An Enhanced Approach of Image Steganographic Using Discrete Shearlet Transform and Secret Sharing

Recently, the internet has made the users able to transmit the digital media in the easiest manner. In spite of this facility of the internet, this may lead to several threats that are concerned with confidentiality of transferred media contents such as media authentication and integrity verification. For these reasons, data hiding methods and cryptography are used to protect the contents of digital media. In this paper, an enhanced method of image steganography combined with visual cryptography has been proposed. A secret logo (binary image) of size (128x128) is encrypted by applying (2 out 2 share) visual cryptography on it to generate two secret share. During the embedding process, a cover red, green, and blue (RGB) image of size (512x512) is divided into three layers (red, green and blue). The blue layer is transformed using Discrete Shearlet Transform (DST) to obtain its coefficients. The first secret share is embedded at the coefficients of transformed blue layer to obtain a stego image. At extraction process, the first secret share is extracted from the coefficients of blue layer of the stego image and XORed with the second secret share to generate the original secret logo. According to the experimental results, the proposed method is achieved better imperceptibility for the stego image with the payload capacity equal to (1 bpp). In addition, the secret logo becomes more secured using (2 out 2 share) visual cryptography and the second secret share as a private key.

Nowadays, millions of users are able to transmit the digital media through the internet easily. This feature of the internet leads to a number of challenges and threats regarding the security of transmitted media contents such as (copyright protection, media authentication and integrity verification) [1][2][3][4] . Therefore, data hiding and cryptography methods are to be the essential requirements for protecting the contents of digital media 3 . Data hiding methods perform the security for the digital media by embedding a secret data in another digital media called a cover media 5 . In other word, they make an existence of the secret data invisible at the cover media 6 . While, cryptography methods change the secret data into illegible form [7][8] , some applications of data hiding are designed by combining them with cryptography 9,10 .
Data hiding approaches can be divided into two main methods, namely steganography and watermarking 3 . Steganography is similar to watermarking in general concept of data hiding. That means, they are hidden in an existence of the secret data by camouflaging it within another digital media such as (image, video, text or sound) 6 . However, steganography is different from watermarking according to three main requirements: imperceptibility, payload capacity and robustness 4,11 . Imperceptibility means the cover media should keep the perceptually of stego media (cover media after applying embedding process) after the secret data embeds in it 7,12 . Generally, stego media such as image must preserve its visual quality from a distortion that are generated during the secret data embedding process. Payload capacity stands for a number of the secret data bits that can be embedded in the cover media 13 .
Robustness refers to an ability of the secret data to resist against the attack such as (common image processing, compression,… etc) 4 .
The requirements mentioned above are used as evaluation measurements for data hiding approaches. Steganography techniques especially image steganography are concentrated on the high stego image imperceptibility and the maximum payload capacity 7 . Whenever, watermarking methods focus on the robustness as an essential requirement 7,14 . The most image steganographic methods aim to enhancing the stego image imperceptibility and maximizing the payload capacity. However, there is a trade-off between these requirements when designing the image steganography application. Increasing the embedding bits of secret data may lead to degradation in the stego image quality and it decreases the stego image imperceptibility 1,15 . In addition, there is another problem related to the secret data may be subject to various kinds of the stego image attacks and it allows an adversary to extract/detect the embedded secret data bits 6 . Therefore, a hybrid method of steganography and cryptography can achieve confidentiality for the hidden secret data 10 .
In this paper, a new approach of combined image steganography and cryptography has been proposed. The suggested scheme is concentrated on the two main requirements of image steganography (imperceptibility, and payload capacity). Also, the security of the embedded secret logo can be achieved using the visual cryptography. Consequently, the proposed method is divided into three main processes. Firstly, the secret logo is encrypted using (2 out 2 share) visual cryptography to generate two secret shares (one for embedding process and another used as a private key for an extraction processing). Secondly the embedding process, a cover image is divided into (red, green and blue (RGB)) layers and the blue layer is transformed into frequency domain using discrete shearlet transform (DST). Then, one of the secret shares is embedded in the coefficients of the blue layer to generate the stego image. Finally, the embedded secret share is extracted from the coefficients of blue layer of the stego image and XORed with the second secret share to obtain the original secret logo. According to the experimental results, the suggested approach achieves a better image quality and high value of Peak Signal to Noise Ratio (PSNR). In addition, the proposed method attains best embedding capacity equal to one bit per pixel (bpp) and the confidentiality of secret logo is improved by applying visual cryptography. This paper is organized as follows. The pervious proposed methods of data hiding are demonstrated in the related works. The theoretical background of shearlet system and its transformations is explained in the shearlet transform. The (2 out 2 share) scheme for the secret logo is described in visual cryptography. The proposed method illustrates the secret logo embedding and extraction processes of a new image steganographic approach. An evaluation of the suggested method performance is discussed in the experimental results. Finally, conclusion summarizes the contributions and limitations of the proposed method followed by references.

Related Works
Based on the survey, some of the proposed methods that are based on DST have been applied for image watermarking. As mentioned before, image watermarking methods are generally concentrated on the robustness for the embedded watermark due to using it for copyright protection or integrity verification of digital images. In this study, a new method of image steganography that depends on DST has been suggested. Therefore, this approach can be the first study based on DST for image steganography. Unfortunately, there are no studies that used DST to design image steganographic approaches.
There are a several methods of data hiding have been proposed by researchers. Some of these methods are applied at spatial domain of images 5,11,15 and others are used in transform domain of images 1,3,4,9,12,13,16 . In 1 , the researchers suggested a method of image watermarking that based on DST. A cover image is decomposed by applying DST. Then, Chou's visual model is used to estimate the Just Noticeable Distortion (JND) values for each coefficient of the decomposed cover image. At embedding process, the most significant and largest coefficient values of JND are used for embedding a watermark bits. Finally, the watermarked image is obtained by applying Inverse DST. Based on the experimental results, the proposed method achieves high imperceptibility for the watermarked image and good robustness for the watermark.
Priya et al 3 proposed a medical image watermarking using Integer Wavelet Transform (IWT). A cover image is transformed using IWT into four sub-bands and the low frequency sub-band is interpolated using neighbor nearest interpolation. An electronic patient information is used as a watermark and it is embedded at the interpolated low frequency sub-band to generate a watermarked image.
This method presents a good imperceptibility as its experimental results. Zhao et al 4 suggested another method of image watermarking. The cover image is transformed into directional sub-bands by applying nonsubsample shearlet transform. The strongest directional subband is selected for embedding process and it transformed into a singular value matrix using Singular Value Decomposition (SVD). A watermark is embedded at the singular value matrix to obtain a watermarked image. The result of proposed method shows high imperceptibility and more robustness.
Ananth and Sudhakar 5 proposed a combined technique of image steganography and cryptography. A watermark is encoded by applying barcode encoder and it embedded at the cover image using Least Significant Bit (LSB) substitution method. The proposed method presents good imperceptibility for a stego image and increases the secrecy of the secret data. In 9 , Sun and Guo proposed hybrid method of cryptography and steganography. The cover image is decomposed into low pass sub-bands and high pass sub-bands using Contourlet Transform (CT). The suitable high pass sub-bands are selected for embedding process and they are divided into 4x4 blocks. The secret image is encrypted using Hill Cipher and it embedded at each block using the coefficient 2-LSB. All blocks are corrected by using 2 k correction method and they merged to obtain a stego image. According to its results, the proposed method achieves confidentiality for the secret image and better imperceptibility for stego image. Sun 11 suggested a new method of image steganography based on Bit-plane complexity segmentation (BPCS). A cover image and a secret image are transformed from Pure Binary Code (PBC) into Canonical Gray Code (CGC). According to its results, this method presented better PSNR value and high embedding capacity. Ahmaderaghi et al 12 proposed a blind image watermarking approachusing DST. The method is implemented the decision theory for blind extraction of watermark. For this reason, a Probability Density Function (PDF) is applied on the distribution of DST coefficients for different sub bands using Laplacian channel. Finally, maximum likelihood detection that depends on Laplacian model for DST coefficients is applied under the detection rules of Neyman-Pearson criterion for improving the robustness. The experimental results show that the proposed method achieves good imperceptibility, improved payload capacity and superior robustness. In 13 , Hemalatha et al presented a method of image steganography based on IWT. A cover RGB image is converted into YCbCr color system. Then, IWT is applied on Cb, Cr channels and the secret audio signal. Two bits of the secret audio signal are embedded at 2 nd and 3 rd bit planes of high frequency of the Cb and Cr coefficients. Based on its results, the proposed approach achieves good imperceptibility and robustness. Hamza 15 presented a method of image steganography using LSB. The secret logo is scrambled using Arnold's Cat Map and Blum Blum Shub. The cover image is divided into blocks and entropy of each block is calculated. The block of maximum entropy is selected to embed to one bit of the secret logo at 1 st LSB of the selected block. According to its experimental results, the proposed method achieves better imperceptibility and high security. Mostaghim and Boostani 16 proposed a method of image steganography using Discrete Wavelet Transform (DWT) and visual cryptography. A chaotic system is used to generate on secret share based on visual cryptography. Then, this secret share is XORed with a secret logo to generate a scrambled secret logo. A DWT is applied on a cover image and the scrambled secret logo is embedded at the low frequency coefficients of the cover image. Experimental results show that the suggested approach presents good imperceptibility and increases the security of the secret logo.

Shearlet Transform
Recently, shearlet is the most successful scheme for representing the multi-dimensional data such as (digital image) efficiently 17,18 . It is able to represent the anisotropic features sparsely through the optimal encoding for some classes of multivariate data 18 . Shearlet provides new tools for analysis and processing massive dimensional data, which are limited in Fourier and wavelet system. It achieved an efficient computation and a number of shearing directions are not restricted when compared with a contourlet. In addition, it differs from directional filter bank that supports shearing size without any constraint 19 . Therefore, using a window with small sized cannot lead to lose its performance.
The Shearlet Transform (ST) is used to handle the image anisotropic and directional features. In addition, it is able to capture the geometric information of edges effectively 1,18,19 . ST can be described as affine function that contains a single mother of shearlet function 12 . The shear parameter that captured the direction of the singularities such as (lines and curves) is calculated according to scaling, shear and translation parameters. A Laplacian pyramid and directional filtering are used to apply the shearlet transform 1,12 . For the cover image CI and mother function ∈ 2 (ℝ 2 ), ST of ∈ 2 (ℝ 2 ) is the mapping 18 scale (a > 0), s the orientation and t is the translation indices. Shearlets can be obtained using dilating, shearing and translating 12, 19 on the mother function ∈ 2 (ℝ 2 ). The dilation is defined as matrix: = ( 0 0 √ ) where ∈ ℝ + and shear is defined by a matrix = ( 1 0 1 ) where ∈ ℝ. DST can be constructed by an appropriate sampling a continuous shearlet transform on a set S. Therefore, different approaches of the discrete shearlet systems have been proposed aiming to form an orthonoml basis or ∈ 2 (ℝ 2 ) of a tight frame 18,19 . The mother function of DST is defined as: (1) A DST has been applied on a (blue layer) of the cover image (Lena) as shown in Fig.1. The blue layer only is transformed using DST because of this layer of the cover image will be used for secret share embedding process.

Visual Cryptography:
Visual cryptography is a method for encrypting the writing materials such as (handwritten notes or pictures) visually 20 . It maintains the secrecy of such data optimally. Naor and Shamir 20 are proposed (k, n) visual cryptography approach in 1994. An original image is split into (n) shares and any (k) shares that can be stacked together to reconstruct the original image 16 . A (2 out, 2 share) is the simplest method of visual cryptography that split the original binary image (black and white) into two secret shares. Each secret share is appeared completely as random pattern of the original binary image. The shares are given to each participant. Then to obtain the original image, the participants must stack the secret shares one above another one.
Visual cryptography achieves the confidentiality for the entire secret image by each secret share does not give any information about it and the original secret image is obtained only if the secret shares stack together. This method is divided into two processes: ciphering process and deciphering process. At ciphering process, a plain data such as binary-image is converted into a set of transparent images called shares. In deciphering process, these shares are stacked one above the other to generate the original binary-image. For this reason, the deciphering process is done using the human visual system and it does not need complex calculations 16,20,21 . To generate (2 out 2 share) for the secret-logo that used in embedding process. The following steps are applied on the secret-logo.  Pick each pixel of the secret-logo and compare a color of pixel according to the following condition:  If the color of pixel is white, then select randomly a pair of the white color probabilities form Table 1 and put a first probability at a secret share one and a second probability or (offset) in a secret share two.  If the color of pixel is black, then choose randomly a pair of the black color probabilities form Table 1 and place a first probability in a secret share one and a second probability in a secret share two.  The condition that mentioned above is repeated on the entire pixels of the secret-logo.  The result is two secret shares.  The proposed method is implemented the (2 out 2 share) scheme on the secret logo to generate two secret shares. A binary image of the secret logo with size (128x128) is spilt up into two secret shares; each one is randomly scrambled image of size (128x256). The width of each secret share will be resized to double during the process of generating it, because of the (2 out 2 share) scheme must put the probabilities for each color (white or black) according to the Table.1. The result of generating two secret shares for the secret logo shows in Fig.2.

Proposed Method
In this section of paper, the proposed approach of image steganographic is illustrated in details. The suggested method is divided into two main processes (embedding process and extraction process). During the embedding process, the cover image is partitioned into three layers (red, green, and blue). The blue layer is selected to embed the secret share one in it. The reason for choosing the blue layer because of Human Visual System (HVS) is less sensitive to modification at blue color. Also, the blue color achieves high value of PSNR for the proposed approach. Then, DST is applied on the blue layer to obtain its coefficients. The entire coefficients are used to embed the secret share one. The following formula is used to embed one bit of secret share at each coefficient: Where BC is the coefficient of blue layer, S1 is the bit of secret share one, 1≤ i ≤ 128, and 1≤ j ≤ 256.
For the cover image of size (512x512), the secret share one is embedded (8) times in its blue layer coefficients. The modified blue layer BC' is combined with red and green layers to obtain the stego image. The block diagram of embedding process is shown in the Fig.3. At the extraction process, the stego image and the riginal cover image are partitioned into three layers (red, green, and blue). The blue layer of each one are transformed using DST. Then, the formula that defined below is used to extract one bit of secret share one from each coefficient: Where BC is the coefficient of blue layer (original cover), BC' is the coefficient of blue layer (stego) and S1 is the bit of secret share one, 1≤ i ≤ 128, and 1≤ j ≤ 256. The secret share one can be extracted (8) times from the stego image of size (512x512). The extracted secret share one is XORed with a secret share two to obtain the original secret logo. Figure 4 shows the block diagram of extraction process.

Experimental Results
In this section, the proposed approach has been implemented by using MatlabR2019b that runs on Sony Vaio laptop, Intel Corei3-3227U CPU 1.9 GHz, 4 GB RAM, and Windows 10 Home 64-bit operating system, to evaluate its performance. Therefore, three programs have been written; the first program is used for secret share generating, the second program is applied for embedding process and the third program is employed for extraction process. The colored-images of size (512x512) are used as the cover images for testing and evaluating the suggested approach as shown in Fig.5. The secret logo is a binary image of size (128x128).
Apply Equation (2)   (4) Where CI is the cover image and SI is the stego image. M and N is the size of each image and 1≤ i ≤ M, and 1≤ j ≤ N. PSNR is used to compute the impact on the image quality between cover image and stego image. If PSNR value is high, that means the better image quality of stego image and vice versa. A decibel (dB.) is PSNR metric. The following formula is used to calculate the PSNR: PSNR = 10 * log 10 ( 255 2 (5) Structural similarity (SSIM) is used as a metric to measure the similarity between the cover image and the stego image. This measurement is developed to enhance the traditional measurements such as MSE and PSNR that have proven inconsistent for human eye perception 1 . Therefore, SSIM is more adaptable with nature of HVS 8 . The maximum value of SSIM is equal to 1 and it represents the identical between the cover image and the stego image.
( , ) = where x is the cover image and y is the stego image. are the mean of x and y, 2 2 are the variance of x and y. ( ) is the co-variance of x and y. 1 2 are two constants used for avoiding null denominator. The bpp can be calculated according to the following equation: = * (7) where the number of the embedded bits are represented the total size of the secret share one that is embedded in the cover image. The size of the cover image is (M=512 and N=512), that means the total size of it is equal to 512*512=262144 pixels. As mentioned before, the size of the secret share is (128x256) and the total bits is equal to 128*256= 32768 bits. During the embedding process, the secret share one will be embedded eight times in the blue layer coefficients and the total number of the embedded bits will become (32768*8=262144 bits). Consequently, each pixel of the blue layer will be hiding one bit of the secret share one. PSNR, SSIM and bpp after testing a performance of the proposed method are shown in Table 2. Another method for evaluating the proposed method can be done by comparing it with other methods that proposed in the related works. Table 3 shows the performance comparison between the suggested approach and another method that proposed by Sun and Guo 9 . Meanwhile, other methods that proposed in 1, 3, 4, 12 are the image watermarking. As mentioned early, image watermarking is different form image steganography in its essential requirement of robustness. The image steganography methods that proposed in 13   According to the results of Table.2 and Table.3, the proposed method is achieved high value of PSNR for all stego images and it has been preserved the imperceptibility. The SSIM values for all stego images are approximately equal to one. That means, there are higher similarity between the cover image and the stego image. The payload capacity is (262144) bits for the stego image of size (512x512) which the rate of embedding equal to (1 bpp). However, the payload capacity for Sun and Guo 9 method is (131,072) bits and the embedding rate equal to (0.5 bpp). Therefore, the proposed method has achieved best value of payload capacity. The secret logo is attained more secrecy using (2 out 2 share) visual cryptography. In addition, the secret logo is split up into two secret shares: one secret share is embedded in the stego image and the second secret share is used as private key during the extraction process. Without this private key, the original secret logo cannot be obtained correctly.
Statistical steganalysis is used to detect abnormal modification in the structural characteristics of the stego image. Histogram analysis is one of the most important criteria for the statistical steganalysis 16 . A histogram of the stego image is compared with a histogram of the cover image to identify the distribution of pixels or the unusual shapes that occurred due to embedding process. In order to evaluate the proposed approach against the histogram analysis, the histograms for each cover image and stego image are calculated as shown in Fig.6. According to the Fig.6, the histogram of each image cover and its stego image is uniformity and there are usual shapes among them.

Cover Image (Baboon) Stego Image (Baboon) Cover Image(Boats) Stego Image(Boats)
Cover Image (Tiffany) Stego Image (Tiffany) Cover Image(Peppers) Stego Image(Peppers) Figure 6. The histograms for each cover image and stego image

Conclusion:
In this study, a new method of image steganography has been proposed. the method is based on DST and secret sharing. According to the experimental results, the two main requirements of image steganography have been achieved: better imperceptibility and high embedding capacity. Based on histogram analysis, the histogram of each cover image and its stego image are in uniformity. Therefore, using DST instead of other transformations such as (wavelet, contourlet and discrete cosine) is the best for image steganography methods. Using (2 out 2 share) visual cryptography with one share as the private key is enhanced the security of secret logo. Because, if the attacker was able to extract the secret share one from the stego image, it could not obtain the original secret logo without the secret share two. Finally, the suggested approach is non-blind and it required the original cover image at the extraction process. Therefore, this limitation can be addressed for future works.