The paper presents an assessment of the efectiveness of the main methods of steganography based on the pixel diference. The performance of these methods was evaluated using key metrics, signal-to-noise ratio, mean squared error, quality and structural similarity indices, and through pixel diference histogram analysis. To evaluate the efectiveness of the selected steganography methods under the same conditions, a demonstration software implementation for Windows was developed that works with images in shades of gray. The analysis of the performance parameters of the selected steganography methods allows for the formulation of recommendations for their use in the context of accuracy, reliability and eficiency of information embedding, as well as from the point of view of the quality of information embedding and resistance to stegoanalysis.
The proposed by Gandharba Swain method enhances hiding capacity and PSNR by using eightdirectional PVD and LSB substitution, efectively resisting RS and PDH analysis. It exploits edges in multiple directions and combines LSB substitution with PVD for robust security. The algorithm ofers two variants: Type 1, with higher PSNR, and Type 2, with greater hiding capacity, allowing users to choose based on their needs. However, the complexity increases due to eight-directional PVD and careful selection of embedding locations, leading to higher computational resource requirements. The method processes 3×3 pixel blocks and calculates eight diference values for each block. Key characteristics include operation on non-overlapping 3×3 pixel blocks, with the central pixel undergoing modified LSB substitution. It uses a (2n+1)-ary notational system for embedding, enhancing the process. The approach is adaptive, embedding more bits in high-textured regions compared to low-textured ones, optimizing hiding capacity [5].
The proposed by Anita Pradhan, K. Raja Sekhar, and Gandharba Swain adaptive PVD steganography algorithm ofers enhanced hiding capacity and reduced detection risk by utilizing horizontal, vertical, and diagonal edges in six-pixel blocks. Its adaptive quantization ranges, based on pixel correlations, improve performance with higher hiding capacity and less distortion, as shown by improved PSNR values. The algorithm is robust against PDH and RS steganalysis, providing better security than traditional methods. However, the complexity of the adaptive approach may increase computational demands, potentially reducing eficiency. The algorithm uses 2 × 3 and 3 × 2 pixel blocks, known as variant 1 and variant 2, respectively, to avoid step efects and enhance capacity and imperceptibility. Overall, it is presented as an advancement by balancing high capacity, security, and image quality [6, 7].
The OPVDMF method proposed by Aditya Kumar Sahu and Gandharba Swain enhances embedding capacity and PSNR in image steganography by using pixel overlapping, which optimizes space within image blocks. It uses the diference between the first four pixels and the fifth pixel for data embedding, with pixel adjustments to minimize distortion, maintaining image quality. However, the method’s complexity may pose challenges, requiring precise calculations during embedding and extraction. Key characteristics include operation on 1x5 pixel blocks and a modulus function to compute stego-pixels, ensuring image integrity. The method shows competitive performance in PSNR, embedding capacity, and execution time compared to existing techniques. Its security is verified using RS analysis, enhancing its reliability for secure data hiding [8].
The OPVD method proposed by Aditya Kumar Sahu and Gandharba Swain in the same paper as OPVDMF is a steganography technique designed to enhance EC and PSNR by utilizing pixel overlapping. This method divides image blocks into four sub-blocks, using the first and fifth pixels, the fifth and second, the third and fifth, and the fifth and fourth pixels for data embedding. This approach allows for increased EC as one pixel is used in multiple sub-blocks, significantly improving performance compared to existing techniques. The OPVD method operates on 1x5 pixel blocks, ensuring eficient use of space and maintaining image quality through pixel adjustments to minimize distortion. A key advantage of OPVD is its competitive PSNR, with a reported value of 37.01 dB, indicating high image quality post-embedding. Additionally, the method demonstrates a slightly reduced execution time compared to other methods, enhancing its practicality. However, the complexity of the OPVD method may present challenges, requiring precise calculations during the embedding and extraction phases. Despite this, its security is robust, successfully resisting RS analysis, which verifies its reliability for secure data hiding [8].
The proposed by Reshma Sonat and Gandharba Swain steganography method combines quotient value diferencing (QVD) with pixel value correlation (PVC) to enhance data hiding capabilities. This approach is designed to overcome the fall-of boundary problem (FOBP) commonly associated with PVD techniques, ensuring that the stego-images remain imperceptible. The method involves a two-stage data embedding process on 3x3 pixel blocks, where QVD and remainder substitution are applied to ifve central pixels, followed by PVC embedding on the four corner pixels. Additionally, the method demonstrates robustness against detection by RS and PDH tests, as the PDH curves do not exhibit a zigzag pattern, and the RS test is unable to detect the steganography technique. However, the time complexity of the method is linear, depending on the length of the secret data, which may impact performance in scenarios involving large data volumes. Overall, the proposed method ofers a novel and efective solution for secure data hiding with improved performance metrics [9].
MSE, or Mean Squared Error, in steganography, is a statistical measure of the diference between an original image and an image that has been altered using steganographic techniques. This is a quantitative indicator that allows you to evaluate the degree of changes made to the image when embedding a secret message. The formula for calculating MSE is:
MSE =
1 × ∑︁ ∑︁ ( − )2 , =1 =1 where is the pixel of the cover image, is the corresponding stego pixel, and and are the pixel dimensions of the image. The sum passes across all pixels of the image, and the square of the intensity diference of each pixel in the original and steganographed images is calculated.
The smaller the MSE, the smaller the diference between the original and the steganographed image, which is generally considered preferable in the context of steganography because it means that the changes made to embed the message are less noticeable [9, 10].
PSNR, or Peak Signal-to-Noise Ratio, in steganography, is a measure used to evaluate image quality after applying steganographic techniques. It measures the ratio of the maximum possible signal strength (i.e., the original image) to the noise power made by changes made when embedding a secret message. The formula for calculating PSNR is as follows:
PSNR = 10 · log 10 ︂( 2 )︂
MSE
,
(
The PSNR is higher when the MSE error is smaller, which means that the steganographed image is closer to the original. A high PSNR often indicates better steganographic image quality, but it is important to consider that it may not always adequately assess the visibility of steganographic changes, especially in the context of human perception [10].
The SSIM, or Structural Similarity Index Measure, in steganography, is a method of assessing the quality of images based on human perception. It is used to measure the similarity between two images, usually between the original and steganographed (altered) images. SSIM more accurately reflects visual changes in an image than MSE or PSNR because it takes into account changes in structure, brightness, and contrast. The formula for calculating SSIM is:
SSIM(, ) =
(2 + 1)(2 + 2) ( 2 + 2 + 1)( 2 + 2 + 2) , where and are the image windows in the original and steganographed images, respectively. , are the average pixel values in and . 2, 2 are the pixel variance in and . is covariance between and ; and 1, 2 are constant variables to avoid division by zero.
SSIM values close to 1 usually indicate high similarity between images, while values closer to 0 indicate low similarity [11].
QI, or Quality Index, also known as the Universal Quality Index (UQI), is a metric used to evaluate the quality of an image. This index is used to compare two images, usually the original and modified (e.g., steganographed). UQI evaluates the similarity between these images in three aspects: brightness, contrast, and structure.
hiding capacity BPB = image size in bytes .
hiding capacity
BPP = image size in pixels .
BPP or Bits Per Pixel measures the number of bits of a secret message that can be embedded in
each pixel in an image. A higher BPP allows you to embed more information into an image, but it can
increase the chances of detection or afect the visual quality of the image. It is calculated using the
formula [9, 7]:
(
The UQI can have a value between -1 and 1, where values closer to 1 indicate high similarity between images. The maximum value can be 1 if the original image and the same image are the same [12].
BPB or Bits Per Byte measures the number of bits of a secret message that can be embedded in each byte of a medium. A high BPB means that more information can be embedded in the medium, but it can increase the risk of steganography detection. It is calculated using the formula: =
4 ( 2 + 2) [()2 + ()2] ,
To demonstrate the capabilities of the selected steganography methods and evaluate their efectiveness under the same conditions, a demonstration software implementation for Windows working with grayscale images was developed. In the desktop program, you can select an image, enter the text to embed, and get the result in the form of five stegoimages in which information is embedded according
Name to the appropriate algorithms. It is also possible to retrieve text that has been extracted using the appropriate extraction algorithms for each of the methods. After carrying out these operations, it is possible to compare the results of the performance evaluation parameters, which are calculated for each method.
The choice of C#, combined with Windows Forms and System.Drawing, creates a strong platform for developing and demonstrating efective pixel diference-based steganography techniques. This allows not only the eficient implementation of steganography algorithms, but also provides convenience in visualizing the results necessary for the analysis and comparison of diferent techniques. Additionally, C#’s ability to seamlessly integrate with other technologies and libraries provides flexibility in expanding and improving the project.
For verification, we use standard gray images (8 bits per pixel) from the SIPI database with a size of 512x512 pixels and 256x256 pixels. Let’s consider and comment on the results of several experiments: Author names can have some kinds of marks and notes: • 100% embedding capacity in a 512x512 textured image (with a suficient number of edge zones) with a size of 256 kB; • 100% embed capacity in 256x256 mostly smooth image size 256 kB; • 6.4 kilobytes of secret message in a 256x256 medium-textured image of 64 kB.
Let’s start with an image with the following options: • 512x512 pixels; • 256 kilobytes.
First, we will embed the maximum amount of data in the image, to do this, we will generate a random message of 100,000 bytes to check the maximum embedding capacity for each method and get the following result.
As for the integrity of the message, all methods showed good results, we did not find any significant artifacts in the extracted data.
It can be seen (Table 1) that OPVDMF has the highest embed capacity, but at the same time it has the highest embed-in and extraction time. The best results here, in our opinion, have an eight-directional method that embeds and extracts messages very quickly, while having a capacity slightly lower than OPVDMF and QVD/PVC – 15600000 bits versus 1600000 for OPVDMF and QVD/PVC.
According to the performance indicators (Table 2), it can be seen that QVD/PVC shows the worst results, which coincides with the visual perception of the steg image. The adaptive method has the best results, and the eight-directional method, taking into account its results in capacity and speed.
If you look at the analysis using the pixel diference histogram (Figure 1), you can see that all the histograms of stego images are significantly diferent, but the most natural one can be noted in the eight-directional method.
Name 8-Directional QVD/PVC Adaptive OPVD OPVDMF
Hiding T, ms
Extract. T, ms
Next, let’s run tests with an image with the following parameters: • 256x256 pixels; • 64 kilobytes; • Large Smooth Area.
In this case, we will also embed the maximum number of bits.
In terms of embedding eficiency (Table 3), if we exclude the QVD/PVC and OPVDMF methods due to their poor performance in such conditions, the eight-directional method is the clear winner. Expectedly,
Name
MSE according to the results of the performance evaluation (Table 4), QVD/PVC and OPVDMF show the worst results, which coincides with the visual analysis of the image. The adaptive method has a clear advantage, being significantly ahead of the eight-directional and OPVD methods.
When analyzed using the pixel diference histogram (Figure 2), the histograms can be arranged by plausibility as follows: eight-directional method; Adaptive PVD; OPVD; OPVDMF; QVD/PVC.
There is a problem in extracting a message from such an image, the smoother the image, the more artifacts from embedding are visible on it, and also the worse the integrity of the message. 5.3. 10% of image size 256x256 Now let’s check the ideal conditions for each method, as a container – an image of the surface of the echo with a suficient number of edge zones and the presence of smooth ones. Let’s embed 10% of the image size with each method – 6400 bytes.
As a result of the extraction, all methods did an equally good job of embedding and deleting the message.
Based on the embedding metrics (Table 5), since the number of embedded bits, and therefore the number of bits per byte and per pixel, is the same, we can only estimate the performance of embedding and extracting. In this case, the eight-directional method is again far ahead of the others. The slowest method is adaptive. The fastest are QVD/PVC, OPVD and OPVDMF are somewhat slower and at the
Name
QI same level.
According to the results of the performance evaluation (Table 6), the QVD/PVC and OPVDMF methods, as it was noticeable visually in the stego images, have approximately the same and worse indicators. Among others, the adaptive method is the most efective.
Based on the pixel diference histograms (Figure 3) you can see that QVD/PVC is closest to the original.
In conclusion, it can be noted that steganography based on pixel diference is an important and promising direction in the field of information security. Considering the various steganography techniques presented in this paper, its significance in the context of modern data security and privacy requirements becomes apparent. Methods that have been analyzed and compared in detail, including the eightdirectional method, the adaptive PVD method, the OPVD method, the OPVDMF method, and the QVD/PVC method demonstrate the depth and complexity of modern steganography. The analysis of the eficiency parameters of the selected steganography methods gives an idea of the importance of these methods in the context of accuracy, reliability, and eficiency.
Generally, PVD methods can be used in digital forensics to embed metadata within images. This metadata can include information about the origin, authenticity, and history of the digital content, which is crucial for forensic investigations. The adaptive PVD method, for instance, ofers high capacity and security, making it suitable for embedding detailed forensic data without compromising image quality. Also, such methods can be adapted for network steganography, where data is hidden within network protocols. This can be used to transmit sensitive information across networks without detection. For example, the eight-directional method, which is robust against detection by RS and PDH tests, could be adapted to hide data within network packets, ensuring secure communication over potentially insecure channels.
Based on the results of the software implementation and the tests carried out, it can be concluded that the eight-directional (V-1) method has the highest speed of operation and fairly balanced other characteristics while having the problem of going beyond the values from 0 to 255 (FOBP). The adaptive method and the OPVD method showed the greatest ability to embed in mostly smooth images. The OPVDMF method, in my opinion, has shown the worst results, it has a FOBP problem, it does not integrate well into smooth areas of the image and is slow, but at the same time it is very easy to implement programmatically. The most dificult in terms of software implementation was the method based on the diference in coeficient values and the correlation of pixel values, it demonstrates better embedding capacity and has a fairly natural histogram of the pixel diference, this method really solves the FOBP problem, while being slow and poorly coping with smooth areas of the image. In general, we can conclude that the adaptive method, based on the results of a comprehensive analysis, is the most optimal: it has a simple software implementation, FOBP has not been noticed for it, has good performance indicators, and is quite invisible to the human eye. But we pay for such advantages with average performance, poor resistance to steganoanalysis, and the smallest embed capacity.
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