Open Access

ARTICLE

# A New Generative Mathematical Model for Coverless Steganography System Based on Image Generation

1 Department of Computer Science, Faculty of Science, Minia University, Minia, Egypt

2 Department of Computer Science, Faculty of Computers and Artificial Intelligence, Damietta University, New Damietta, Egypt

3 Department of ICT Convergence, Soonchunhyang University, Asan, 31538, Korea

4 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

5 Department of Computational Mathematics, Science, and Engineering (CMSE), Michigan State University, East Lansing, 48824, MI, USA

* Corresponding Author: Yunyoung Nam. Email:

*Computers, Materials & Continua* **2023**, *74*(3), 5087-5103. https://doi.org/10.32604/cmc.2023.035364

**Received** 18 August 2022; **Accepted** 03 October 2022; **Issue published** 28 December 2022

## Abstract

The ability of any steganography system to correctly retrieve the secret message is the primary criterion for measuring its efficiency. Recently, researchers have tried to generate a new natural image driven from only the secret message bits rather than using a cover to embed the secret message within it; this is called the stego image. This paper proposes a new secured coverless steganography system using a generative mathematical model based on semi Quick Response (QR) code and maze game image generation. This system consists of two components. The first component contains two processes, encryption process, and hiding process. The encryption process encrypts secret message bits in the form of a semi-QR code image whereas the hiding process conceals the pregenerated semi-QR code in the generated maze game image. On the other hand, the second component contains two processes, extraction and decryption, which are responsible for extracting the semi-QR code from the maze game image and then retrieving the original secret message from the extracted semi-QR code image, respectively. The results were obtained using the bit error rate (BER) metric. These results confirmed that the system achieved high hiding capacity, good performance, and a high level of robustness against attackers compared with other coverless steganography methods.## Keywords

In the computer and internet era, securing transmitted data is considered a necessary process. Therefore, an effectiveness system must be an alternative for solving this need [1]. Securing the transmission communication channels against any attackers is an important conventional operation [2]. Many methodologies like steganography are used to secure data [3]. The smarter the generated steganography system, the higher its robustness level.

Steganography is a technique used to hide a piece of information in any other type without changing the second information to appear as an original one [4]. Some researchers define steganography as “hiding in plain sight” because the sent message is secretly out in the open for all to see. Some forms of steganography are even done unnoticed from the sender to the message recipient [5].

Generally, steganography consists of two components. The first is called embedding which is responsible for concealing the secret message within a cover file. The second component is called extraction which retrieves the secret message from the sent stego file, the cover file [6].

In 2013, a group of researchers proposed hiding data without using a cover file. This method is called coverless steganography. Coverless steganography can execute by a cover generation using the secret message bits themselves. This generated cover implies the secret message which may be an image, video, audio, or text file. The other form of coverless steganography involves building an image database consisting a number of natural images, which are then divided into subblocks. Finally, the secret message bits are compared for matching with these image subblocks [6].

Tan et al. [7] used motion analysis of videos to develop a coverless steganography technique. Robust histograms of oriented optical flow (RHOOF) were generated for all videos found in the database which was then indexed. These indices and RHOOF hash sequences are transmitted to the message recipient as a mapping. The RHOOF hash sequences were computed from the sent video which helped in retrieving the secret message. All of the videos used as a cover did not lose any of their respective contents during the transmitting and receiving processes.

Saad et al. [8] generated a jigsaw puzzle image with the aid of the cover image to build a new coverless image steganography technique. This approach uses a natural image as a cover image, then splits it into similar subblocks row by row then column by column. The zeros and ones of the secret message bitstream were represented by blanks and tabs for each puzzle piece, respectively. The created jigsaw puzzle image is received as a stego image wherein the recipient has the ability to retrieve the message from the stego using the secret message retrieval algorithm.

The main contribution of this paper is to design a new generative mathematical model for a coverless image steganography system based on semi-QR code images and maze game image generation driven by secret messages. The generated system is able to secure data through any digital communication channel without exposure to attackers during the transmission process.

The paper is arranged as follows: Section 2 details the proposed method. Section 3 introduces the performance evaluation metric. Section 4 discusses the experimental results. Finally, Section 5 summarizes the conclusion.

The proposed system seeks to build a robust system that can securely hide a huge amount of data before transmitting these to the receiver. The system consists of two components: (1) encryption and hiding, and (2) extraction and decryption. Each of the respective sender and receiver terminals has one component. At the first terminal, the secret message bits are encrypted in the form of a semi-QR code image. Then, this encrypted image is converted into the maze game image through hiding process. At the second terminal, the QR code image is extracted from the maze game image during the extraction process. Finally, the secret message bits are retrieved by decrypting the extracted QR code. The structure of the proposed system is illustrated in Fig. 1.

In 1994, the Japanese automotive company, Denso Wave, [9,10] developed the Quick Response (QR) code which is a type of two-dimensional matrix barcode [11,12]. While a barcode is a machine-readable optical label that stores data about an item, a QR code can attach to any data type. In practice, QR codes often contain data such as a tracker, an identifier, or a location that points to a website, an application, or information for a map, respectively. A QR code uses many standardized encoding modes (i.e., numeric, alphanumeric, and byte/binary) to efficiently store data [13]. Recently, QR codes have been used in many industries for their valuable properties such as fast readability and high storage capacity. Other QR code applications include product tracking, item identification, time tracking, document management, and general marketing [14].

The architecture of QR codes consists of black squares arranged together in a square grid on a white background. These squares can be read by any QR reader such as a mobile camera or a scanner. Reed–Solomon error correction is used to proceed with the image interpretation process. Finally, the required data are then extracted from patterns that are present in both the horizontal and vertical components of the image [14].

This component is used at the sender terminal. It consists of two processes: encryption and hiding. During the encryption process, the secret message is transformed into the semi-QR code image. Meanwhile, in the hiding process, the generated semi-QR code is inserted as an input hidden data in the form of a maze game image. These two processes are illustrated in Fig. 1.

This process plays a vital role in the system by encrypting the secret message into a semi-QR code image. The encryption process presented in Algorithm 1 is as follows: (1) the secret message is inserted into the system and translated into binary (i.e., zeros and ones); (2) a binary image of size 300 × 300 pixels is created and set its pixels to white ones; (3) the QR code is generated using the secret message bits (i.e., if the current secret message bit is zero, set the image pixel to black; else, let it remain white) which is repeated sequentially until all bits of the secret message are represented; (4) the created binary image is fully used except for the regions of the four finder patterns as shown in Fig. 2; (5) finally, the pixel size (PS) and the size of the four finder patterns (FP) are determined from Eqs. (1) and (2), respectively.

where W is the width of the binary image in pixels and L is the length of the secret message in bits.

where PS is a matrix of size PS*PS and its value is calculated as shown above in Eq. (1).

If the real length of the secret message is less than any length mentioned in Eq. (1), then fake bits are added to complete the final length which is represented in QR code. Also, a terminator is used to separate the real bits and fake bits. The final represented bits (FRB) are calculated as follows:

where RB is the real bit of the secret message, T is a terminator of value “11111111” which is considered an indicator for the end of the real bits, and FB is the fake bit with random binary bitstreams. Fig. 3 illustrates a sample semi-QR code generated by the system with different data lengths and pixel sizes.

In this process, the semi-QR code is transformed into the maze game image. The following mathematical model explains and describes the equations used in the hiding process. These equations determine the number of rows and columns used for generating the maze game image (MSR model).

The mathematical model for calculating R and C of the maze game image (MSR Model).

Maze = {String S}; L = length (S).

Step 1: According to the length of the semi-QR code image, calculate R and C which refer to the number of rows and columns of the maze, respectively.

Step 2: Assume that the generated maze initially consists of a grid with R rows and C = R + 1 columns, for example R = 2 and C = 3, as shown in Fig. 4, as follows:

Note that each row and each column contain a set of vertical and horizontal walls, respectively. Where the green arrow is the entrance of the maze and the red is the exit.

Step 3: The maximum number of interior vertical walls, V = R * (C – 1) = 2 * 2 = 4 walls and the maximum number of interior horizontal walls, H = (R – 1) * C = 1 * 3 = 3 walls.

Step 4: The total number of walls should be greater than or equal to the length of the binary bits, L, V + H ≥ L, this condition should be validated to ensure that the maze can contain all binary bits.

Step 5: Substitute for the values of V and H from step 3 to obtain the final value of R and C.

Substitute for C = R + 1 as written in the assumption in step 2 to obtain.

Division by 2 and return the square root to obtain.

By determining the value of R and C using the MSR model, the maze game image is easy to generate. The hiding process is responsible for transforming the generated semi-QR code image into the maze game image. Algorithm 2 explains hiding the semi-QR code image in the form of a maze game image when the semi-QR code image is inserted as an input: (1) the binary bits which represent the secret message are obtained; (2) after calculating the values of R and C using the previous mathematical model, the MSR model, a grid of size R × C is created; (3) then the binary bits are fed to the grid by scanning it row by row according to the bit value wherein if the bit value equals zero, then remove the current wall, else, let the existence of the current wall remain; (4) the remaining binary bits are represented in the grid column by column; (5) finally, the final form of the grid represents the output maze game image. This image is considered to be the stego image sent to the receiver.

The receiver terminal uses the second component to retrieve the secret message from the maze game image delivered from the sender. Retrieving the secret message is performed through two processes: extraction and decryption. The extraction process is responsible for extracting the semi-QR code from the maze game image. In the decryption process, the secret message is retrieved from the extracted semi-QR code image.

In this process, the semi-QR code image is reobtained from the maze game image. Algorithm 3 describes the steps of semi-QR code reconstruction when the binary bits are obtained from the maze game image: (1) the maze image is scanned row by row to detect all interior vertical walls where each absent wall represents the bit zero and each existing wall represents the bit one; (2) all recovered bits retrieved from the previous scanning are collected together; (3) the maze image is rescanned column by column to detect all interior horizontal walls where the bits are collected as with the previous steps; (4) finally, all collected bits are concatenated, and are used to generate the semi-QR code image which is the input for the decryption process.

This process is the final process in the system which is responsible for retrieving the secret message from the semi-QR code image obtained from the extraction process. The decryption algorithm in Algorithm 4 works as follows: (1) the system scans the inserted binary semi-QR code image to determine the size of the FP; (2) calculate the PS to locate the pixel’s representation region; (3) check each pixel if its value is zero and return the bit 0, otherwise, return the bit 1; (4) repeat previous step for all pixels, collapse each 8 bit together and translate them into char; (5) finally, concatenate these chars and return the secret message.

3 Performance Evaluation Metric

To evaluate the performance of the coverless steganography system, with different lengths of the secret message, the BER measurement has been used. BER measures the ability of the system to retrieve the secret message successfully. It applies the XOR operation between the secret message bits and the retrieved bits to calculate the similarity ratio in bits. BER [15] is given by the following:

where e is the number of invalid retrieved bits, n is the length of the original secret message, p is the original bitstreams, and q is the retrieved bitstreams. If the value of e equals zero, this means there are no errors (i.e., the original secret message and the retrieved message are identical) and the system escaped from any attack thereby achieving 100% in the robustness ratio. Else, if the value of e is greater than zero, this means that the bits have been altered or lost through the retrieval process and the system is not 100% robust against this attack.

4 Experimental Results and Comparisons

This section describes the experiments that have been conducted to study the performance of the proposed coverless steganography system compared with other systems and to check the ability of the system to represent a maximum amount of data in a secure form. MATLAB was used for conducting the results [3,16,17].

4.1 Designed Coverless Steganography System

The proposed system consists of two components wherein each component contains two processes. Fig. 5 shows the interfaces of the two processes of the first component, encryption and hiding, for the system. The two processes of the second component, extraction and decryption, are illustrated with the interfaces in Fig. 6.

One of the primary goals of the proposed system is to improve hiding capacity. The hiding capacity is considered an important measurement to evaluate the efficiency of any steganography system. This refers to the amount of data that the system can hide successfully [18]. Table 1 compares the hiding capacity of the proposed system with other systems.

The comparison confirmed that the hiding capacity of the proposed system is the largest among the capacities of the other coverless steganography systems which is 3432 bits. More hiding capacity can be obtained from the system which is up to 22328 bits.

Table 2 shows the number of generated images required to hide different sizes of data. The proposed system uses the smallest number of images compared with other systems which is 2.3 images for hiding 1 kilobyte of data.

Robustness can be defined as the ability of a system to resist toward different attacks. This can be measured by evaluating the status of the retrieved message, if retrieved 100% correctly or not. The system was tested, evaluated, and validated through the experimental results driven by different attacks such as image scaling, adding noise, and jpeg compression. Robustness can be measured with the success rate metric (SR) which determines how many bits are retrieved correctly with no errors. SR is calculated based on the BER value defined in Eq. (4), and is defined as the following:

The closer the SR value to 100%, the higher the robust level of the system and vice versa. If the value of SR equals to 100% this means that the retrieved message is fully retrieved with no modified or lost bits during the retrieval process. Contrarily, if SR < 100% this is an indication that there are altered bits changed by the attackers.

Image scaling (in/out) is considered an effective parameter as an attack due to its ability to modify and destroy the secret message bits [28] during retrieval through the transmission channel. SR values are calculated at different image scaling ratios from 0.3 to 10 as shown in Table 3.

The results confirmed that the system achieved a 100% SR for all scaling ratios, except at ratio 0.3, which means that the system retrieves the secret message correctly with no altered or damaged bits. At scaling ratio 0.3, the system fails to retrieve the secret data in a fully correct form.

4.3.2 JPEG Image Compression Attack

Almost all transmission communication channels, such as Facebook, WhatsApp, and Yahoo compress sent images [29]. This compression may effect on the transmitted images and damage the data in which this image represents. Jpeg compression is performed at different image qualities, 90%, 80%, 70%, 60%, and 50%, as shown in Table 4, which compares the SR value of the proposed system with the other systems. The format of the original image file was .PNG and its size was 150 KB. The compressed image file sizes were 95, 80, 55, 33, and 20 KB, corresponding to the image qualities mentioned above.

This comparison showed that the system achieved 100% as a SR for all image qualities, this means that the system has not been affected by the JPEG compression attack.

Adding noise to any image affects its quality and may corrupt the data that the image represents due to this attack alters the values of a random set of the image pixels. For example, if the image type is a binary image, then adding noise inverses the pixel value (i.e., a black pixel is flipped into a white pixel and vice versa). The number of changed pixels is determined according to the noise density, which represents a portion of the image size that the noise is added. These black/white dots can be easily detected by human eyes. The system robustness is evaluated by applying a “salt and pepper” noise attack [30] at different densities varying from 0.01 to 0.09, see Table 5.

As shown in Table 5, the results showed that the proposed system is the best one among all compared systems. All SR values were 100% which mean that the retrieved message is matched to the original secret message with zero BER value. Salt and pepper noise attack, using different densities, does not penetrate the system to achieve 100% robustness.

This section studies the strength of the system by applying many different attacks such as communication channel attacks [31] during sending and receiving messages, image format conversion, and color space conversion. Table 6 shows the SR values for all these attacks.

As shown in Table 6, the system resists all attacks with 100% SR. This is an indication that the system can protect the retrieved message without no damaged or lost bits.

This paper presented two algorithms for hiding and extracting secret messages. Building any coverless steganography system faces challenges in hiding capacity limitation and the robustness resisting level. Therefore, a new efficient and effective coverless steganography system based on a generative mathematical model and the creation of semi-QR code and maze game images has been designed. The novelty of this system is to generate the Stego image from only the secret message without using any assistant factors. The proposed system works as follows: at the sender terminal, the secret message is fed to the system generating an encrypted semi-QR code image using the encryption algorithm, where the image is inserted as an input to the hiding algorithm to obtain the maze game image which is considered to be the stego image sent to the receiver. On the other hand, the receiver inserts the received maze game image into the extraction algorithm to reobtain the semi-QR code image then the secret message is retrieved from that image using the decryption algorithm.

To evaluate the effectiveness of this system, results have been carried out using two different evaluation measures, namely the bit error rate and SR. When using either the proposed hiding or extraction algorithms, the experimental results showed that the proposed system achieved satisfactory results conclusion, 3432 bits, and 2.3 images were the hiding capacity and the number of images required to hide different sizes of data, respectively. Also, the proposed system can hide and retrieve up to 22328 bits successfully.

In addition, a comparison has been made between the proposed coverless steganography system and other systems using the BER and SR measures. This comparison showed that the two proposed algorithms gave better success rates than the others, with lower BER values; and higher SR, as introduced in Tables 1–5. This indicates that the proposed coverless steganography system has solved almost all problems in other traditional steganography systems.

Finally, in future work, more OSNs [32–35] can be used as communication channels used for transmitting the secret message. Also, image retrieval [36,37] can play a vital role in generating the new natural images used as Stego images for coverless steganography. Different data types, such as text audio, and videos [38–55], may be used for generating many robust coverless steganography systems.

Funding Statement: This work was supported by the Korea Technology and Information Promotion Agency (TIPA) for SMEs grant funded by the Korea government (Ministry of SMEs and Startups) (No.S3271954), and the National Research Foundation of Korea (NRF) grant funded by the korea government (MSIT) (No. 2022H1D8A3038040), and the Soonchunhyang University Research Fund.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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## Cite This Article

A. Seddik, M. Salah, G. Behery, A. El-harby, A. I. Ebada*et al.*, "A new generative mathematical model for coverless steganography system based on image generation,"

*Computers, Materials & Continua*, vol. 74, no.3, pp. 5087–5103, 2023.