a
specific size. To execute such an attack, the adver-
sary would need to access the ciphertexts of 2 cho-
sen plaintexts. Once the attacker has this informa-
tion in his possession, he can easily extract the secret
keys. According to the authors, the largest image size
that they were able to handle with their available com-
putational resources was limited to 256 × 256 pixels.
Thus, in this case, the key recovery and the encryption
Te¸seleanu, G.
Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map.
DOI: 10.5220/0012307800003648
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 10th International Conference on Information Systems Security and Privacy (ICISSP 2024), pages 467-473
ISBN: 978-989-758-683-5; ISSN: 2184-4356
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
467

Table 1: Broken chaos based image encryption algorithms.
Scheme (Yen and Guo, 2000) (Matoba and Javidi, 2004) (Wang et al., 2012) (Huang et al., 2014) (Khan, 2015) (Song and Qiao, 2015) (Chen et al., 2015)
Broken by (Li and Zheng, 2002) (Wang et al., 2019) (Arroyo et al., 2013) (Wen et al., 2021) (Alanazi et al., 2021) (Wen et al., 2019) (Hu et al., 2017)
Scheme (Hu et al., 2017) (Niyat et al., 2017) (Hua and Zhou, 2017) (Pak and Huang, 2017) (Liu et al., 2018) (Shafique and Shahid, 2018) (Sheela et al., 2018)
Broken by (Li et al., 2019a) (Li et al., 2018) (Yu et al., 2021) (Wang et al., 2018) (Ma et al., 2020) (Wen and Yu, 2019) (Zhou et al., 2019)
Scheme (Wu et al., 2018) (Yosefnezhad Irani et al., 2019) (Khan and Masood, 2019) (Pak et al., 2019) (Mondal et al., 2021) (Essaid et al., 2019)
Broken by (Chen et al., 2020) (Liu et al., 2020) (Fan et al., 2021) (Li et al., 2019b) (Li et al., 2021) (Tes¸eleanu, 2023)
processes have a complexity of O (2
32
) and O(2
33
),
respectively. However, if the attacker has already
computed the Hill key, then only 1 chosen plaintext is
required and the complexity of the recovery process
is O (1). Keeping all these in mind, using the attack
described in this paper we managed to reduce the se-
curity of the scheme from 149 bits to 32, and once the
Hill key is recovered to 0. Note that we could not de-
vise an efficient chosen ciphertext attack, due to the
repetition code embedded in the encryption scheme.
Structure of the Paper. We provide the necessary
preliminaries in Section 2. An alternative description
of Mfungo et al.’s scheme is outlined in Section 3.
In Section 4 we show how an attacker can recover all
three secret keys in a chosen plaintext scenario. We
conclude in Section 5.
2 PRELIMINARIES
Notations. In this paper, the subset {1,...,s − 1} ∈
N is denoted by [1, s). The action of selecting a ran-
dom element x from a sample space X is represented
by x
$
←− X, while x ← y indicates the assignment of
value y to variable x. By H and W we denote an im-
age’s height and width.
2.1 Mfungo et al. Image Encryption
Scheme
In this section we present Mfungo et al.’s encryp-
tion (Algorithm 2) and decryption (Algorithm 3) al-
gorithms as described in (Mfungo et al., 2023). Note
that W and H must be divisible by 4.
The first step of the encryption process consists
in breaking the image in 4 × 4 blocks and then circu-
lar shifting row i of each block to the left by i posi-
tions. The exact function is provided in Algorithm 1
as shi f t rows. Note that the function takes as input
one of the following matrices
shi f t ←



0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2



or
inv shi ft ←



0 1 2 3
3 0 1 2
2 3 0 1
1 2 3 0



,
one for encryption and the other one for decryp-
tion. Then the top values of the resulting matrix
are preserved, while all values in even columns
1
are
xor-ed with the top value of the previous odd col-
umn. In the case of odd columns, the values are
xor-ed with the top value of the next column, ex-
cept their top value. The corresponding function
is xor between pairwise columns from Algorithm 1.
Using a secret 4 × 4 matrix h, each row of each 4 × 4
block is multiplied with h. Hill encryption is pre-
sented in Algorithm 1, Hill. The resulting image is
then xor-ed with k
(1)
. Another diffusion layer is then
added, i.e. the rows are moved down with 3 positions
(see Algorithm 1, shi f t columns). The Kronecker xor
transformation is then applied. More precisely, the
authors apply the Kronecker product between the im-
age and itself, with the following modifications: the
product between two elements from two distinct posi-
tions is replaced by xor, while the ones from the same
position remain unaltered. The pseudo-code is given
in the Kronecker xor trans f ormation function from
Algorithm 1. Finally, we perform a final xor with the
second key k
(2)
.
To decrypt we simply perform all the inverse op-
erations in reverse order. Note that when reversing
the Kronecker xor transformation, we should recover
the matrices from all W × H block and take a major-
ity vote for each byte. This is done in order to provide
protection against data loss and noise alteration. Ba-
sically, the compression of the Kronecker xor trans-
formation is used as a repetition code. Since, we con-
sider the ideal case when oracle answers are relayed
unaltered, we simply recover the image from the first
W × H block.
3 A NEW LOOK AT MFUNGO et
al.’s SCHEME
In this section we present an alternative description
of Mfungo et al.’s scheme. More precisely, we show
1
except their top values
ICISSP 2024 - 10th International Conference on Information Systems Security and Privacy
468

Algorithm 1: Helper Functions.
1 Function shi f t rows(P,shi f t)
2 for i ∈ [0,W ) and at each step increment i with 4 do
3 for j ∈ [0, H) do
4 for k ∈ [0, 4) do
5 index ← i + shi f t
k, j mod 4
6 Q
i+k, j
← P
index, j
7 return Q
8 Function xor between pairwise columns(P)
9 for i ∈ [0,W ) do R
i,0
← P
i,0
10 for i ∈ [0,W ) and at each step increment i with 2 do
11 for j ∈ [1, H) do
12 R
i, j
← P
i, j
⊕ P
i+1,0
13 R
i+1, j
← P
i+1, j
⊕ P
i,0
14 return R
15 Function Hill(P,h)
16 for i ∈ [0,W ) and at each step increment i with 4 do
17 for j ∈ [0, H) do
18
S
i, j
← P
i, j
h
0,0
+ P
i+1, j
h
0,1
+ P
i+2, j
h
0,2
+ P
i+3, j
h
0,3
mod 256
S
i+1, j
← P
i, j
h
1,0
+ P
i+1, j
h
1,1
+ P
i+2, j
h
1,2
+ P
i+3, j
h
1,3
mod 256
S
i+2, j
← P
i, j
h
2,0
+ P
i+1, j
h
2,1
+ P
i+2, j
h
2,2
+ P
i+3, j
h
2,3
mod 256
S
i+3, j
← P
i, j
h
3,0
+ P
i+1, j
h
3,1
+ P
i+2, j
h
3,2
+ P
i+3, j
h
3,3
mod 256
19 return S
20 Function shi f t columns(P, n)
21 for i ∈ [0,W ) and j ∈ [0,H) do
22 T
i, j
← P
i, j+n mod H
23 return T
24 Function Kronecker xor trans f ormation(P)
25 for i ∈ [0,W ) and j ∈ [0,H) do
26 for k ∈ [0,W ) and ℓ ∈ [0,H) do
27 if i = k and j = ℓ then U
i·W+k, j·H+ℓ
← P
i, j
28 else U
i·W+k, j·H+ℓ
← P
i, j
⊕ P
k,ℓ
29 return U
30 Function compress Kronecker xor trans f ormation(P)
31 for i ∈ [0,W ) and j ∈ [0,H) do
32 if i = 0 and j = 0 then T
i, j
← P
i, j
33 else T
i, j
← P
i, j
⊕ P
0,0
34 return T
how to combine k
(1)
and k
(2)
into a single key k
(3)
.
The alternative encryption and decryption algorithms
are provided in Algorithms 4 and 5.
We further show how we derived the equivalent
description of lines 4-7, Algorithm 2. After the
shi f t row operation we obtain
T
i, j
← S
i, j+3 mod H
⊕ k
(1)
i, j+3 mod H
.
Applying the Kronecker transformation we get
U
i·W+k, j·H+ℓ
← T
i, j
= S
i, j+3 mod H
⊕ k
(1)
i, j+3 mod H
when i = k and j = ℓ and
U
i·W+k, j·H+ℓ
← T
i, j
⊕ T
k,ℓ
= S
i, j+3 mod H
⊕ k
(1)
i, j+3 mod H
⊕ S
k,ℓ+3 mod H
⊕ k
(1)
k,ℓ+3 mod H
= (S
i, j+3 mod H
⊕ S
k,ℓ+3 mod H
)
⊕ (k
(1)
i, j+3 mod H
⊕ k
(1)
k,ℓ+3 mod H
),
Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map
469

Algorithm 2: Encryption algorithm.
Input: A plaintext P, two secret keys k
(1)
and
k
(2)
, and a secret matrix h
Output: A ciphertext C
1 Q ← shi f t rows(P,shi f t)
2 R ← xor between pairwise columns(Q)
3 S ← Hill(R,h)
4 for i ∈ [0,W ) and j ∈ [0,H) do
S
i, j
← S
i, j
⊕ k
(1)
i, j
5 T ← shi ft columns(S, 3)
6 U ← Kronecker xor trans f ormation(T )
7 for i ∈ [0,W
2
) and j ∈ [0, H
2
) do
C
i, j
← U
i, j
⊕ k
(2)
i, j
8 return C
Algorithm 3: Decryption algorithm.
Input: A ciphertext C, two secret keys k
(1)
and k
(2)
, and a secret matrix h
Output: A plaintext P
1 for i ∈ [0,W
2
) and j ∈ [0, H
2
) do
U
i, j
← C
i, j
⊕ k
(2)
i, j
2 T ←
compress Kronecker xor trans f ormation(U)
3 S ← shi f t columns(T, −3)
4 for i ∈ [0,W ) and j ∈ [0,H) do
S
i, j
← S
i, j
⊕ k
(1)
i, j
5 R ← Hill(S,h
−1
)
6 Q ← xor between pairwise columns(R)
7 P ← shi f t rows(Q,inv shi f t)
8 return P
otherwise. Finally, we get
C
i·W+k, j·H+ℓ
← U
i·W+k, j·H+ℓ
⊕ k
(2)
i·W+k, j·H+ℓ
= S
i, j+3 mod H
⊕ (k
(1)
i, j+3 mod H
⊕ k
(2)
i·W+k, j·H+ℓ
)
when i = k and j = ℓ and
C
i·W+k, j·H+ℓ
← U
i·W+k, j·H+ℓ
⊕ k
(2)
i·W+k, j·H+ℓ
= (S
i, j+3 mod H
⊕ S
k,ℓ+3 mod H
)
⊕ (k
(1)
i, j+3 mod H
⊕ k
(1)
k,ℓ+3 mod H
⊕ k
(2)
i·W+k, j·H+ℓ
),
otherwise. Note that if we compose
Kr = Kronecker xor trans f ormation with
sc = shi f t columns we get
Kr(sc(S, 3)) = S
i, j+3 mod H
if i = k and j = ℓ and
Kr(sc(S, 3)) = S
i, j+3 mod H
⊕ S
k,ℓ+3 mod H
,
otherwise. Therefore, if we define k
(3)
as follows
k
(3)
i·W+k, j·H+ℓ
= k
(1)
i, j+3 mod H
⊕ k
(2)
i·W+k, j·H+ℓ
,
if i = k and j = ℓ and
k
(3)
i·W+k, j·H+ℓ
= k
(1)
i, j+3 mod H
⊕ k
(1)
k,ℓ+3 mod H
⊕ k
(2)
i·W+k, j·H+ℓ
otherwise, we get the equivalent description of lines 4-7,
Algorithm 2 provided in lines 4-6, Algorithm 4.
Algorithm 4: Equivalent encryption algorithm.
Input: A plaintext P, a secret key k
(3)
, and a
secret matrix h
Output: A ciphertext C
1 Q ← shi f t rows(P,shi f t)
2 R ← xor between pairwise columns(Q)
3 S ← Hill(R,h)
4 T ← shi ft columns(S, 3)
5 U ← Kronecker xor trans f ormation(T )
6 for i ∈ [0,W
2
) and j ∈ [0, H
2
) do
C
i, j
← U
i, j
⊕ k
(3)
i, j
7 return C
Algorithm 5: Equivalent decryption algorithm.
Input: A ciphertext C, a secret key k
(3)
, and a
secret matrix h
Output: A plaintext P
1 for i ∈ [0,W
2
) and j ∈ [0, H
2
) do
2 U
i, j
← C
i, j
⊕ k
(3)
i, j
3 T ←
compress
Kronecker xor trans f ormation(U )
4 S ← shi f t columns(T, −3)
5 R ← Hill(S,h
−1
)
6 Q ← xor between pairwise columns(R)
7 P ← shi f t rows(Q,inv shi f t)
8 return P
4 CHOSEN PLAINTEXT ATTACK
A chosen plaintext attack (CPA) is a scenario in which
the attacker A briefly gains access to the encryption
machine O
enc
and is permitted to query it with vari-
ous inputs. In this way, A generates specific plaintexts
that can facilitate his attack and uses O
enc
to obtain the
ICISSP 2024 - 10th International Conference on Information Systems Security and Privacy
470

corresponding ciphertexts. We demonstrate in this pa-
per that Mfungo et al.’s image encryption scheme is
vulnerable to such attacks.
In the first step of our attack we aim to retrieve
k
(3)
. This can be easily done if we encrypt an image I
0
with all its pixels set to 0. By setting all the pixels to 0,
after passing the image through lines 1-5, Algorithm 4
we end up with the same image I
0
. Therefore, we
retrieve the key from k
(3)
i, j
= C
i, j
.
Let
P
[0,4),[0,4)
=



P
0,0
P
1,0
P
2,0
P
3,0
P
0,1
P
1,1
P
2,1
P
3,1
P
0,2
P
1,2
P
2,2
P
3,2
P
0,3
P
1,3
P
2,3
P
3,3



.
Now we aim to find the secret matrix h. Hence, we
create an image I
h
such that
P
[0,4),[0,4)
←



1 0 0 0
0 0 0 0
1 0 0 1
1 0 1 0



and the remaining pixels are set to 0. Since we are
only interested in the first 4 × 4 block, we will only
study its evolution. Thus, after the shi f t row and
xor between pairwise columns operations we obtain
Q
[0,4),[0,4)
←



1 0 0 0
0 0 0 0
0 1 1 0
0 1 0 1



and
R
[0,4),[0,4)
←



1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1



.
Therefore, we obtain that
S
[0,4),[0,4)
←



h
0,0
h
1,0
h
2,0
h
3,0
h
0,1
h
1,1
h
2,1
h
3,1
h
0,2
h
1,2
h
2,2
h
3,2
h
0,3
h
1,3
h
2,3
h
3,3



.
is the transpose of h. Since we already know k
(3)
and
the remaining operations are easily reversible, it re-
sults that we can retrieve h from the ciphertext cor-
responding to I
h
. The formal description of our CPA
attack is provided in Algorithm 6.
The complexity of Algorithm 6 is O(H
2
W
2
+
2HW ) and we need 2 oracle queries. Note that
Mfugo et al.’s encryption scheme has a complexity
of O (2H
2
W
2
+ 8HW ) and according to the authors
the maximum image size that they experimented on
is H = W = 256. Thus, in this case, our attack has
Algorithm 6: CPA attack.
1 %recover k
(3)
2 for i ∈ [0, H) and j ∈ [0,W ) do P
i, j
← 0
3 Send the plaintext P to the encryption oracle
O
enc
.
4 Receive the ciphertext C from the encryption
oracle O
enc
.
5 k
(3)
← C
6 %recover h
7 P
0,0
,P
1,0
,P
2,0
,P
3,0
← 1,0, 0, 0
8 P
0,1
,P
1,1
,P
2,1
,P
3,1
← 0,0, 0, 0
9 P
0,2
,P
1,2
,P
2,2
,P
3,2
← 1,0, 0, 1
10 P
0,3
,P
1,3
,P
2,3
,P
3,3
← 1,0, 1, 0
11 Send the plaintext P to the encryption oracle
O
enc
.
12 Receive the ciphertext C from the encryption
oracle O
enc
.
13 for i ∈ [0,W
2
) and [0,H
2
) do
U
i, j
← C
i, j
⊕ k
(3)
i, j
14 T ←
compress Kronecker xor trans f ormation(U)
15 S ← shi f t columns(T, −3)
16 h
T
← S
[0,4),[0,4)
17 return k
(3)
,h
a complexity of O (2
32
), while Mfugo et al.’s scheme
has one of O (2
33
). Remark that if we already recov-
ered h in a previous iteration, we only need to run
lines 2-5, Algorithm 6. Thus, the complexity becomes
O(1) and we need 1 oracle query.
5 CONCLUSIONS
In (Mfungo et al., 2023), the authors presented a
scheme for encrypting images using a combination of
the Kronecker xor product, Hill cipher, and a chaotic
map. They claimed that their proposal provided a
security strength of 149 bits. However, our analy-
sis of the scheme’s security has revealed that its ac-
tual strength is only O(2
32
) in the worst-case sce-
nario. Note that the attack only requires two ora-
cle queries. Consequently, the proposed cryptosystem
fails to meet the necessary security strength needed to
protect confidential information.
REFERENCES
Alanazi, A. S., Munir, N., Khan, M., Asif, M., and Hus-
sain, I. (2021). Cryptanalysis of Novel Image Encryp-
Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map
471

tion Scheme Based on Multiple Chaotic Substitution
Boxes. IEEE Access, 9:93795–93802.
Arroyo, D., Diaz, J., and Rodriguez, F. (2013). Cryptanaly-
sis of a One Round Chaos-Based Substitution Permu-
tation Network. Signal Processing, 93(5):1358–1364.
Chen, J., Chen, L., and Zhou, Y. (2020). Cryptanalysis of a
DNA-Based Image Encryption Scheme. Information
Sciences, 520:130–141.
Chen, J.-x., Zhu, Z.-l., Fu, C., Zhang, L.-b., and Zhang, Y.
(2015). An Efficient Image Encryption Scheme Using
Lookup Table-Based Confusion and Diffusion. Non-
linear Dynamics, 81(3):1151–1166.
Essaid, M., Akharraz, I., Saaidi, A., and Mouhib, A. (2019).
A New Approach of Image Encryption Based on
Dynamic Substitution and Diffusion Operations. In
SysCoBIoTS 2019, pages 1–6. IEEE.
Fan, H., Zhang, C., Lu, H., Li, M., and Liu, Y. (2021).
Cryptanalysis of a New Chaotic Image Encryption
Technique Based on Multiple Discrete Dynamical
Maps. Entropy, 23(12):1581.
Hosny, K. M. (2020). Multimedia Security Using Chaotic
Maps: Principles and Methodologies, volume 884.
Springer.
Hu, G., Xiao, D., Wang, Y., and Li, X. (2017). Cryptanal-
ysis of a Chaotic Image Cipher using Latin Square-
Based Confusion and Diffusion. Nonlinear Dynamics,
88(2):1305–1316.
Hua, Z. and Zhou, Y. (2017). Design of Image Cipher Using
Block-Based Scrambling and Image Filtering. Infor-
mation sciences, 396:97–113.
Huang, X., Sun, T., Li, Y., and Liang, J. (2014). A Color
Image Encryption Algorithm Based on a Fractional-
Order Hyperchaotic System. Entropy, 17(1):28–38.
Khan, M. (2015). A Novel Image Encryption Scheme
Based on Multiple Chaotic S-Boxes. Nonlinear Dy-
namics, 82(1):527–533.
Khan, M. and Masood, F. (2019). A Novel Chaotic Im-
age Encryption Technique Based on Multiple Discrete
Dynamical Maps. Multimedia Tools and Applications,
78(18):26203–26222.
Li, M., Lu, D., Wen, W., Ren, H., and Zhang, Y. (2018).
Cryptanalyzing a Color Image Encryption Scheme
Based on Hybrid Hyper-Chaotic System and Cellular
Automata. IEEE access, 6:47102–47111.
Li, M., Lu, D., Xiang, Y., Zhang, Y., and Ren, H. (2019a).
Cryptanalysis and Improvement in a Chaotic Image
Cipher Using Two-Round Permutation and Diffusion.
Nonlinear Dynamics, 96(1):31–47.
Li, M., Wang, P., Liu, Y., and Fan, H. (2019b). Crypt-
analysis of a Novel Bit-Level Color Image Encryp-
tion Using Improved 1D Chaotic Map. IEEE Access,
7:145798–145806.
Li, M., Wang, P., Yue, Y., and Liu, Y. (2021). Cryptanaly-
sis of a Secure Image Encryption Scheme Based on a
Novel 2D Sine–Cosine Cross-Chaotic Map. Journal
of Real-Time Image Processing, 18(6):2135–2149.
Li, S. and Zheng, X. (2002). Cryptanalysis of a Chaotic
Image Encryption Method. In ISCAS 2002, volume 2,
pages 708–711. IEEE.
Liu, L., Hao, S., Lin, J., Wang, Z., Hu, X., and Miao, S.
(2018). Image Block Encryption Algorithm Based on
Chaotic Maps. IET Signal Processing, 12(1):22–30.
Liu, Y., Qin, Z., Liao, X., and Wu, J. (2020). Cryptanaly-
sis and Enhancement of an Image Encryption Scheme
Based on a 1-D Coupled Sine Map. Nonlinear Dy-
namics, 100(3):2917–2931.
Ma, Y., Li, C., and Ou, B. (2020). Cryptanalysis of an
Image Block Encryption Algorithm Based on Chaotic
Maps. Journal of Information Security and Applica-
tions, 54:102566.
Matoba, O. and Javidi, B. (2004). Secure Holographic
Memory by Double-Random Polarization Encryption.
Applied Optics, 43(14):2915–2919.
Mfungo, D. E., Fu, X., Wang, X., and Xian, Y. (2023).
Enhancing Image Encryption with the Kronecker Xor
Product, the Hill Cipher, and the Sigmoid Logistic
Map. Applied Sciences, 13(6).
Mondal, B., Behera, P. K., and Gangopadhyay, S. (2021). A
Secure Image Encryption Scheme Based on a Novel
2D Sine–Cosine Cross-Chaotic (SC3) Map. Journal
of Real-Time Image Processing, 18(1):1–18.
Muthu, J. S. and Murali, P. (2021). Review of Chaos De-
tection Techniques Performed on Chaotic Maps and
Systems in Image Encryption. SN Computer Science,
2(5):1–24.
Niyat, A. Y., Moattar, M. H., and Torshiz, M. N. (2017).
Color Image Encryption Based on Hybrid Hyper-
Chaotic System and Cellular Automata. Optics and
Lasers in Engineering, 90:225–237.
¨
Ozkaynak, F. (2018). Brief Review on Application of Non-
linear Dynamics in Image Encryption. Nonlinear Dy-
namics, 92(2):305–313.
Pak, C., An, K., Jang, P., Kim, J., and Kim, S. (2019). A
Novel Bit-Level Color Image Encryption Using Im-
proved 1D Chaotic Map. Multimedia Tools and Ap-
plications, 78(9):12027–12042.
Pak, C. and Huang, L. (2017). A New Color Image En-
cryption Using Combination of the 1D Chaotic Map.
Signal Processing, 138:129–137.
Shafique, A. and Shahid, J. (2018). Novel Image Encryption
Cryptosystem Based on Binary Bit Planes Extraction
and Multiple Chaotic Maps. The European Physical
Journal Plus, 133(8):1–16.
Sheela, S., Suresh, K., and Tandur, D. (2018). Image En-
cryption Based on Modified Henon Map Using Hy-
brid Chaotic Shift Transform. Multimedia Tools and
Applications, 77(19):25223–25251.
Song, C. and Qiao, Y. (2015). A Novel Image Encryption
Algorithm Based on DNA Encoding and Spatiotem-
poral Chaos. Entropy, 17(10):6954–6968.
Tes¸eleanu, G. (2023). Security Analysis of a Color Im-
age Encryption Scheme Based on Dynamic Substi-
tution and Diffusion Operations. In ICISSP 2023.
SCITEPRESS.
Wang, H., Xiao, D., Chen, X., and Huang, H. (2018). Crypt-
analysis and Enhancements of Image Encryption Us-
ing Combination of the 1D Chaotic Map. Signal pro-
cessing, 144:444–452.
ICISSP 2024 - 10th International Conference on Information Systems Security and Privacy
472

Wang, L., Wu, Q., and Situ, G. (2019). Chosen-Plaintext
Attack on the Double Random Polarization Encryp-
tion. Optics Express, 27(22):32158–32167.
Wang, X., Teng, L., and Qin, X. (2012). A Novel Colour
Image Encryption Algorithm Based on Chaos. Signal
Processing, 92(4):1101–1108.
Wen, H. and Yu, S. (2019). Cryptanalysis of an Image
Encryption Cryptosystem Based on Binary Bit Planes
Extraction and Multiple Chaotic Maps. The European
Physical Journal Plus, 134(7):1–16.
Wen, H., Yu, S., and L
¨
u, J. (2019). Breaking an Image
Encryption Algorithm Based on DNA Encoding and
Spatiotemporal Chaos. Entropy, 21(3):246.
Wen, H., Zhang, C., Huang, L., Ke, J., and Xiong, D.
(2021). Security Analysis of a Color Image Encryp-
tion Algorithm Using a Fractional-Order Chaos. En-
tropy, 23(2):258.
Wu, J., Liao, X., and Yang, B. (2018). Image Encryption
Using 2D H
´
enon-Sine Map and DNA Approach. Sig-
nal processing, 153:11–23.
Yen, J.-C. and Guo, J.-I. (2000). A New Chaotic Key-Based
Design for Image Encryption and Decryption. In IS-
CAS 2000, volume 4, pages 49–52. IEEE.
Yosefnezhad Irani, B., Ayubi, P., Amani Jabalkandi, F.,
Yousefi Valandar, M., and Jafari Barani, M. (2019).
Digital Image Scrambling Based on a New One-
Dimensional Coupled Sine Map. Nonlinear Dynam-
ics, 97(4):2693–2721.
Yu, F., Gong, X., Li, H., and Wang, S. (2021). Differ-
ential Cryptanalysis of Image Cipher Using Block-
Based Scrambling and Image Filtering. Information
Sciences, 554:145–156.
Zhou, K., Xu, M., Luo, J., Fan, H., and Li, M. (2019).
Cryptanalyzing an Image Encryption Based on a
Modified Henon Map Using Hybrid Chaotic Shift
Transform. Digital Signal Processing, 93:115–127.
Zolfaghari, B. and Koshiba, T. (2022). Chaotic Image
Encryption: State-of-the-Art, Ecosystem, and Future
Roadmap. Applied System Innovation, 5(3):57.
Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map
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