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Adaptive Matrix Pattern Steganography
on RGB Images
Amirfarhad Nilizadeh1,∗, Shirin Nilizadeh2, Wojciech Mazurczyk3,
Cliff Zou1and Gary T. Leavens1
1University of Central Florida, Orlando, Florida, USA
2University of Texas Dallas, Dallas, Texas, USA
3Warsaw University of Technology, Warsaw, Poland
E-mail: af.nilizadeh@Knights.ucf.edu
∗Corresponding Author
Received 25 May 2021; Accepted 28 June 2021;
Publication 13 August 2021
Abstract
Almost all spatial domain image steganography methods rely on modifying
the Least Significant Bits (LSB) of each pixel to minimize the visual dis-
tortions. However, these methods are susceptible to LSB blind attacks and
quantitative steganalyses.
This paper presents an adaptive spatial domain image steganography
algorithm for hiding digital media based on matrix patterns, named “Adap-
tive Matrix Pattern” (AMP). The AMP method increases the security of
the steganography scheme of largely hidden messages since it adaptively
generates a unique codebook matrix pattern for each ASCII character in
each image block. Therefore, each ASCII character gets a different codebook
matrix pattern even in different regions of the same image. Moreover, it uses
a preprocessing algorithm to identify the most suitable image blocks for
hiding purposes. The resulting stego-images are robust against LSB blind
attacks since the middle bits of green and blue channels generate matrix
patterns and hiding secrets, respectively. Experimental results show that AMP
Journal of Cyber Security and Mobility, Vol. 11 1, 1–28.
doi: 10.13052/jcsm2245-1439.1111
© 2021 River Publishers
2A. Nilizadeh et al.
is robust against quantitative steganalyses. Additionally, the quality of stego-
images, based on the peak signal-to-noise ratio metric, remains high in both
stego-RGB-image and in the stego-blue-channel. Finally, the AMP method
provides a high hiding capacity, up to 1.33 bits per pixel.
Keywords: Steganography, Steganalysis, LSB, Matrix Pattern.
1 Introduction
Digital image steganography is one of the most popular techniques for hiding
a secret message in an image [26,36,71]. Images have a high capacity, which
is enough for steganographic purposes; also, images are currently widely
used, e.g., in social media networks. Data hiding techniques in images can
be classified into three main groups: spatial domain, transform domain, and
adaptive steganography [5]. Spatial domain steganography hides a secret
message by changing pixel values [26], classic algorithms in the spatial
domain are Least Significant Bits (LSB) [4,27], LSB Matching (LSBM) [47],
Pixel-Value Differencing (PVD) [80], Exploiting Modification Direction
(EMD) [82], and Synch [8]. Transform domain steganography systems hide
the message by changing the frequency coefficients of images [65], such as
JSteg [67], YASS [70], Uniform Embedding Distortion (UED) [20], and J-
UNIWARD [24] that are classic algorithms in the transform domain. Finally,
adaptive steganography algorithms hide the message in either the spatial
or transform domains. These algorithms have a pre-processing phase (such
as STC coding method [14]) that can choose the most suitable area of the
image for hiding a secret message with minimum changes [18, 68] like Edge
Adaptive (EA) [41], HUGO [61], Wavelet Obtained Weights (WOW) [23],
High-pass, Low-pass, and Low-pass (HILL) [37], J2-UNIWARD [9] and
Natural Steganography (NS) [7].
Almost all the spatial domain image steganography methods change the
LSB part of pixels [1, 4, 11, 16, 48] because human eyes are not sensitive to
these changes. However, they are sensitive to unintentional processes such
as randomly flipped bits, image filters, and image compression algorithms [6,
39]. The LSB blind attacks use this sensitivity because only flipping one bit in
the LSB part of a pixel can destroy the entire hidden message. These attacks
are completely blind, and they consider any image as a potential stego-image
and try to destroy the secret message.
Steganalysis algorithms are another kind of attack to detect the existence
of a hidden message in a stego-image [28, 66]. Many of these algorithms
Adaptive Matrix Pattern Steganography on RGB Images 3
have no information about the steganography algorithm’s specification and
are known as blind steganalysis [3, 19, 42]. Also, quantitative steganalysis
algorithms try to detect the existence and estimate the hidden message’s
length in the stego-image [62]. Many blind and quantitative steganalysis
algorithms have been developed to detect the existence of a hidden message
in a stego-image [10, 12, 13, 17, 31, 33, 43, 50, 60, 64, 75, 79].
This paper proposes a steganography method that hides information in
the middle bits of images instead of the image’s LSB part. This can affect
the stego-image quality. To limit this impact, we present a novel adaptive
multimedia spatial domain steganography algorithm based on matrix pat-
terns called “Adaptive Matrix Pattern” (AMP). We show that our proposed
steganography method is resistant to LSB blind attacks and steganalysis
algorithms, maintains the quality of stego-image, and has a high capacity.
In this work, an RGB image is considered to have three channels, each
represented with N×Mpixels. Also, each pixel is an 8-bit non-negative
integer. An AMP algorithm modifies one channel’s pixels (typically the
blue channel because the human eye is less sensitive to differences in this
channel) by a matrix pattern, which is adaptively generated from the cover
image’s texture. We propose dividing an RGB image into non-overlapping
square-sized blocks, and ordering them based on their suitability for hiding
messages, considering the smoothness and complexity of neighboring pixels.
For each block, a codebook consisting of 257 unique dynamically-sized
matrix patterns is generated, representing 256 ASCII codes and an end of
message character, which increases the hidden message’s security. In other
words, each character gets a different codebook matrix pattern even in differ-
ent regions of the same image. This method enables hiding any digital media
in the image, such as text, voice, video, encrypted data, etc. The 4th and 5th
bits of each block’s green and blue channels are used for generating matrix
patterns and hiding a secret message. Using these bits instead of LSB bits
increases our steganography algorithm’s robustness against LSB blind attacks
and well-known blind and quantitative steganalysis. Also, our experimental
results show that the AMP steganography method provides high transparency
for stego-images.
Considering the above, the contributions of this paper are as follows:
1. This work supports all 256 ASCII characters, while the earlier MP
works [49, 51, 54, 83] supported only 49 and 95 English keyboard
characters. Thus, any digital media can be hidden as a message like a
cryptographically encoded message. (A steganography work is practical
4A. Nilizadeh et al.
when it can hide encrypted messages to increase security.) Also, the
proposed AMP method provides a large capacity for hiding information
as it uses six pixels (in the blue channel) to hide each byte.
2. Our proposed algorithm is adaptive in the spatial domain. A pre-
processing algorithm identifies the suitable blocks for hiding, consid-
ering the smoothness and complexity of neighboring pixels in each
block. Some blocks cannot hide information, while others can hide
more information. Also, some blocks with different textures need fewer
changes to hide the same message; such blocks receive a higher priority.
3. This is the first time that a Matrix Pattern (MP) steganography algorithm
has been evaluated on a large image dataset; we used 10,000 images
from BOSSBase [59] (instead of 13 images in earlier MP studies [49,
51, 54, 55, 83]). Results show that our proposed AMP method is robust
against well-known quantitative steganalysis methods while maintaining
the quality of stego-images in both stego-RGB-image and stego-blue-
channel.
The source code of this research is available on a GitHub repository [53].
2 Related Work
The most closely related work is spatial domain steganography algorithms
because they hide secret messages by changing pixel values and handling
large messages (unlike algorithms that use the transform domain). Related
spatial algorithms also divide cover images into non-overlapping blocks
to detect noisy blocks in which hidden data will be less detectable by
steganalysis methods.
Almost all existing steganography works based on blocks use the least
significant bits (LSB) part of each pixel and thus are vulnerable to blind
LSB attacks and quantitative steganalysis algorithms. For example, Hsiao’s
“Block-based reversible data embedding” [25] divides an image into blocks,
which are then classified into one of three classes: smooth, normal, and
complex. Then, it uses the LSB portion of each pixel for hiding a secret
message. Also, a recent work [69] uses the knight’s tour to hide the message
in the image’s blocks by modifying LSB. Pixel Value Ordering (PVO) [38]
is another work that uses prediction error expansion in each non-overlapping
block in the hiding process. Many works use the PVO algorithm [44,58,78].
Also, a work presented by Weng et al. [77] divides images into 3×1non-
overlapping blocks; their proposed work at most can hide 2 bits by using
Adaptive Matrix Pattern Steganography on RGB Images 5
3 pixels. Another example is Kawaguchi’s “Bit-Plane Complexity Segmenta-
tion Steganography” (BPCS) [30]. In BPCS, a secret message is changed into
some noisy blocks; then, they are embedded into the cover image by replacing
other suitably noisy cover blocks (LSB part of pixels in the block). Another
method similar to BPCS is “A Block Complexity based Data Embedding”
(ABCDE) by Hoki [21]. In another work [40], the secret message is hidden
in the noisy blocks of an image, where the LSBM method is applied on each
block [47]. Also, PVD [80] divides an image into non-overlapping blocks of
two consecutive pixels. In the PVD method, a secret message is mostly hidden
in the noisy blocks compared to the smooth blocks. Many steganography
works are based on the PVD algorithm [29, 46, 56, 72, 81].
It is also worth noting that the above-mentioned algorithms are only
defined for gray-scale images, not RGB images like the AMP method pro-
posed in this paper. Also, some related works are using RGB images for
hiding secret messages, like the work presented by Pervez and Gutub [57]
that uses one of the channels as an indicator and the two remaining channels
for hiding the message. It is assumed that a shared key and a partition scheme
are agreed upon between the sender and the receiver in their work. Some other
steganography works (like [45,73]) improve their technique and use the same
indicator idea.
All of the above steganography techniques (both block-based and RGB
works) make changes in the LSB part of an image with different embedding
algorithms. Thus, a simple LSB attack would destroy the hidden message.
Lastly, this paper is based on matrix pattern (MP) steganography [51].
That work selects non-overlapping square-sized blocks based on a pseudoran-
dom generator, and it supports only 49 matrix patterns (English characters)
instead of 257 matrix patterns (ASCII characters) by our proposed AMP
work. Moreover, in [51] the 4th to 7th bits of the image are used for generating
and hiding matrix patterns. Another work based on the MP method [55]
uses both MP and LSB algorithms to hide a secret message. The other prior
work [54] is a block-based spatial steganography version of MP, in which
blocks are selected randomly, and 95 codebook matrix patterns are generated
from each block to assign all English keyboard characters. The present AMP
algorithm builds upon these works but with fewer limitations. Another work
based on the MP method is presented by Zhou et al. [83], which combines
the MP method (which supports 95 characters) with PVD [80] to increase the
capacity. Also, Mowafi et al. [49] presented a paper based on MP, but instead
of using RGB channels, they use YCbCr color space. In their work, they used
the MP version that supported 95 characters. All the above MP works used
6A. Nilizadeh et al.
small image datasets (13 images) for their evaluation. Also, earlier MP works
only could hide text messages in an image. However, in the real world, a
steganography framework should hide encrypted messages to increase secu-
rity. Furthermore, they used random and pseudorandom generators, while
pre-processing is used in our work to select the most suitable blocks, which
enhances the information-carrying capacity of the algorithm while providing
high stego-image quality.
3 The Proposed Method
In this section, a new adaptive steganography algorithm based on the matrix
pattern is proposed. The AMP steganography method does not encode indi-
vidual bits; instead, it encodes each character (byte). It divides an image
into non-overlapping square-sized blocks. Then, it automatically generates
unique matrix patterns from the block texture and assigns each to an ASCII
character. Each block in the image has its unique codebook matrix pattern
based on the block’s texture. There is one matrix pattern for each of the 256
ASCII characters plus one matrix pattern for the end-of-message. Thus, all
kinds of digital media can be considered a stream of characters (bytes) as
a secret message and then hidden in the cover image. The algorithms for
matrix pattern generation and embedding are the same as algorithms used in
our prior MP work [54]. However, selecting suitable blocks to generate 257
unique matrix patterns from the block’s texture and provide a high-quality
stego-image is one of the challenges. Thus, the proposed AMP work uses a
pre-processing algorithm instead of random or pseudorandom algorithms to
select the most suitable blocks.
3.1 Pre-Processing Analysis
Selecting the most suitable image region to hide secret messages will increase
the quality of the stego-image, which makes the steganography method more
secure. In the MP method, selecting the most suitable blocks is more critical
because a codebook of matrix patterns will be generated based on the block’s
texture. The codebook will be used to hide the secret message in the same
block. In this paper, instead of using pseudorandom or random algorithms (as
in previous work on MP), we use a pre-processing algorithm for detecting
the most suitable blocks to generate a codebook matrix pattern and hide a
secret message with minimum changes, which will increase the message’s
secrecy.
Adaptive Matrix Pattern Steganography on RGB Images 7
In the “Block Texture Pattern Detection” paper [52], the gray-scale blocks
are divided into four different classes: edge and simple,edge and complex,
smooth and simple and smooth and complex. The capacity and transparency
of three different steganography methods containing LSB, PVD, and MP are
evaluated in each class. Smoothness and complexity are two measures used
in that prior work [52], and they will be discussed next alongside the effects
of this classification on the MP method.
In [52], the user selects a fixed size, B, for the B×Bblocks, which use
in the MP method to generate codebook and hiding secret messages. Then,
all the blocks are changed from RGB to intensity blocks using Equation (1),
which defines the intensity of each pixel P(r, g, b).
Intensity(P(r, g, b)) = (r+g+b)
3(1)
After that, the variance of the pixels’ intensities in a block is computed as
a measure of the degree of smoothness shown with Equation (2).
Smoothness(Block) = V ar(Intensity(P(r, g, b))|
P(r, g, b)∈Block)(2)
A straightforward algorithm is used to compute the complexity of a block.
First, the average of the pixels in the intensity block is calculated. Next, the
gray-scale block (intensity block) is changed to a binary block by changing all
pixels with an intensity at least as large as the average to white and all others
to black. All the black to white and white to black changes are counted in
horizontal, vertical, and diagonal orders. Finally, to normalize the complexity
measure, the total number of changes in these directions is divided by the
maximum number of possible block changes. The complexity is calculated
with Equation (3).
Complexity(Block) = TChanges(Block)
B·(B−1) + 2 ·(B−1)2(3)
In this equation, “B” determines the size of a B×Bblock, and
“TChanges(Block)” is the number of total changes in all horizontal, vertical,
and diagonal orders in a given block, Block.
The prior work [52] shows that the “smooth and complex” blocks provide
the highest MP method capacity. Also, “smooth and complex” blocks have
better transparency than “edge and simple” and “edge and complex.” Also,
“smooth and simple” blocks are not suitable for embedding information.
8A. Nilizadeh et al.
Furthermore, the evaluation presented indicates that “edge and complex” has
nearly 10% better capacity than “edge and simple.” These results highlight
some important facts related to the MP method: imagine a uniform B×B
block, where all the pixels are the same. In this block, it is impossible
to generate different matrix patterns because their generation is based on
subtraction and the difference between neighboring pixels. If all the pixels
are the same, it will generate a matrix pattern with zero values. Thus, if a
block is entirely “smooth and simple”, it is impractical to generate enough
unique matrix patterns for the block. One of the AMP method’s challenges is
detecting suitable blocks that can generate 257 matrix patterns to support all
ASCII characters.
By comparing “edge and complex” and “smooth and complex” blocks,
which have the same factor in “complexity”, “smooth and complex” has a
better capacity. This is because in the edge areas, but not in smooth areas,
the difference in two pixels’ values while generating a matrix pattern can be
higher. Also, in the edge area, the values of matrix patterns are higher. Thus,
it is more probable that pixel overflow happens during the embedding phase
by adding matrix patterns to the blue channels’ values. In this case, the null
matrix is embedded, and it will decrease the transparency, while no character
is hidden there. Consequently, “edge and complex” and “edge and simple”
areas have less capacity than “smooth and complex” areas.
In this paper, blocks are ordered based on these four classes. The “smooth
and complex” blocks are the most suitable, followed by “edge and complex”,
“edge and simple,” and finally “smooth and simple” ones.
3.2 Matrix Pattern Generation
In AMP, the user selects two fixed sizes, a number of pixels, B, that deter-
mines the block size, B×B, and sizes for the matrix patterns, also in pixels,
t1and t2, the matrix patterns size are t1×t2. Also, the user provides a
cover RGB image and a secret message. Some requirements that the user
must consider for selecting block and matrix pattern sizes are: t1< B,
t2< B, and the number of characters supported (257) must be less than
(B−t1+ 1) ×(B−t2+ 1).
After selecting one B×Bblock, the algorithm selects the first top left
t1×t2matrix in the green channel and uses that to generate the first matrix
pattern for the block. We use [g(i, j)](t1×t2)to denote this matrix.
In the matrix pattern generation process, each pixel’s first three bits in the
green channel are ignored (by considering them zero) because they are used
Adaptive Matrix Pattern Steganography on RGB Images 9
in blind LSB attacks. After that, the first row (top row) of the matrix pattern is
made to be zero and, the second row of the green matrix-cover is subtracted
from the first row of the green matrix-cover to produce the second row of the
matrix pattern. This continues until the algorithm computes the value of the
cover’s row t1minus the value of row t1−1of the green matrix-cover, which
generates the t1row (bottom row) of the matrix pattern. Equation (4) explains
how a matrix pattern is generated.
M P (i, j) = (0,if i= 0
g(i, j)−g(i−1, j ),otherwise (4)
We write [M P (i, j)](t1×t2)for the matrix pattern created by Equation (4).
To generate the second matrix pattern, for the second (ASCII) character, the
top left t1×t2matrix (used for generating the first matrix pattern) in the green
channel will be shifted one column to the right. The same process shown
in Equation (4) will then generate the second matrix pattern. The process
of shifting one column and generating a new matrix pattern continues until
enough unique matrix patterns (257) are generated, or the process reaches
the end of the block’s row (by one column shifting each time). If it reaches
the end of the row, it shifts one row down and starts again from the leftmost
column of the block, until all 256 ASCII characters and the “end of message”
character get a unique matrix pattern. A generated matrix pattern that is
not unique for the block and assigned to an ASCII character in the block
codebook earlier will be ignored.
In this work, the 4th and 5th bits are used to generate matrix patterns
based on our prior work [54]. Therefore, if there is at least one value
higher than 24 or lower than -24 in the generated matrix pattern, it will be
ignored1. In matrix pattern generation, if 257 unique matrix patterns cannot
be generated from a block to assign all 256 ASCII characters and the end-of-
message character, then that block will be considered a useless block. Thus,
no character can be hidden in the block.
The left matrix in Table 1 shows an example of 3×4pixel values of
a green channel. The right matrix in this figure shows pixel values after
ignoring the first three bits. Also, Table 2 shows three 3×2matrix patterns
generated based on the 3×4matrix in the figure 1. The first two columns
of the right matrix of the Table 1 are used to generate the first matrix pattern
shown in the left matrix in Table 2. Then, the second and third columns in
1Note that 24 is 16 + 8, so the restriction to the interval [−24,24] keeps the values in the
4th and 5th bits.
10 A. Nilizadeh et al.
Table 1 Left Matrix: Values of a green channel; Right Matrix: The green channel with the
ignored first three LSB bits
182 184 182 182
182 182 182 182
182 182 185 182
176 184 176 176
176 176 176 176
176 176 184 176
Table 2 Three generated matrix patterns
0 0
0 -8
0 0
0 0
-8 0
0 8
0 0
0 0
8 0
Table 1 (after one column shifting) are used to generate the second matrix
pattern shown in the middle matrix of Table 2. The third and fourth columns
in Table 1 are used to generate the second matrix pattern shown in the right
matrix of Table 2.
3.3 Embedding Phase
In the AMP method, the blue channel of a block is used in the embedding
process. In this phase, the matrix pattern assigned to the secret message’s
first character is selected from the block’s codebook matrix pattern. In the
embedding phase, the first top left t1×t2matrix of the blue channel of the
block will be chosen; the notation [b(i, j)](t1×t2)indicates this matrix.
To embed the matrix pattern into the [b(i, j)](t1×t2)(that will produce
the stego-matrix), no changes will be made on the first row (top row) of the
blue matrix. Then, values of the first row of the stego-matrix are added to
the values of the second row of the matrix pattern to produce the values of
the second row of the stego-matrix. This process will continue until row t1
(bottom row) of the stego-matrix is produced; by adding row t1−1of the
stego-matrix to row t1of the matrix pattern. This process is described by
Equation (5). In this equation, the [M P (i, j)](t1×t2)is embedded in the block
[b(i, j)](t1×t2).
Em(i, j ) = (b(0, j),if i= 0
Em(i−1, j ) + MP (i, j ),otherwise (5)
We write [Em(i, j )](t1×t2)for the the stego-matrix in the blue channel.
For embedding the secret message’s second character into the block, the
second t1×t2matrix of the blue channel of the block will be selected (by
shifting t2columns to the right of the block location, which was used to
Adaptive Matrix Pattern Steganography on RGB Images 11
embed the first matrix pattern). Then, the matrix pattern, which is assigned
to the second secret message character, will be embedded using Equation (5).
The process of shifting and embedding will continue until it reaches the end
of the block’s row. Then, it will shift t1rows down, and it will move to
the leftmost t1×t2matrix in the new row. This process will continue to
embed all the secret message characters, and if the space of the block is not
enough, the process will continue with the next block using a new matrix
pattern codebook. Lastly, when the entire secret message is embedded in the
blocks, the matrix pattern assigned to the end-of-message character will be
embedded.
Pixel overflow can happen during the embedding of a matrix pattern. In
this case, a null matrix pattern with all zero values is embedded instead of
the matrix pattern. The null matrix pattern is a pre-defined matrix pattern for
all of the blocks, and it is not included in the 257 matrix patterns generated
during the matrix pattern generation phase. The null matrix pattern does not
make values of pixels in the stego-image zero; only values of matrix pattern
are zero, and it will be embedded as explained in Equation 5 like other matrix
patterns.
During the embedding process, the sizes of blocks (B) and the matrix
pattern (t1and t2), and the order of blocks from the most to least suitable one
are embedded with the same process. These values are embedded in the top
left 64 ×64 block(s) with 3×2matrix pattern sizes. All of the information
embedded in this specific 64 ×64 block(s) are numerical digits. Thus, 12
unique codebook matrix patterns are generated for these 64 ×64 blocks. Ten
of them are assigned to numerical digits, one matrix pattern is assigned to
a space character for separating values, and one is assigned to the end-of-
message character.
The left matrix of Table 3 shows pixel values of the 3×6cover blue
channel. The right matrix of Table 3 is a stego-matrix that embeds the three
generated matrix patterns shown in Table 2. The left matrix pattern in Table 2
is embedded in the first 3×2pixels values of the right matrix of Table 3
(first and second left columns). Also, the middle and right matrix patterns
of Table 2 are embedded in the second 3×2pixels values (third and fourth
columns) and third 3×2pixels values (fifth and sixth columns) of the right
matrix of Table 3.
Algorithm 1 shows the embedding pseudocode based on the AMP
algorithm at the sender side.
12 A. Nilizadeh et al.
Table 3 Left Matrix: Pixel values of a cover blue channel; Right Matrix: Pixel values after
embedding three matrix patterns
212 208 208 205 207 207
214 206 207 207 207 207
210 209 203 203 207 207
212 208 208 205 207 207
212 200 200 205 207 207
212 200 200 213 215 207
Algorithm 1: Embedding(Image, M sg, B, t1, t2)
Data: RGB image, message, B, t1,t2
Result: stego-image
/* (t1×t2) is matrix pattern size */
/* B is size of blocks */
Ord := Pre-Processing analysis (Sec 3.1);
/* Ord is the order of most suitable block to least */
Embed B, t1,t2, and Ord in the top left 64 ×64 block(s);
repeat
Block := Next B×Bblock in Ord;
CB := Generating codebook matrix pattern from Block (Sec 3.2 and Eq 4);
repeat
Ch := Next ASCII character of Message;
Pat := Assigned matrix pattern to Ch by CB;
Embed Pat to the block (Eq 5);
until (No more space in Block or Ch is end-of-message);
until (Ch is end-of-message);
3.4 Extraction Phase
To extract the embedded secret message, first, the operation Ex extracts the
size of both blocks and the matrix patterns (recovering Band t1and t2) and
the order of the blocks’ locations; they are embedded in the top left 64 ×64
block(s) of the image. Extracting these values is the same as the extraction
phase (using Equation (6)), which is explained later in this section. After that,
the extracted block locations (selected with the pre-processing algorithm) are
placed in the queue order. Then, the codebook matrix pattern of the first
block in the queue is generated using Equation (4), which is discussed in
Section 3.2. The green channel does not change in the embedding phase.
Thus, generated codebook matrix pattern on the receiver side is the same as
the sender side.
The first t1×t2matrix (stego-matrix) on the top left of the blue channel of
the stego-block is selected to extract the first embedded matrix pattern. Recall
the first row values (top row) of the matrix patterns are zeros. To extract the
values of the second row of the embedded matrix pattern from the t1×t2
Adaptive Matrix Pattern Steganography on RGB Images 13
stego-matrix, the pixel values in the second row of stego-matrix (from the
blue channel) will be subtracted from the first row of the stego-matrix. Then,
to extract the third row of the embedded matrix pattern, the pixel values of
the third row of the stego-matrix (from the blue channel) will be subtracted
from the second row of the stego-matrix. This process continues until the
subtraction of row t1from row t1−1extracts the values of row t1(bottom
row) of the hidden matrix pattern. Equation (6) describes how the extraction
of the matrix patterns is performed.
Ex(i, j) = (0,if i= 0
Em(i, j)−Em(i−1, j ),otherwise (6)
In Equation (6), “Ex” refers to the extracted matrix pattern, and
“Em” is the stego-matrix, shown as [Em(i, j)](t1×t2). Also, the notation of
[Ex(i, j )](t1×t2)indicates the extracted matrix pattern, which is the same
as one of the matrix patterns in the block’s codebook. Then, to extract the
second matrix pattern, the second stego-matrix in the block will be selected
by shifting t2columns to the right from the first stego-matrix. This shifting
and extracting process will continue until it reaches the end of the selected
block column. Then, it will shift t1rows down, and it will start again from
the leftmost t1×t2matrix in the new row of the block. Each extracted matrix
pattern from the blue channel is assigned to the ASCII character hidden in
each t1×t2matrix based on the block’s codebook. The null matrix pattern
with all zero values is a pre-defined matrix pattern for all of the blocks.
Extracting a null matrix pattern will show that no character (byte) is hidden
in this matrix. All hidden characters (bytes) in the block are extracted by
following the same process. Then, the same process will continue by selecting
the next block in the queue until the end-of-message character is detected.
Algorithm 2 shows the pseudocode of extracting an embedded message
from the RGB stego-image using AMP.
4 Implementation and Evaluation
This section includes details related to the inputs, outputs, limitations, and
implementation of the proposed adaptive steganography method. We also
characterize the dataset of 10,000 RGB images used during experiments.
Finally, AMP’s resistance against well-known quantitative steganalysis is
evaluated, and the quality of stego-images is measured using PSNR.
14 A. Nilizadeh et al.
Algorithm 2: Extracting(RGBStegoI mage)
Data: RGB Steg-Image
Result: Extracted Message
Extract B, t1,t2, Ord from top left 64 ×64 block(s);
/* B is size of blocks */
/* (t1×t2) is matrix pattern sizes */
/* Ord := order of blocks that was used in the embedding phase */
repeat
Block := Next B×Bblock in Ord;
CB := Generating codebook matrix pattern from Block (Sec 3.2 and Eq 4);
repeat
Pat := Extract a matrix pattern from Block (Eq 6);
Ch = assign the Pat to a character using CB;
writeByte(Ch);
until (Extracted the entire Block’s Pats or Ch is end-of-message);
until (Ch is end-of-message);
4.1 Implementation
We use MATLAB R2018a for the implementation and evaluation of the
AMP algorithm. Inputs of the proposed method are a secret message and
an arbitrary RGB cover image. Also, the sender selects a value for the size of
the blocks (B) and two values (t1and t2) for the size of the matrix patterns.
Then, the AMP method hides the secret message in the blue channel of the
cover image as described earlier. As a result, at the output, we have an RGB
stego-image (or a warning if not all of the message could be hidden in the
cover image). At the receiver side, the input of the AMP algorithm is an RGB
stego-image. For the receiver, the output is the secret message that is extracted
from the stego-image.
The cover image can be in any format with three channels. However, the
output can only be an image format with three channels that do not use lossy
compressions, such as the PNG, Bitmap, TIFF, and PPM formats. Like all
known spatial domain works, a lossy compression algorithm, such as JPEG
or JPEG2000, cannot be used to transmit stego-images produced by the AMP
algorithm.
The source code of an AMP implementation is available on a GitHub
repository [53].
Adaptive Matrix Pattern Steganography on RGB Images 15
4.2 Images Dataset and Evaluation
The image dataset that was used in previous MP evaluations was small (13
images) [49, 51, 54, 55, 83]. In this paper, instead, we use the 10,000 images
of the BOSSBase dataset [2]. The RAW RGB images of BOSSBase were
resized and cropped to create a new dataset of 10,000 RGB images with 512×
512 size. UFRaw 0.22 was used for changing RAW images to the PPM image
format with three channels. A script provided for the BOSS competition was
used for resizing and cropping [2, 35]. Also, for the embedding process, a
random secret message was generated each time, which has the characteristic
of an encrypted message.
In our evaluation, the size of the matrix pattern was 3×2, and 4th and
5th bits were used for generating and embedding matrix patterns (previous
works on the MP method showed that these are the most suitable size and
bits [51,54]). Thus, 6 pixels are used for hiding a byte in our study. Also, the
block size was chosen as 128 ×128. In previous MP works, the block size
was 64 ×64. However, AMP needs to generate 257 unique matrix patterns,
and blocks of size 64 ×64 cannot provide it. This paper did not evaluate the
optimal block size; however, our initial evaluation showed that blocks with a
size of 128 ×128 have good results.
We created four different stego-image datasets from the same set of
cover images, distinguishing the datasets based on each image’s percentage
capacity used in the embedding process. The size of each blue channel during
the experimental evaluation is 512 ×512, and the size of each matrix pattern
is 3×2. Thus, the maximum number of possible ASCII characters (bytes) that
can be hidden in an image is (512 ×512)/(3 ×2), which is 43,690 characters
(349,520 bits)2. It shows that AMP provides a large capacity for hiding.
Most of the spatial domain steganography works hide bits by replacing or
using a correlation among neighboring pixels in the LSB parts. Thus, their
hiding capacity is bits per pixel (bpp), and bpp is a known measure used in
steganography research. However, this work uses every 6 pixels for hiding
a byte (8 bits); it can increase the steganographic capacity up to 1.33 times
more than simple LSB replacement, which its capacity is 1 bpp. In our first
dataset, 5% of bpp is used for hiding in the blue channel. In the other three
stego-image datasets, 10%, 20%, and 40% bpp of blue channel capacity is
used for hiding random secret messages, respectively. Our results showed
that some of the 10,000 images in the cover image dataset could not hide
2The maximum possible capacity is lower, as a 64 ×64 block(s) of the cover image is used
for hiding the selected sizes and the order of blocks.
16 A. Nilizadeh et al.
Figure 1 Left images are cover images, other four images contain 5%, 10%, 20% and 40%
bpp embedded messages from left to right.
such messages. Recall from section 3.1 that, in some images, the texture of
most of the blocks is “smooth and simple”, and the AMP algorithm cannot
generate enough matrix patterns for them. Also, changing the 4th and 5th bits
of pixels in “smooth and simple” blocks will decrease the quality of stego-
image, which is one of the limitations of hiding in the middle bits instead of
the LSB. In our 5, 10, 20, and 40 percentage stego-image datasets, we have
9430, 9202, 8746, and 7611 images, respectively. These four stego-image
datasets and their cover image datasets are used to measure the quality of
stego-images with PSNR and evaluate the resistance of the AMP algorithm
against some well-known quantitative steganalysis works. Figure 1 shows
three images from the BOSSBase dataset (images number 1, 10 and 100 in
the dataset) and their stego-images. Left images are cover images, and the
other four images contain 5%, 10%, 20%, and 40% bpp embedded messages
from the left to the right.
The quality of stego-images is evaluated with PSNR. Each pair of cover
and its stego-image are used for computing PSNR. The RGB and blue
channel of each pair is used for this evaluation. The Luminance signal
(Equation 7) is used to compute the brightness of each RGB cover and its
stego-image [22, 74]
Luminance(P(r, g, b)) = (0.2126 ·r) + (0.7152 ·g) + (0.0722 ·b)(7)
Adaptive Matrix Pattern Steganography on RGB Images 17
Table 4 PSNR Results (10,000 images)
PSNR [dB] 0.05 0.10 0.20 0.40
RGB 58.5307 55.4773 52.4981 49.5129
Blue 54.7529 51.6831 48.6934 45.6973
Table 5 Quantitative Steganalysis Results (10,000 images)
Capacity (bpp) SP Triples WS
Cover (5%) 0.0131 −0.0034 0.0014
0.05 0.0135 −0.0037 0.0013
Cover (10%) 0.0130 −0.0035 0.0013
0.10 0.0138 −0.0041 0.0011
Cover (20%) 0.0134 −0.0036 0.0013
0.20 0.0147 −0.0045 0.0011
Cover (40%) 0.0141 −0.0040 0.0013
0.40 0.0172 −0.0061 0.0010
Table 4 shows the average of PSNR results. The average of PSNR values
for both RGB images and blue channels is much higher than 30dB. This
shows that the quality of stego-images is kept after hiding a message [74,76].
Results are rounded to four decimal places.
In the quantitative steganalysis evaluation three prior works are used:
sample pairs (SP) [10,34], triples analysis [31] and weighted-stego (WS) [32,
33]. We obtained the source code from Prof. Fridrich’s website with their
initial values [15]. These quantitative steganalysis works estimate the length
of a hidden message in an image [63]. In this experimental work, the blue
channel of stego-images and their cover images are used for evaluation.
Table 5 shows the result of the average estimation for these three quantitative
steganalysis works. Results are rounded to four decimal places.
Table 5 shows that the average estimation of hidden message length for
both stego-images and their cover images are similar. Also, the estimated
average length of hidden message in stego-images are not correct. Thus, these
steganlysis works are not successful against AMP.
To summarize, AMP is resistant against quantitative steganalysis works,
and also it provides high transparency and high capacity for hiding a large
digital secret message.
5 Conclusion
This paper describes an Adaptive Matrix Pattern (AMP) steganography
algorithm for hiding digital media within the RGB image including
18 A. Nilizadeh et al.
cryptographically encrypted messages. This work increases security by gen-
erating a unique codebook matrix pattern for each region of an image. A
pre-processing algorithm is used for ordering and selecting image blocks,
which enhances the transparency and information-carrying capacity of the
algorithm.
Experimental results using the BOSSBase dataset show that AMP is
resistant to known quantitative steganalysis works and provides high-quality
stego-images. Also, the first 3 LSB pixels are not used in the embedding
process; thus, blind LSB attacks cannot destroy the hidden message.
Acknowledgement
Thanks to Dr. Fridrich, Dr. Cogranne, Dr. Pevny, and Dr. Holub for answering
our emails and sharing scripts to transfer the RAW RGB images of the
BOSSBase dataset to 512 ×512 RGB images.
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Biographies
Amirfarhad Nilizadeh is a Ph.D. Candidate in Computer Science at Uni-
versity of Central Florida (UCF). Currently, he is a research and teaching
assistant at UCF. His research interests focus on formal methods, software
engineering, and cybersecurity. He was an intern researcher at CyLab Secu-
rity & Privacy Institute at Carnegie Mellon University in summer 2018. He
was a university lecturer professor at Azad University for three years, 2014–
2016.
Shirin Nilizadeh is Assistant Professor at the Department of Computer-
Science and Engineering, the University of Texas at Arlington. She received
her Ph.D. in Security Informatics from the Indiana University Bloomington
(IUB). For her dissertation on Privacy-aware Decentralized Architectures for
Socially Networked Systems, she received a two-year fellowship from the
school of Informatics and Computing at IUB. Following her doctorate, she
held post-doctoral positions in CNets at IUB from 2014–2015, in SecLabat
University of California Santa Barbara from 2015–2017, and then in Cy-
Lab at Carnegie Mellon University from 2017–2018. Her research focuses
on security and privacy in the context of systems and social networks using
techniques from machine learning and big data analytics.
Adaptive Matrix Pattern Steganography on RGB Images 27
Wojciech Mazurczyk received the M.Sc., Ph.D., and D.Sc degrees in
telecommunications from the Warsaw University of Technology (WUT),
Poland, in 2004, 2009, and 2014, respectively. He is currently a University
Professor with the Institute of Computer Science at WUT and a Researcher
at the Faculty of Mathematics and Computer Science, FernUniversitaet, Ger-
many. Since 2016, he has been the Editor-in-Chief of the Journal of Cyber
Security and Mobility and since 2018 as an Associate Editor for the IEEE
Transactions on Information Forensics and Security.
Cliff Zou received his Ph.D. degree from the Department of Electrical &
Computer Engineering, the University of Massachusetts at Amherst, in 2005,
and MS and BS degree from the University of Science & Technology of
China in 1999 and 1996, respectively. Currently, he is an Associate Professor
in the Department of Computer Science and the Program Coordinator of the
Digital Forensics Master’s program at the University of Central Florida. His
research interests focus on cybersecurity and computer networking. He has
published more than 80 peer-reviewed research papers and has obtained more
than 6100 Google Scholar Citations. He is a Senior Member of the IEEE.
28 A. Nilizadeh et al.
Gary T. Leavens is a professor in the department of Computer Science
at UCF. After joining UCF in August 2007, he became associate chair in
2008, and was department chair from 2010-2021. He led a successful faculty
cluster proposal in cyber security and privacy. His research is in formal
methods. Previously Dr. Leavens was a professor of Computer Science at
Iowa State University in Ames, Iowa, where he started in 1989, after receiving
his doctorate from MIT. Before graduate studies at MIT, he worked at Bell
Telephone Laboratories in Denver Colorado as a member of technical staff.
