Dual-image reversible data hiding (RDH) is a technique for hiding important messages. This technology can be used to safely deliver secret messages to the recipient through dual images in an open network without being easily noticed. The recipient of the image must receive the two stego-images before the secret message can be completely retrieved. Imperceptibility is one of the main advantages of data hiding technology; to increase the imperceptibility, the quality requirements of the stego-images are relatively important. A dual steganographic image RDH method, called a DS-CF scheme that can achieve a better steganographic image quality using the center folding (CF) strategy. In this paper, we developed a translocation and switching strategy (TaS) to shorten the distances between the stego-pixel coordinates and the cover pixel coordinates after information being hidden. Compared with the DS-CF scheme, our proposed DS-TaS scheme can effectively improve the quality of the steganographic images at the same level of embedding capability. The experimental results show that the PSNR of our DS-TaS scheme at
With the advances in information technology, the Internet has become an indispensable tool in human life; in particular, the Internet of Things along with 5G networks will produce a higher speed and greater data transmission on the network. Many transactions in a virtual environment can be easily, quickly, effectively, and conveniently conducted. However, data in these transactions may be illegally stolen, monitored, tampered, copied, and/or damaged during the transfer process. Therefore, security is a prerequisite in the virtual environment, and convenient functions in a secure environment have been in high demand.
To protect digital data and privacy from being infringed, encryption technology has been more commonly used. The sending parties use a key to generate the cipher text of the digital data and transmit the cipher text to the receiving parties. The data party uses the same key to restore the digital data; therefore, even if it is stolen during the transmission process, the original data cannot be known without the key. However, because the data during the transmission process are unintelligible cipher text, although it is impossible to know the original data, it is easy for the person of interest to know whether the data are cipher text, and if so, tamper with or destroy them. Even if the receiving party has the key, the data of the original sender cannot be smoothly obtained. Therefore, if privacy and important data are hidden in the transmitted media, such as pictures, images, sounds, texts, and other digital data, and not easily detected, they can be safely transmitted to the recipient without being detected or tampered with. To achieve the goal of information security, hiding plays an extremely important role in data transmission in a virtual environment.
Information hiding technology can be divided into non-reversible [
The dual-image reversible data hiding (RDH) method uses the original image to generate two identical images, and then uses these two generated images to hide the secret message. This method is similar to the secret sharing method in cryptography, which involves splitting the secret in an appropriate manner. Each share after splitting is managed by a different participant, and secret information cannot be recovered by a single participant. Secret information can only be obtained through cooperation among these players.
This study proposes a translocation and switching (TaS) strategy that uses translocation and switching operations to effectively shorten the distance between the cover pixel coordinates and the stego-pixel coordinates. We use the TaS strategy to hide information on dual images, which is called the DS-TaS scheme. The DS-TaS scheme improves the image quality of the DS-CF scheme under the same payload, and can achieve almost the same quality of the dual images.
The contributions of this research are as follows: We developed a translocation and switching strategy, referred to as the TaS strategy, to shorten the distances between the stego-pixel coordinates and the cover pixel coordinates after information hiding. To effectively improve the image quality, we proposed a dual steganographic image reversible data hiding method called the DS-TaS scheme based on the TaS strategy. The DS-TaS scheme carries out (2, 2) secret sharing through a simple information hiding process, preventing over-concentration of secrets and providing efficient dispersal of information for security and load balancing.
In 2007, Chang et al. proposed an exploiting modification direction (EMD) method based on dual-image reversible information hiding [
In 2009, Lee et al. proposed a two-image reversible information hiding method based on the position and direction [
In 2015, Lu et al. proposed a two-image reversible information hiding method with a central fold strategy [
The DS-CF scheme uses the concept of the averaging method to hide
where
The DS-CF scheme of the central fold strategy recodes the secret values to reduce the difference between the stego-pixel and the original pixel, thereby improving the stego-image quality. The hiding process is as shown in
In 2017, Yao et al. proposed using the selection strategy of shiftable pixels [
In this section, Section 3.1 elaborates on the viewpoints of this research method and describes how to use the translocation and switching strategy (TaS strategy) to optimize the quality of the stego-image. Section 3.2 proposes a reversible dual image information hiding method based on the TaS strategy.
The DS-CF scheme method takes one cover pixel
It is worth noting that the position of the red frame in
This research proposes a translocation and switching (TaS) strategy, which uses translocation and switching operations to effectively shorten the distance between the cover pixel coordinates and stego-pixel coordinates. The TaS strategy can make full use of
The proposed TaS strategy defines two manipulation functions: translocation () and switching ().
The translocation function is
Through the
Taking
Again, taking
For the switching manipulation, when
Assuming
Using the TaS strategy, we propose a dual stegano image RDH method, referred to as the DS-TaS scheme. In contrast to the DS-CF scheme, our DS-TaS scheme takes out two secret messages
Input: An original image
Output: Two stego-images
Step 1: For
Step 2: Extract two sets of secret bytes each time, namely, (
Step 3: Use the center-folding strategy to convert
Step 4: If the condition
Step 5: If the conditions of Step 4 are true, use the TaS strategy to calculate the two pairs of stego-pixels (
Case 1:
Case 2:
Case 3:
Step 6: Let
The following sections describe the process of using the TaS strategy to embed information. Let
Case 1: When
For the black part shown in
The probability of occurrence of the condition is observed as follows, where the image size is
Case 2: When
The number of pixels that the image will be modified into is shown below.
Case 3: When
The two pairs of stego-pixels hidden are as follows:
The number of pixels that the image will be modified into is the same as in Case 2.
Input data: Stego-image
Output data: Cover image
Step 1: First, take out two pairs of pixels {
Step 2: Restore the pixel pair {
Step 3: Calculate
Case 1: if
Case 2: if
Case 3: if
Step 4: By
Step 5: Convert
Section 4.1 describes the experiment environment and metrics evaluation. Section 4.2 presents the reduction in the number of shifted pixels through the proposed DS-Tas scheme. Finally, Section 4.3 shows the results and benefits of the DS-TaS scheme compared with other methods.
The experiment uses MATLAB R2017ab software to implement the proposed method and compare the results with those of other methods. We used six commonly applied standard grayscale images (size 512 × 512) as test images, i.e., Lena, Goldhill, Peppers, Baboon, Barbara, and Boat, as shown in
The distortion in a stego-image can be measured based on the peak signal-to-noise ratio (PSNR), which can be computed using
The bits per pixel (bpp) provide the average embedding capacity for each pixel. The higher the bpp value is, the greater the embedding capacity. The total embedding capacity must be divided by 2 to apply dual images to hide the secret information.
We calculated the length of the secret information that can be carried by each pixel
Observing the various evaluation indicators in the Lena image, when
The DS-TaS scheme is used to optimize the DS-CF scheme [
As shown in
In
Case 1 | Case 1 | Case 1 | Case 2 | Case 3 | |
Number of adjust pixels | 32,954 | 8,291 | 2,048 | 4,092 | 4,123 |
MSE reduction | 32,954 | 33,164 | 32,768 | 32,656 | 32,984 |
In the proposed DS-TaS scheme, when
Method | Measure | Lena | Goldhill | Peppers | Boat | Baboon | Barbara |
---|---|---|---|---|---|---|---|
Lee et al., 2009 [ |
PSNR1 | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 |
PSNR2 | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 | |
PSNR (Avg) | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 | 52.39 | |
Capacity (bit) | 393,276 | 393,078 | 393,490 | 393,040 | 393,212 | 393,270 | |
bpp | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | |
Lee et al., 2011 [ |
PSNR1 | 49.63 | 49.63 | 49.64 | 49.63 | 49.61 | 49.62 |
PSNR2 | 49.63 | 49.62 | 49.63 | 49.63 | 49.63 | 49.63 | |
PSNR (Avg) | 49.63 | 49.63 | 49.64 | 49.63 | 49.62 | 49.63 | |
Capacity (bit) | 560,801 | 560,740 | 560,572 | 561,255 | 560,686 | 561,223 | |
bpp | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | |
Lu et al., 2015 [ |
PSNR1 | 49.20 | 49.23 | 49.19 | 49.20 | 49.21 | 49.22 |
PSNR2 | 49.21 | 49.18 | 49.21 | 49.21 | 49.20 | 49.20 | |
PSNR (Avg) | 49.21 | 49.21 | 49.20 | 49.21 | 49.21 | 49.21 | |
Capacity (bit) | 524,288 | 524,288 | 524,192 | 524,208 | 524,204 | 524,288 | |
bpp | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
Jafar et al., 2016 [ |
PSNR1 | 48.70 | 48.72 | 48.71 | 48.70 | 48.71 | 48.70 |
PSNR2 | 48.71 | 48.71 | 48.71 | 48.71 | 48.71 | 48.71 | |
PSNR (Avg) | 48.71 | 48.72 | 48.71 | 48.71 | 48.71 | 48.71 | |
Capacity (bit) | 650,369 | 650,726 | 627,637 | 650,781 | 650,799 | 650,781 | |
bpp | 1.24 | 1.24 | 1.20 | 1.24 | 1.24 | 1.24 | |
Lu et al., 2018 [ |
PSNR1 | 50.78 | – | 50.86 | – | – | – |
PSNR2 | 50.78 | – | 50.88 | – | – | – | |
PSNR (Avg) | 50.78 | – | 50.87 | – | – | – | |
Capacity (bit) | 531,426 | – | 528,882 | – | – | – | |
bpp | 1.01 | – | 1.01 | – | – | – | |
Chen et al., 2020 [ |
PSNR1 | 49.91 | 49.91 | 49.91 | 49.91 | 49.91 | 49.91 |
PSNR2 | 49.92 | 49.92 | 49.92 | 49.92 | 49.92 | 49.92 | |
PSNR (Avg) | 49.92 | 49.92 | 49.92 | 49.92 | 49.92 | 49.92 | |
Capacity (bit) | 597,688 | 597,688 | 597,688 | 597,688 | 597,688 | 597,688 | |
bpp | 1.14 | 1.14 | 1.14 | 1.14 | 1.14 | 1.14 | |
Lu et al., 2021 [ |
PSNR1 | 50.26 | – | 50.25 | – | – | – |
PSNR2 | 50.25 | – | 50.26 | – | – | – | |
PSNR (Avg) | 50.26 | – | 50.26 | – | – | – | |
Capacity (bit) | 550,458 | – | 549,648 | – | – | – | |
bpp | 1.05 | – | 1.05 | – | – | – | |
He et al., 2021 [ |
PSNR1 | 55.17 | – | 53.40 | 52.05 | – | 54.97 |
PSNR2 | 55.17 | – | 53.40 | 52.05 | – | 54.97 | |
PSNR (Avg) | 55.17 | – | 53.40 | 52.05 | – | 54.97 | |
Capacity (bit) | 30,000 | – | 30,000 | 30,000 | – | 30,000 | |
bpp | 0.06 | – | 0.06 | 0.06 | – | 0.06 | |
Lu et al.(k = 2) 2015 [ |
PSNR1 | 51.14 | 51.14 | 51.14 | 51.14 | 51.12 | 51.14 |
PSNR2 | 51.14 | 51.15 | 51.14 | 51.14 | 51.16 | 51.14 | |
PSNR (Avg) | 51.14 | 51.15 | 51.14 | 51.14 | 51.14 | 51.14 | |
Capacity (bit) | 524,288 | 524,192 | 524,280 | 524,244 | 524,210 | 524,288 | |
bpp | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
Lu et al.(k = 3) [ |
PSNR1 | 46.37 | 46.39 | 46.37 | 46.37 | 46.39 | 46.37 |
PSNR2 | 46.37 | 46.37 | 46.37 | 46.38 | 46.37 | 46.38 | |
PSNR (Avg) | 46.37 | 46.38 | 46.37 | 46.38 | 46.38 | 46.38 | |
Capacity (bit) | 786,432 | 786,258 | 785,670 | 786,432 | 786,258 | 786,432 | |
bpp | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 | |
Proposed (k = 1) | PSNR1 | 54.15 | 54.13 | 54.15 | 54.16 | 54.15 | 54.15 |
PSNR2 | 57.17 | 57.18 | 57.16 | 57.16 | 57.19 | 57.17 | |
PSNR (Avg) | 55.66 | 55.66 | 55.66 | 55.66 | 55.67 | 55.66 | |
Capacity (bit) | 262,144 | 262,096 | 262,140 | 262,122 | 262,144 | 262,144 | |
bpp | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | |
Proposed (k = 2) | PSNR1 | 51.43 | 51.41 | 51.42 | 51.43 | 51.43 | 51.41 |
PSNR2 | 51.42 | 51.43 | 51.42 | 51.42 | 51.43 | 51.43 | |
PSNR (Avg) | 51.43 | 51.42 | 51.42 | 51.43 | 51.43 | 51.42 | |
Capacity (bit) | 524,288 | 524,192 | 524,280 | 524,244 | 524,288 | 524,288 | |
bpp | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | |
Proposed (k = 3) | PSNR1 | 46.66 | 46.66 | 46.65 | 46.65 | 46.66 | 46.64 |
PSNR2 | 46.66 | 46.65 | 46.64 | 46.65 | 46.65 | 46.65 | |
PSNR (Avg) | 46.66 | 46.66 | 46.65 | 46.65 | 46.66 | 46.65 | |
Capacity (bit) | 786,432 | 786,288 | 786,420 | 786,366 | 786,288 | 786,420 | |
bpp | 1.500 | 1.500 | 1.500 | 1.500 | 1.500 | 1.500 |
In
Metrics | Lena | Goldhill | Peppers | Boat | Baboon | Barbara |
---|---|---|---|---|---|---|
SSIM(Avg) | 0.9979 | 0.9986 | 0.9979 | 0.9983 | 0.9992 | 0.9986 |
VIF(Avg) | 0.9712 | 0.9739 | 0.9718 | 0.9703 | 0.9762 | 0.9731 |
PCC(Avg) | 0.9997 | 0.9997 | 0.9998 | 0.9996 | 0.9996 | 0.9998 |
In this study, a translocation and switching strategy (TaS strategy) is proposed that uses switching and transposition functions to calculate a “re-encoding substitute” of a confidential message such that the changes from the original pixels are significantly reduced, thus effectively improving the image quality. The results show that when the hiding capacity is the same, the quality of the stego-image of the proposed DS-TaS scheme is better than that of the other methods. Compared with the DS-CF scheme proposed, the proposed DS-TaS scheme can effectively improve the quality of stenographic images. Not only does our method achieve a better performance in terms of the image quality, it also has more options than the DS-CF method in terms of the embedding capacity for each stego-pixel. It can hide 0.5 bits for each stego-pixel and can be applied to produce higher-quality stego-images.
Our proposed DS-TaS RDH scheme produces high image quality, and the quality of the 2 images is similar, so an attacker cannot suspect that the image carries a secret message. In addition, because of the spirit of (2, 2) secret sharing, a legal person with two secret images can fully extract the secret information. Therefore, this dual-image-based technology can avoid excessive concentration of information, thereby achieving risk dispersion and load balancing.
In the future, the method will be strengthened by combining it with other reversible dual-image approaches to improve the quality of information hiding images and increase imperceptibility requirements.
We are grateful to all authors who participated in this research.