An E ﬃ cient DCT-SVD Steganographic Approach Applied to JPEG Images

To prove the origin of images in social media, this work proposes an e ﬃ cient JPEG image steganography approach. After structuring the cover image into blocks of 8*8 pixels, Discrete Cosine Transform is applied to each block of pixels. The latter are quantiﬁed using a quantization table and a matrix of DC coe ﬃ cients from quantized blocks of pixels, is obtained. Singular Value Decomposition is applied to the previous matrix and the secret message is inserted within singular vectors. For extraction purposes, previous transformations are followed reversely. An experimentation is made on seven images and results show that the proposed system outperforms similar studies in three aspects (i) it preserves stego image quality with PSNR of stego images varying between 38 and 54 (ii) it is able to insert a secret message of 257600 bits with the capacity of 4 bits per pixel (iii) it is robust and resistant to attacks such as histogram analysis and chi-square test.


Introduction
Social media gain a large audience since they provide means of instant communication of various types of information [1].The proportion of social media users increased by 10 percent between 2019 and 2020, with 49 % of the global Internet population active on social media [2].However, this popularity makes it a place for malicious people enticed to misinform and deceive people [3][4][5][6].They refer to social engineering techniques and illegal means to compromise information.A major concern is therefore to verify information.Three trends are declined for this concern [7].The first trend exploits cryptographic algorithms to keep integrity of original information by exploiting digital signatures [8], [9].The second trend refers to the use of tattoo which protects the copyright of information by inserting a signature in the original information [10].This signature is not directly visible without appropriate technique.The use of cryptography, on the other hand, is visible because there is a transformation of the original information into encrypted data.Steganography is the third trend.It is the art of hiding secret messages in cover medium such as image file, text file, video file, or audio file [11].Steganography is used to mitigate the problem of transparency related to cryptography and tattooing techniques.Image is the most popular medium due to its high capacity and availability in the Web [12].Image steganography is therefore a good candidate for verification of image and its evaluation criteria are quality of the transformed image (i.e.stego image), capacity bounds to insert the message and robustness to attacks such as histogram analysis and attack of χ 2 .
Several studies have shown that image steganography ensures integrity and confidentiality but is not resistant to statistical attacks [8], [9], [13].This work investigates specifically Joint Photographics Experts Group (JPEG) because (i) it is the popular image format in the web [14] and (2) it performs better concerning security compared to all other image formats [15] has good compression characteristics resistant to attacks.Image steganography related to JPEG provide good robustness but to the detriment of the quality of the image stego and insertion capacity [16], [17], [18], [19], [20], [21].Following these limitations, the aim of this paper is to provide a steganographic system for JPEG images based on SVD insertion to simultaneously guarantee image quality, insertion capacity and robustness to attacks.Since the image steganography approach proposed by Sari et al. [22] fulfills the three criteria, but on various images, we exploit it to adapt to JPEG requirements.Our work makes two main contributions: • We propose a JPEG image steganographic system by adapting the sari et al's work [22] to JPEG.Sari et al. 's work is efficient in terms of capacity, quality and robustness to basic attacks related to image processing.However, the Sari et al's proposal is not adapted to JPEG architecture.Our approach mimics this work by adapting to JPEG format while maintaining performance criteria.
• We perform experiments on seven well-known images and compare with similar approaches to evaluate the final system in terms of image quality, insertion capacity, and robustness.Results reveal that our approach is efficient in quality, insertion capacity and is robust to statistical attacks such as the χ 2 test and the histogram analysis.
The rest of the paper is organized in four sections.Section 2 presents works which are related to JPEG image steganography and which are exploited in this work.Section 3 proposes an approach of image steganography for JPEG images.Section 4 concerns implementation, results and discussions.In this section, criteria such as image quality, insertion capacity and robustness and comparison to similar approaches are made.The document ends with a conclusion and perspectives for further investigations.

Background
In this section, we describe the SVD technique and we present several studies, which deal with JPEG image steganography.

SVD technique
Loukhaoukha and Chouinard [23] indicated that the SVD foundations were settled for real square matrices in the 1870s by Beltrami and Jordan, for complex matrices by Autonne in 1902, and for rectangular matrices by Eckart and Young in the 1939.SVD has been adopted in image processing applications such as image compression, image hiding, and noise reduction [24].It is often very difficult to extract, from a matrix, features of interest to solve a given problem [25] [26].An effective method is to highlight the matrix properties and to factorize that matrix as a scalar of simpler matrices with more structured characteristics.Then, the secret message is dissected and inserted into singular vectors.This process resists attacks which directly analyze images.
Principle of SVD.We consider a real or complex matrix M of size m × n and of rank r.Then, an orthogonal matrix U of size m × m, an orthogonal matrix V of size n × n and a rectangular matrix S of dimension m × n, exist.Formally, the decomposition into singular values of M is the factorization given in Equation 1 [26].
. s 1 , s 2 . . ..s n are the singular values of the matrix M.These values are positive real numbers, which respect the following condition:s 1 > s 2 > s 3 > . . . .> s n [26].
Advantages of SVD in steganography.The use of SVD in steganography is motivated by the following arguments [25] [27].
• The singular values represent the energy of the image, i.e.SVD arranges the maximum of energy of the image in a minimum of singular values; • A good stability is provided by the singular values of an image, i.e., when a small disturbance (a mark or a signature) is inserted in an image, the singular values do not change significantly .It offers robustness against common signal attacks and image processing attacks; • Factorization in SVD is unique.

JPEG image steganography
Several JPEG image steganography approaches has been proposed [16], [17], [18], [19], [20], [21].These approaches are briefly reviewed in this section.JSteg was the first steganography system designed for images compressed in JPEG format [20].During the integration process, JSteg integrates sequentially the secret message An Efficient DCT-SVD Steganographic Approach Applied to JPEG Images bits into the least significant bits (LSB) of certain DCT coefficients quantized and selected based on the zigzag scanning order.JSteg is not suitable for withstanding attacks from the chi-square χ 2 family because LSB is used to integrate the secret message.To increase the number of non-zero quantified DCT coefficients, Chang et al. [16] use a modified quantization table when compressing images based on JPEG.Their approach is also not suitable for chi-square attacks because they rely on LSB substitution to integrate the secret message bits sequentially into the quantized DCT coefficients.OutGuess [19] includes another process of insertion.This process integrates non-sequentially the bits of the secret message by replacing the LSB bits of the quantized DCT coefficients.With this process, OutGuess is able to avoid chi-square attacks.
The three previous proposals have in common that they are all based on direct modification of the quantized DCT coefficients using LSB substitution methods for the integration of secret message bits.Due to the fact that LSB is vulnerable, other substitution methods for inserting the bits of the secret message are employed.The F5 algorithm [21] implements a matrix encoding which improves insertion capacity and provides better security at the same time.F5 algorithm uses matrix encoding and permuted overlap to encode the bits of the message.Although F5 is secure against most statistical attacks like histogram attack, χ 2 attack, it suffers from the narrowing effect and that the receiver cannot distinguish a coefficient of zero value, whether it is steganographically unused or produced due to the modification of absolute values of 1 and -1.Liu et al. [17] proposes a complementary insertion scheme to integrate the secret message into the quantified DCT coefficients.This scheme overcomes the narrowing effect and is able to resist various attacks by steganalysis.All the previous JPEG-based steganographic schemes have the common limitation that one single bit of the secret message can be integrated into each authorized quantized DCT coefficient.So the insertion capacity is 1 bit.Pal et al. [18] proposes a JPEG based steganography scheme able to integrate two bits of secret message through each allowed quantized DCT coefficients and able to resist against some steganographic attacks.Similarly, Chang et al. [16] allow insertion of secret message with pixels of two bits but providing low image quality.None of JPEG based steganography schemes fulfills simultaneously high embedding capacity, image quality and resistance to attacks such as the χ 2 and histogram analysis.The aim of this paper is to propose an attempt to overcome this limitation.Watermarking techniques can offer these properties [28].We are interested in the Sari et al.'s work which offers this fulfillment capability.We propose further a JPEG image steganography scheme by mimicking the Sari et al's insertion of secret message.This proposal is able to provide a 4-bit embedding capacity while preserving quality of image and robustness against attacks.

Proposed approach
In this section, the proposed approach of JPEG image steganography is described.This approach includes two modules as shown in Figure 1.The first module is responsible to encode and hide the secret message and the second module is responsible to extract and decode the hidden message.The insertion and extraction of the secret message relies on DCT and SVD.The first module is broken down into five layers.The first layer aims to transform the image into blocks of 8 * 8 pixels.
The second layer is responsible for DCT transformation.This layer decorrelates blocks of pixels from the input image.The third layer is responsible for quantization.In this layer, the blocks of pixels decorrelated in the previous layer are quantified.The fourth layer concerns the insertion phase of the secret message.In this layer, the secret message is inserted within the cover image.
The fifth layer refers to entropy encoding.In this layer, data are compressed to finally generate the JPEG image file.The second module also has five layers but each layer performs reverse operations of the corresponding layer in the first module.The following sections provide technical details of each layer in the first module.

Structuring in 8 × 8 blocks of pixels
In this layer, the image taken as input is subdivided into 8 × 8 blocks on which the following layers perform independently.When the width and the length of that image are not multiples of 8, we add columns by repeating the last until reaching a multiple of 8.The principle is the same concerning lines.This breakdown is due to the following reasons.
Applying DCT to all N × N pixels of an image requires cutting because it allows data units to reduce the compression rate and faster.Correlations between pixels of an image are of short range.Each pixel has a value that is close to its neighbors, but has nothing to do with the values of distant neighbors.2.

DCT transformation
where: • DCT (i,j) represents the value of the DCT at the point of coordinates (i, j) in the block of 8x8 pixels.
• Pixel (x, y) represents the value of the pixel of coordinates (x, y) in the block of the original image of 8x8 pixels.
The DCT coefficients include the DC coefficient and the AC coefficients.The DC coefficient is the coefficient which has zero frequency in both dimensions whereas the AC coefficients are the 63 others having non-zero frequencies.Most of the spatial frequencies have zero or near-zero amplitude and not need to be encoded.
Since the DCT matrix transformation is an orthogonal transformation, it is associated with an inversion method to be able to extract the secret message within the JPEG file from the stego image.The inverse DCT on each of the 8x8 blocks is defined in Equation 3.

Quantification
Quantification follows the DCT transformation.Here, the DCT blocks obtained from the upper layer are quantified.Each element of the upper layer's matrix is divided by its corresponding element in the quantification matrix.The quantification matrix characterizes the sensitivity of the eye in each frequency zone.This matrix is therefore rounded down to the nearest whole number after dividing by the coefficient of quantification.For a block F of the matrix's image, its quantization is expressed as in Equation 5.Where Q represents the quantification matrix.The reverse quantization is represented in Equation 6.
In the proposed scheme, the quantification table is the modified quantification table defined in [29].This table is significantly different from the standard JPEG quantization table.The modified quantification matrix has the following advantages: • It improves the capacity of insertion or concealment within the original image [30].This table allows us to hide more data.
• This table also allows the stego image to limit distortions visible to the human eye.
In case the quantization operation is performed correctly, two situations occur.Very few zeros appear on the left of the DCT coefficient matrix (blocks of pixel) and information in the matrix is typically concentrated in the upper left region of blocks of pixels.

Insertion of secret message
In this layer, the process of concealing the secret message in the image is performed.Figure 2 depicts this process.
The DCT blocks of pixels are divided into DC coefficient and AC coefficients.In the matrix's image, the DC coefficients of each sub-block (blocks of pixels) are gathered to obtain the DC coefficient matrix.
The DC matrix is composed of only DC coefficients of blocks of pixels of the image matrix.The size of the matrix of DC coefficient is [N /8] × [M/8] when the image matrix is of size N × M .The SVD technique is then applied to the matrix of DC coefficients.The expression in the form U * S * V is exploited after transformations.The process of insertion is the resumption of the principle of insertion proposed by Sari et al. [22].It has two advantages: (i) good performance and (ii) the DC coefficients selected as the place for insertion, are useful and robust against various attacks.The principle of integration is as follows: Where • S' is the singular value after insertion; • S is the singular value of the DC matrix; • α is the intensity factor of the insertion; • L m is the secret message.
After the insertion, reverse SVD is applied on matrices U , S and V using the formula U * S * V T .This formula provides the reverse of SVD transformation where V T is the transpose of the orthogonal matrix V .The inverse of SVD is helpful to reconstruct the matrix of DC coefficients.The next step consists to reconstruct the blocks of pixels with their DC coefficients.These numbers represent the JPEG output, but they are compressed before being included in the output file.This phase is called entropy encoding and is described in the next section.

Entropy encoding
This layer is dedicated to the process of encoding DC coefficients.This process aims at compressing the data before writing it to an output file.Entropy encoding, illustrated in Figure 4, involves encoding symbols that have a high probability of occurrence with shorter words than symbols that have a low probability of occurrence.However, the DC coefficient of the pixel block and the other 63 DC coefficients are coded separately.
DC coefficients are coded in DPCM (Differential Pulse Code Modulation) using the DC value of the DC coefficient from the previous block as presented in Equation 9.
The goal of this process is to exploit the correlation between the DC values of adjacent blocks and to encode   [31] them more efficiently.These blocks typically contain most of the image energy.The other 63 AC coefficients starting from AC (0,1) are range coded after a Zigzag scan as shown in Figure 5.
The purpose of Zigzag scanning is to facilitate entropy coding by first encountering the coefficients most likely to be non-zero or the low frequency coefficients.The JPEG algorithm employs a combination of RLE(Run Length Encoding) and Huffman or arithmetic encoding.The idea is that the sequence of AC coefficients contains just a few non-zero numbers, with the number zero between them.

Extraction
Now, the extraction process is described.The aim in this process is to extract a secret message from the stego file.This process is depicted in Figure 7

Experimentation and discussions
Experiments are realized on a dataset of seven grayscale images available in literature [18].They all are 512 x 512 as presented in Figure 8.
In the following, results with this dataset are presented and discussed.The performance of the steganography system is assessed in terms of quality of the stego image, insertion capacity and robustness.
The stego image is obtained after performing layers in the first module of the proposed approach.The secret message is inserted in the cover image by modifying the transformed and quantized coefficients (DCT) of the cover medium and these coefficients are further encoded by appropriate entropy encoding to obtain all the compressed data.The compressed data set is considered as a compressed version of the stego image from which the receiver can extract the secret message.The first assessment criteria is fulfilled when the receiver has a good visual or high quality image after the decompression process.Figure 9 illustrates reconstructed images.
The mean-square error (MSE) and the peak signalto-noise ratio (PSNR) are computed to assess the level of visual quality of stego images [32].MSE is the cumulative squared error between the compressed and the original image.It is recommended to have lower the value of MSE because it indicates that both images are nearly similar.PSNR is a ration, which measures the quality between the original and a compressed image.The higher the value of PSNR, the better the quality of the compressed or the reconstructed image.MSE is given in Equation 10.
where IMG 1 is the original image and IMG 2 is the compressed image.M is the number of rows and N is the number of columns.PSNR is given in Equation 11.
where R is the maximum fluctuation in the input image data type.MSE is the mean-square error.
Results about image quality are presented in table 1.We see that PSNR of stego images varies between 38 and 54 which shows that the proposed approach presents very good results in terms of image quality.The following images: boat, goldhill are better reconstructed after applying the proposed steganography system since they have the lowest MSE and the highest PSNR.Our approach is able to provide better PSNR and MSE at the same time.This capability means that even if the secret message is inserted, the stego image is not as different as the original image.Therefore, the image can be propagated without any visible alteration.It can be reconstructed and verified through the system.
As we compare our approach to similar works in table 2 based on PSNR, we find that our proposed approach reaches the highest values of PSNR.This result presents the dominance of our approach.In conclusion, our system outperforms the others in terms of visual quality of the stego images.
The second important concern in steganography is the capacity to insert secret messages without distorting the quality of the stego image, so that the stego image is almost identical to the cover support.Table 3 presents a comparison of our approach to similar works in terms of insertion capacity.Our approach provides a value    The third criteria required to assess a steganographic system is the resilience to attacks.The robustness of our system against histogram analysis and χ 2 attacks is analyzed.Concerning the histogram analysis attack, the aim is to show that there is no difference between the histogram of original image and the histogram of the stego image [18].If there are variances, the system is not resilient to this attack.The histogram of the stego image   is constructed by plotting quantified DCT coefficients from the stego file in order to expose the histogram.The histogram of the original image is directly generated from its pixels.Figure 11 and 14 represent respectively the histogram of the cover image and the histogram of the stego image.We realized that there is no variations.We realize the same on two research works as shown in Figure 12 and in Figure 13 : [18] and [17].But these works have been applied only on the reconstructed images from JPEG bit streams.We also observe that [18] is resilient to histogram analysis since there is almost no variation between the stego and the original cover image.Unlike, Liu and Liao's histogram indicates distortions on the stego image.So this work is susceptible to the histogram analysis attack.
The χ 2 attack holds generally in LSB.This attack detects the existence of the hidden message based on the variation of pair of values (PoVs) in the stego image.The variation of PoVs for any image is identified as follows [18].We consider that X k and Y k are frequency occurrences for pixels 2k and 2k + 1 respectively, for k = 0, 1, 2, ..., 127.Now, D k is the difference of pixels 2k and 2k + 1 of any image, and its formula is given in Equation 12.
where abs (.) represents the absolute function.
Histograms with values of D k are plotted in Figures 14,  15, and 16 only for the Lena image.Figure 14 illustrates D k values for LSB and [16].Figure 15 illustrates D k values for [18] and [20].Figure 16 depicts D k values of the stego image using our approach.Results show that variations of D k are very small in our approach and [18].It is visible since curves are near the abscissa axis.The proposed approach is resilient to the χ 2 test attack since it is based on SVD insertion, which is a technique that offers robustness against common attacks [25].LSB looks to be the most vulnerable regarding its curve.Indeed, D k points points move away from the abscissa axis.Likewise, approaches in [16] and [20] present bad results in terms of D k .Concerning robustness, experiments reveal that our approach is resistant to statistical attacks such as the χ 2 test and histogram analysis.Table summarizes other works taken from the literature, which are evaluated according to criteria defining the performance of a steganographic system.From this table we can therefore say that the proposed approach improves previous works in particular the study [18].
Simulations and development of system have been made on MATLAB R2018a (9.4.0.813654) 64bits.MAT-LAB has been used because this scientific environment provides intensive in-built image processing modules.Compared to similar works, the proposed JPEG image steganography provides better results in terms of image quality, insertion capacity and resilience to attacks such as χ 2 test and histogram analysis.This approach takes  advantage of SVD insertion of a robust image steganography system.These results demonstrate that it is possible to exploit image steganography methodologies to improve JPEG image steganography.However, our system should be tested against more recent attacks such as reverse JPEG compatibility [33].

Conclusion and perspectives
The aim of this work was to propose a JPEG steganography approach that simultaneously guarantees image quality, insertion capacity and robustness to attacks.For that, an approach of insertion of secret text has been designed and implemented with the particularity of adapting the Sari et al. [22]' s embedding approach to JPEG.The experiments performed on seven images revealed that the proposed system (i) is efficient concerning quality of stego image (ii) is able to take 4 bits per pixel for insertion of message (iii) is robust and resistant to attacks such as histogram analysis and attack of χ 2 .A comparison with similar JPEG steganography approaches revealed that the proposed approach provides better properties.
Future works include two main directions.The first direction is to investigate other image steganography approaches that we can exploit to improve performance of the proposed system.The second direction is to reinforce our system to recent attacks.
DCT is one of the most common transformation techniques in image compression (A proposed secure multiple watermarking technique based on DWT, DCT and SVD for application in medicine).DCT is the basis of transformation used in the JPEG standard (Image compression using DCT upon various quantization).DCT is applied to each block of 8x8 pixels obtained in the first layer and provides new blocks of 8x8 pixels.The result provided is represented in a matrix 3 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e2

Figure 1 :
Figure 1: Architecture of the proposed approach

Algorithm 1 : 2 Decomposed 5 Collecting DC coefficients on each block; 6 M 7 msg = 1 ; 12 M
Insertion algorithm Result: JPEG file of the stego image 1 Input: cover image, secret message; DC = SVD(M DC ); 8 while msg message size do 9 S i = S i + αL mi ; DC = U * S * V T ; 13 Reconstruction of each block with DC coefficient; 14 Entropy encoding;

Figure 2 :Figure 3 :
Figure 2: Insertion process . In our approach, the extraction model takes the JPEG file of the stego image as input and returns the hidden message.It is realized in different stages.The first stage concerns entropy decoding of the JPEG compressed image.The second stage concerns extraction of the message concealed in the stego file.The third stage concerns the inverse quantization and the reverse DCT to reconstruct the original image.

Algorithm 2 : 5 M
Algorithm of extraction Result: secret message 1 Input: JPEG file of the stego image ; 2 Reading the JPEG image file; 3 Entropy decoding of the stego image; 4 Collecting the DC coefficients and determining the matrix M DC ; DC = SVD(M DC ); 6 msg = 1; 7 while msg message size do 8 L mi = (S i − S i )/α ; 9 msg = msg + 1 10 end 6 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e2

Figure 11 :
Figure 11: Stego image in our approach

Figure 16 :
Figure 16: D k for our approach

Table 1 :
Assessment of visual quality

Table 3 :
Our approach vs. similar works in terms of insertion capacity (in bits)

Table 4 :
Our approach vs. similar works in terms of robustness.∨ = yes and × = no Approaches/Criteria Quality (psnr>35db) Capacity (in bits) by coefficient Resistance to χ 2 Resistance to histogram