Reversible data hiding with selective bits difference expansion and modulus function

TELKOMNIKA Telecommunication Computing Electronics and Control
Vol. 23, No. 3, June 2025, pp. 727~737
ISSN: 1693-6930, DOI: 10.12928/TELKOMNIKA.v23i3.26310  727
Journal homepage: http://journal.uad.ac.id/index.php/TELKOMNIKA
Reversible data hiding with selective bits difference expansion
and modulus function
Aulia Arham1,2
, Hanung Adi Nugroho2
, Domi Sepri1
1
Department of Information Systems, Faculty of Science and Technology, Universitas Islam Negeri Imam Bonjol, Padang, Indonesia
2
Department of Electrical and Information Engineering, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta, Indonesia
Article Info ABSTRACT
Article history:
Received Apr 26, 2024
Revised Jan 24, 2025
Accepted Mar 11, 2025
The integration of the internet of things (IoT) has significantly enhanced
human life but also raises concerns about information security and privacy.
Information security can be achieved through cryptography, which encrypts
data to make it unreadable, or steganography, which hides data within other
media. For sensitive media, such as military, medical, and forensic imaging,
specialized techniques like reversible data hiding (RDH) are necessary to
ensure the media can be fully restored after data extraction. Many
researchers have proposed improvements to the RDH method in recent
years. In this study, we propose an improved RDH method utilizing
difference expansion and a modulus function. The method embeds data into
the 4-bit, 3-bit, and 2-bit least significant bits (LSB) of the difference value
of pixels, with a range of -2 and 2. The experimental findings demonstrate
that our approach achieves a embedding capacity of 0.2507 bpp with 55.445
dB of peak signal-to-noise ratio (PSNR) for common images and 0.3849 bpp
with 54.6810 dB of PSNR for medical images, using 2-bit difference values.
The results demonstrate that our approach surpasses previous methods and
holds promise for practical applications in IoT systems and the medical
field, where secure and reversible data embedding is essential.
Keywords:
Cryptography
Difference expansion
Information security
Reversible data hiding
Steganography
This is an open access article under the CC BY-SA license.
Corresponding Author:
Aulia Arham
Department of Information Systems, Faculty of Science and Technology
Universitas Islam Negeri Imam Bonjol
Sungai Bangek, Balai Gadang, Koto Tangah, Padang, West Sumatra, Indonesia
Email: auliaarham@uinib.ac.id
1. INTRODUCTION
In recent years, the internet of things (IoT) has transformed the manner in which devices
communicate and interact, providing unmatched connectivity and convenience [1]. However, this
interconnectivity raises significant concerns about data security and privacy. As IoT devices accumulate and
swap extensive quantities of sensitive information, ensuring security information measures becomes
essential. Security systems, notably cryptography and steganography, play pivotal roles in safeguarding IoT
networks and data integrity [2]–[4]. Cryptography involves encoding data to secure its transmission and
storage, making it incomprehensible to unauthorized parties [5], [6]. This technology, through encryption
techniques, ensures data confidentiality, authentication, and integrity, reducing the likelihood of data
breaches or unauthorized access in IoT ecosystems. Similarly, steganography, an art of concealing
information within digital content [7], contributes to IoT security by embedding data in a manner that’s
imperceptible to the human eye or normal data transmission processes. This technique provides an added
layer of security by hiding critical information within innocuous-looking data, preventing potential attackers
from even recognizing the presence of concealed data.

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TELKOMNIKA Telecommun Comput El Control, Vol. 23, No. 3, June 2025: 727-737
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In data hiding, three fundamental components form the core infrastructure: the sender,
communication channel, and recipient [8], [9]. The sender is responsible for conveying sensitive data, while
the recipient represents the intended party to receive this data. Facilitating the transfer process, the
communication channel serves as the conduit for transmitting the data securely. Within the domain of digital
image steganography, the process involves concealing confidential data within a chosen cover image. This
concealment is carried out with precision, ensuring that the resulting stego image can be securely transmitted
over unsecured public networks. The stego image, while appearing ordinary to casual observers, harbors
concealed information, making it a covert carrier for the confidential data during transmission across
potentially insecure channels. In other cases, the reversible data hiding (RDH) method is needed, such as in
medical image, military, and forensic image applications where every bit of pixel is important information
[10]–[14], Figure 1 illustrates the concept of RDH. After extracting the secret data, the RDH method can
revert the image to its original state. This method is applied by expanding pixel value, which can be classified
into three categories: difference: differential extension (DE), prediction-error expansion (PEE), and
histogram shifting (HS).
Figure 1. The concept of RDH methods
The initial introduction of the DE method can be traced back to the research conducted by [15]. This
particular method showcases a highly promising reversible data embedding (RDE) technique with a
substantial capacity. The cover image undergoes an integer wavelet transform, resulting in the acquisition of
the difference values. These values are then expanded to create a space for RDH. Numerous subsequent
studies have made significant improvements to this method [3], [16], [17]. In contrast to DE, which solely
takes into consideration the correlation between two adjacent pixels, the PEE method exploits the local
correlation within a larger neighborhood, thus yielding enhanced performance. PEE has garnered substantial
attention due to its ability to harness the spatial redundancy present in natural images. Rather than regarding
the difference operator as a decorrelation operation, PEE employs a pixel predictor. The initial proposal of
PEE was put forth by Thodi and Rodriguez in [18], and since then, it has been widely adopted by numerous
subsequent RDH works [19]–[23]. Alongside DE, HS stands as another highly successful approach for RDH.
This approach involves the generation of a histogram, which is subsequently modified to achieve RDE. The
first mention of HS-based RDH can be attributed to the work conducted by Ni et al. [24]. Moreover, the same
concept surrounding HS was independently presented in recent years by [25]–[29].
This study intends to propose an improvement on the DE method previously introduced by Maniriho
and Ahmad [3], based on a modulus function that can enhance capacity of embedding and visual quality. In
this method, data embedding is carried out using the difference value of pizel pairs in the cover image. Data
embedding is exclusively performed on difference values ranging from -2 to 2. To obtain the stego image, the
pixel value of the cover image is concatenated with the difference value that has been embedded with data.
The modulus function is used for extraction data and restoration of the cover image. Hossen et al. [17]
suggested improving the method [3] by increasing the block size to 3×1. The experimental results of this
method demonstrate a significant increase in embedding capacity and visual quality.
The rest of this paper is organized as follows. Section 2 explains our approach in detail, covering the
embedding and extraction processes, along with the computational complexities involved. Section 3
discusses the experimental results and offers a comparative analysis with earlier methods, focusing on
aspects such as embedding capacity, performance, and visual quality. Finally, section 4 concludes the study
by summarizing the main findings and presenting valuable insights derived from the data and research
results.

TELKOMNIKA Telecommun Comput El Control 
Reversible data hiding with selective bits difference expansion and modulus function … (Aulia Arham)
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2. METHOD
Improving the performance of data hiding methods is crucial for today’s information security. To
address this need, we propose a novel method to enhance the capabilities of existing techniques, especially
those presented by previous researchers [3]. Our proposed method utilizes the difference values of 4-bit, 3-
bit, and 2-bit LSB of pixels. This approach differs from the previous method [3], which employs 8-bit
difference values from pixels. The consideration of using the LSB difference value of pixels can enhance
embedding capacity, performance, and visual quality by reducing the range of difference values for pixel
pairs. Data is embedded in a difference value between -2 to 2, similar to the previous method [3]. Figures 2
and 3 depict the processes of embedding and extracting in our method.
Figure 2. Embedding process for our method
Figure 3. Extraction process for our method

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2.1. Embedding procedure
The steps of the embedding process are similar to method [3], with the difference lying in the pre-
embedding stage, where the pixel values of the image are divided into two components: the most significant
bits (MSB) and the least significant bits (LSB). Subsequently, the LSB difference value of each pixel is
utilized for data embedding. We propose three methods: first, using the difference in the 4-bit LSB values of
pixel pairs; second, using the difference in the 3-bit LSB value of a pair of pixels; and third, using the
difference in the 2-bit LSB value of a pair of pixels. This procedure of the embedding can be seen in
Figure 2. The step-by-step embedding process is detailed as:
Step 1: Begin by dividing the cover image into 2 × 1-sized blocks. Each pixel value within these blocks is
then converted into 8-bits, producing a pixel vector representation labeled as 𝑥 = (𝑥0, 𝑥1). These
blocks are further expanded into two vectors: 𝑦, comprising the 4-bit, 3-bit, or 2-bit LSB of each 𝑥,
and 𝑧, comprising the 4-bit, 5-bit, or 6-bit MSB of each 𝑥.
Step 2: Use (1) to calculate the difference value of pixel pairs in each block 𝑥 and store them in the vector ℎ.
ℎ = 𝑦1 − 𝑦0 (1)
Step 3: Examine the array ℎ to identify values that satisfy the embedding criteria. Classify these values into
two categories: if a value falls within the range of −2 to 2(−2 ≤ ℎ ≤ 2), mark it as qualified by
setting 𝑄𝐸𝑇 = 1; otherwise, set 𝑄𝐸𝑇 = 0.
Step 4: Retrieve bit of the secret data in vector 𝑏. Apply (2) to embed the data, generating a new difference
value represented as ℎ
̃. Each bit in 𝑏 corresponds to a secret data bit, taking on a value of either 0 or 1.
ℎ
̃ = ℎ + 𝑏 (2)
Step 5: Use (3) to compute the new value of 𝑦
̃ as the sum of 𝑦1 and ℎ. (4) outline the conditions that must
be met for our method in 4-LSB, 3-LSB, and 2-LSB pixels, respectively, to prevent overflow and
underflow. If the conditions are met, the quality embedding table (𝑄𝐸𝑇) is set to 1; otherwise, if 𝑦
falls outside the specified range, 𝑄𝐸𝑇 is set to 0, and 𝑦 remains unchanged.
𝑦
̃1 = 𝑦1 + ℎ
̃ (3)
𝑦
̃ = {
0 ≤ 𝑦1 + ℎ
̃0 ≤ 3. 𝑓𝑜𝑟 (2 − 𝑏𝑖𝑡𝑠)
0 ≤ 𝑦1 + ℎ
̃0 ≤ 7. 𝑓𝑜𝑟 (3 − 𝑏𝑖𝑡𝑠)
0 ≤ 𝑦1 + ℎ
̃0 ≤ 15. 𝑓𝑜𝑟 (4 − 𝑏𝑖𝑡𝑠)
(4)
Step 6: Use (5) to reconstruct the new value of the block pixel 𝑥
̃ for the stego image by combining the 𝑦
̃ and
𝑧 values.
𝑥
̃ = {
𝑥
̃0 = 𝑦
̃0 + 𝑧0
𝑥
̃1 = 𝑦
̃1 + 𝑧1
(5)
2.2. Extraction procedure
The extraction is similar to the embedding process, as illustrated in Figure 3. The steps for
extraction are outlined:
Step 1: Begin by dividing the stego image into 2 × 1-sized blocks. Each pixel value within these blocks is
converted into 8-bits, resulting in a pixel vector representation denoted as 𝑥
̃ = (𝑥
̃0, 𝑥
̃1). These blocks
are further expanded into two vectors: 𝑦
̃, consisting of the 4-bit, 3-bit, or 2-bit LSB of each 𝑥
̃, and 𝑧̃,
consisting of the 4-bit, 5-bit, or 6-bit MSB of each 𝑥
̃.
Step 2: Use (6) to calculate the difference value of pixel pairs in each block 𝑥
̃ and store them in the vector ℎ
̃.
ℎ
̃ = 𝑦
̃1 − 𝑦
̃0 (6)
Step 3: Extracting data from the difference value ℎ
̃ involves utilizing the modulus function and the 𝑄𝐸𝑇
table, as outlined in (7)
𝑏 = ℎ
̃ 𝑚𝑜𝑑 2 , 𝑖𝑓 𝑄𝐸𝑇 = 1 (7)

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Step 4: Use (8) to reconstruct the original difference value of ℎ from ℎ
̃, and use (9) to compute the original
value of 𝑦 from 𝑦
̃. Afterward, use (10) to reconstruct the original pixel value of 𝑥 by combining the
𝑦 and 𝑧̃ values.
ℎ = ⌈
ℎ
̃
2
⌉ , 𝑖𝑓 𝑄𝐸𝑇 = 1 (8)
𝑦 = {
𝑦0 = 𝑦
̃0
𝑦1 = 𝑦
̃1 − ℎ
(9)
𝑥 = {
𝑥0 = 𝑦0 + 𝑧̃0
𝑥1 = 𝑦1 + 𝑧̃1
(10)
3. RESULTS AND DISCUSSION
To compare our proposed method with the method suggested by previous researchers in [3], we
used six grayscale images. These included three common images (Baboon in Figure 4(a), Boat in Figure 4(b),
and Lake in Figure 4(c)) and three medical images (Abdominal in Figure 4(d), Head in Figure 4(e), and CT
scan in Figure 4(f)), obtained from the datasets provided in references [30], [31]. Each image had a resolution
of 512×512 pixels. The experiments were conducted using MATLAB 2022b (license number 41125107) on
an Intel Core i5 processor running at 2.9 GHz with 8 GB of memory.
(a) (b) (c)
(d) (e) (f)
Figure 4. Sample images for testing; (a) Baboon, (b) Boat, (c) Lake, (d) Abdominal, (e) Head, and (f) CT
scan
3.1. Embedding capacity
The results of the embedding capacity experiment are presented in Table 1 and Figure 5. Table 1
shows the capacity for embedding into the image that satisfies the embedding criteria for each method. The
embedding capacity is the ratio of the total number of bits that can be embedded to the image resolution,
measured in bits per pixel (bpp). Figure 5 illustrates how the embedding capacity varies across different

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methods. Specifically, Figure 5(a) shows the maximum number of smooth pair images, and Figure 5(b)
displays the embedding capacity (in bpp) for the images.
Table 1. Embedding capacity comparison
The embedding capacity in (bits) Embedding capacity (bpp)
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Baboon 20,661 35,691 56,161 65,708 0.0788 0.1362 0.2142 0.2507
Boat 34,351 39,468 56,809 64,027 0.1310 0.1506 0.2167 0.2442
Lake 35,952 41,038 57,628 65,393 0.1372 0.1566 0.2198 0.2495
Abdominal 73,262 74,522 83,703 89,193 0.2795 0.2843 0.3193 0.3402
Head 84,306 88,193 96,784 100,902 0.3216 0.3364 0.3692 0.3849
CT scan 85,870 89,425 97,268 99,831 0.3276 0.3411 0.3711 0.3808
(a) (b)
Figure 5. A comparison of our method with the previous approach in terms of; (a) the total number of smooth
pair images and (b) embedding capacity (in bpp)
The experimental results show that our three proposed methods consistently achieve higher embedding
capacities than method [3], as illustrated in Table 1 and Figure 5(a). This affirms that leveraging the difference
values of the LSB in each pixel can enhance the number of pixel pairs meeting the embedding requirements. For
instance, in a common image like Baboon, the embedding capacity of method [3] is 0.0788 bpp, whereas our
proposed method, utilizing the difference value of the 4-bits LSB in each pixel, achieves a embedding capacity
of 0.1362 bpp; for 3-LSB bits, it is 0.2142 bpp, and for 2-LSB bits, it is 0.2507 bpp. Similarly, in medical
images like Abdominal, the embedding capacity of method [3] is 0.2795 bpp, while our proposed method,
employing the difference value of the 4-bits LSB for each pixel, attains a embedding capacity of 0.2843 bpp;
for 3-bits LSB, it is 0.3193 bpp, and for 2-bits LSB, it is 0.3402 bpp. Additionally, the experimental results
reveal that the embedding capacities of method [3] and three of our proposed methods depend on the nature
of the image. The embedding capacity tends to be higher in images with more smooth areas compared to
those with fewer smooth areas, as illustrated in Figure 5(b). This can be observed in Table 1 and Figure 5,
where the load capacity of medical images is significantly greater than that of general images. Based on the
experiments that have been carried out, of three our proposed methods, utilizing the 2-bit LSB difference
value has the highest embedding capacity.
3.2. Performance
The experimental results demonstrate that our proposed method excels in accurately extracting data
and restoring the stego image to its original form, while preserving its visual quality. Regarding
computational efficiency, our method outperforms method [3] across all experiments, as shown in Table 2.
For the Baboon image, method [3] is capable of embedding only 4,666 bits of data per second. In contrast,
our proposed method, utilizing the 4-bit LSB difference value, can embed 8,486 bits of data per second, and
for the 3-bit LSB, it achieves 13,125 bits per second, while for the 2-bit LSB, it embeds 15,238 bits per
second. Similarly, in medical images such as Abdominal images, method [3] can embed only 20,562 bits of
data per second. On the other hand, our proposed method, using the 4-bit LSB difference value, achieves
20,805 bits per second, and for the 3-bit LSB, it embeds 23,387 bits per second, while for the 2-bit LSB, it

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embeds 24,463 bits per second. Among three our proposed methods, using the 2-bit LSB difference value
results in the fastest computational time.
Table 2. Comparison of computational time
Computational time (second) Embedding data in 1 seconds (bits)
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Baboon 4.43 4.21 4.28 4.31 4,666 8,486 13,125 15,238
Boat 3.59 3.62 3.60 3.61 9,561 10,918 15,780 17,746
Lake 3.77 3.79 3.76 4.14 9,546 10,819 15,318 15,815
Abdominal 3.56 3.58 3.58 3.65 20,562 20,805 23,387 24,463
Head 3.59 3.58 3.57 3.60 23,516 24,669 27,141 28,044
CT scan 3.85 3.59 3.58 3.90 22,315 24,903 27,177 25,631
3.3. Visual quality
Visual quality analysis was conducted to ensure that embedding data in the cover image did not
significantly reduce its visual quality, causing distortion. The evaluation aimed to comprehend the impact of
embedding capacity on the visual quality of the stego image, focusing on assessing fidelity and perception.
Generally, as the embedded data increases, the visual quality of the stego image decreases. In this research,
the peak signal-to-noise ratio (PSNR) is utilized to measure and compare the quality of the cover image and
stego image using (11). The evaluation is performed with various data sizes ranging from 1 kb to 105 kb,
with 5 kb intervals based on each method’s capabilities.
𝑃𝑆𝑁𝑅 = 10 log10
2552
1
𝑚×𝑛
∑ ∑ |𝐼(𝑖,𝑗)−𝐼′(𝑖,𝑗)|2
𝑛−1
𝑗
𝑚−1
𝑖
(11)
Table 3 provides a detailed PSNR measurement for embedding data with the maximum embedding
in the test image for each method. Figure 6 compares the PSNR performance of our method with the previous
method [3] across different embedding data sizes in each test image: Baboon (Figure 6(a)), Boat
(Figure 6(b)), Lake (Figure 6(c)), Abdominal (Figure 6(d)), Head (Figure 6(e)), and CT scan (Figure 6(f)).
The visual quality of the stego image with our proposed method is notably high. In various experiments, our
proposed method exhibits a lower PSNR value compared to method [3], notably in 4-bit and 3-bit our
methods. This is due to the larger volume of data embedded in our proposed method compared to method [3].
For a more accurate comparison, visual quality is presented in Figure 6, where the test compares equivalent
data embedding sizes. The results consistently show that our proposed method achieves higher visual quality
compared to the method in reference [3]. For example, in Baboon image with 20 kb of embedded data, the
method in reference [3] achieves a PSNR value of 55.3858 dB, while our proposed method outperforms with
values of 55.8161 dB in the 4-bit method, 56.5974 dB in the 3-bit method, and 60.5744 dB in the 2-bit
method, as illustrated in Figure 6(a). Similarly, in Abdominal image with 60 kb of embedded confidential
data, the method in [3] achieves a PSNR value of 54.0969 dB, whereas our proposed method demonstrates
higher values, with 54.2734 dB in the 4-bit method, 54.3657 dB in the 3-bit method, and 56.6550 dB in the
2-bit method, as illustrated in Figure 6(d). Based on these results, our proposed method consistently delivers
higher visual quality. Among the three proposed methods, the use of 2-bit LSB difference values achieves a
significant increase in PSNR values compared to the method in reference [3].
Table 3. Comparing the quality of stego image using PSNR
Embedding capacity (bpp) PSNR (dB)
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Maniriho and
Ahmad [3]
Proposed
4-bits
Proposed
3-bits
Proposed
2-bits
Baboon 0.0788 0.1362 0.2142 0.2507 55.2637 53.3199 52.1074 55.4145
Boat 0.1310 0.1506 0.2167 0.2442 53.1846 53.0564 52.2202 55.5230
Lake 0.1372 0.1566 0.2198 0.2495 52.9833 52.8596 52.0315 55.4190
Abdominal 0.2795 0.2843 0.3193 0.3402 52.9395 53.0756 52.6446 54.8443
Head 0.3216 0.3364 0.3692 0.3849 54.1959 53.8259 53.2164 54.6810
CT scan 0.3276 0.3411 0.3711 0.3808 53.7179 53.3644 52.8870 54.6022

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(a) (b)
(c) (d)
(e) (f)
Figure 6. A comparison of our method with the previous method [3] in terms of PSNR across various
embedding data sizes for the following images; (a) Baboon, (b) Boat, (c) Lake, (d) Abdominal, (e) Head, and
(f) CT scan
4. CONCLUSION
The IoT provides numerous benefits to everyday life; however, its interconnected design introduces
considerable challenges related to privacy and data security. Two primary techniques for addressing these
issues are cryptography and steganography. Information security can be achieved through cryptography,
which encrypts data to make it unreadable, or steganography, which hides data within other media. For
sensitive media, such as military, medical, and forensic imaging, specialized techniques like RDH are
necessary to ensure the media can be fully restored after data extraction. The DE method is widely
recognized as an effective RDH technique because it allows the media to be restored to its original state after
the secret data is extracted. In this research, we present an improved version of an RDH technique, which
uses the difference values of the 4-bit, 3-bit, and 2-bit LSB of pixels. Our method embeds data within the
difference values ranging from -2 to 2. Experiments conducted on three common images and three types of

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medical images show that our approach achieves a high embedding capacity while maintaining excellent
visual quality. The results indicate that our method outperforms existing techniques in terms of embedding
capacity, performance, and visual fidelity. Furthermore, it provides strong security as a fragile data hiding
approach, ensuring high-quality stego images even with substantial data embedding, thereby reducing the
chances of detection by adversaries. To further enhance this method, future work should explore the potential
of pixel difference values to increase both the embedding capacity and image quality. Additionally,
encrypting sensitive data before embedding could be a promising direction for strengthening security in
future research.
ACKNOWLEDGMENTS
The authors sincerely thank the Research and Community Service Institution (LPPM) of UIN Imam
Bonjol Padang for their support in publishing this article, through the Litapdimas Research Grant 2024.
FUNDING INFORMATION
This research was funded by the Institute for Research and Community Service (LPPM), State
Islamic University (UIN) Imam Bonjol Padang, under Grant Number 625/2024.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author
contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author C M So Va Fo I R D O E Vi Su P Fu
Aulia Arham ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Hanung Adi Nugroho ✓ ✓ ✓ ✓ ✓ ✓ ✓
Domi Sepri ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
C : Conceptualization
M : Methodology
So : Software
Va : Validation
Fo : Formal analysis
I : Investigation
R : Resources
D : Data Curation
O : Writing - Original Draft
E : Writing - Review & Editing
Vi : Visualization
Su : Supervision
P : Project administration
Fu : Funding acquisition
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no conflict of interest.
INFORMED CONSENT
This study did not involve human participants, personal data, or identifiable information; therefore,
informed consent was not applicable.
ETHICAL APPROVAL
This study did not involve human participants or animals; therefore, ethical approval was not
required.
DATA AVAILABILITY
https://github.com/4rh4m/Reversible-data-hiding-with-selective-bits-difference-expansion-and-
modulus-function
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BIOGRAPHIES OF AUTHORS
Aulia Arham received the B.Sc. degree in Informatics Engineering from the
Sekolah Tinggi Manajemen Informatika dan Komputer Duta Bangsa (STMIKDB), Surakarta,
Indonesia and the M.S. degree in Electrical Engineering at Universitas Gadjah Mada,
Yogyakarta, Indonesia, in 2016. Since 2018, he is appointed as lecturer in the Department of
Information System, Faculty of Science and Tehnology, Universitas Islam Negeri Imam
Bonjol, Padang, Indonesia. His research interests are watermarking, steganography,
crytography, security, image processing, and medical imaging. He can be contacted at email:
auliaarham@uinib.ac.id.
Hanung Adi Nugroho received the B.Eng. degree in electrical engineering from
Universitas Gadjah Mada, Indonesia, 2001 and Master of Engineering degree in Biomedical
Engineering from the University of Queensland, Australia in 2005. In 2012, he received his
Ph.D. deegree in Electrical and Electronic Engineering from Universiti teknologi Petronas,
Malaysia. Currently, he is a Professor and also a Head of Department of Electrical and
Information Engineering, Faculty of Engineering, Universitas Gadjah, Yogyakarta, Indonesia.
His current research interests include biomedical signal and image processing and analysis,
computer vision, medical instrumentation, and pattern recognition. He can be contacted at
email: adinugroho@ugm.ac.id.
Domi Sepri received the B.Eng. degrees in Informatics Engineering from
Universitas Islam Negeri Sultan Syarif kasim, Pekanbaru, Indonesia, in 2014 and M.S degree
in Universitas Putra Indonesia YPTK Padang in 2016. He has been designated as a lecturer
within the Department of Information Systems at the Faculty of Science and Technology,
Universitas Islam Negeri Imam Bonjol, located in Padang, Indonesia. His research interests
are analysis information system and data science. He can be contacted at email:
domisepri@uinib.ac.id.

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