Steganography in RGB Images Using Adjacent Mean

Steganography is the practice of hiding information or data in a seemingly innocuous cover medium, such as message, file, image, audio, and video. In the past decades, many approaches of steganography in images were proposed for various applications. In social communication and the information highly exposed society, steganography requires high embedding capacity to transmit secret data efficiently. Generally, there is a trade-off between fidelity and embedding capacity. In this paper, we propose a novel and efficient data hiding algorithm in 24-bit color images with super high embedding capacity and acceptable peak signal-to-noise ratio (PSNR) using spatial-domain-adjacent mean. In the proposed algorithm, the embedding rate is about 7.4 bits per pixel (bpp) when the PSNR is nearly 30, and the embedding rate is about 8.88 bpp when the PSNR is nearly 25. The advantage of the proposed method is no need to transform data in another domain and without training data. Experiments also demonstrate the imperceptibility under some state-of-art steganalysis. The proposed steganography provides an efficient way to transmit sensitive information in the information highly exposed society.


I. INTRODUCTION
Steganography is the technique of concealing secret data within a non-secret, ordinary, message or file in order to avoid detection. In an approach of data hiding in images, the sender hides the embedding data into a cover image to derive the stego image and sends the stego image to the receiver, and then the receiver extracts the embedding data from the stego image. The embedding data can be an encrypted file, message, image, audio, or video, which is encrypted by the sender and can be decrypted by the receiver. The fidelity of a data hiding scheme for images is usually measured by peak signal-to-noise ratio (PSNR) between the cover image and the stego image, and the embedding capability is usually measured by the payload and the embedding rate. Generally speaking, there is a trade-off between fidelity and embedding capability. In the past decades, various approaches of data hiding in images were proposed for various applications.
For general applications, the data hiding scheme requires the balance of fidelity and embedding capability. In 2013, directed adaptive LSB substitution method, and Setiadi et al. [11] proposed an image steganography algorithm based on DCT with one-time-pad (OTP) encryption. In 2018, Farhan and Alwan [12] proposed an improved method using a two exclusive-or to binary image in RGB color image steganography. In 2019, Tyagi [13] proposed steganography protected using Shamir's threshold scheme and permutation framework.
For medial and military applications, the data hiding scheme requires high fidelity of the stego image and the reversible property, which can recover the original cover image without any distortion from the stego image after the hidden embedding data have been extracted. Many reversible data hiding algorithms for images were proposed [14][15][16][17][18][19][20][21]. However, most of the reversible data hiding schemes have extremely low embedding capability. In this case, a lot of reversible data hiding algorithms [22][23][24][25][26][27][28][29][30][31][32][33] were proposed for encrypted images to increase the embedding capability; meanwhile, keeps high fidelity. However, embedding secret data in a meaningless image deviate from the essence of steganography. Transmitting a non-ordinary image may attract the notice. A clear overview and classification of Steganography was proposed in [34] and two types of methodology were listed as spatial and transform domain. The authors proposed a hybrid Steganography using pixel value difference and modulus function [35]. Another research works [36] proposed addition and subtraction logics on LSB planes. Also, the authors used LSB matching and pixel difference [37]. In [38], the authors improved [35] to the optimal version of that kind of methodology. Related work in [39][40][41] are proposed to use transform domain to achieve hiding data with integer wavelet transform. Transform domain based methods need more timeconsuming to processing data. Neural networking based methods are proposed recently [42][43][44][45][46][47], authors used long short-term memory in [42]; Deep learning is adopted in [43]; Generative Adversarial Nets (GAN) is used in [44,46]; Author used the source in ImageNet database with deep learning [45]. Machine learning based methods need pretraining dataset to use and also might suffer the quality of dataset.
In some undemocratic sociality or organizations, the speech and expression of the members are monitored and regulated by the supervisors. The supervisors have the authority to ask members to reveal the transmitted information even if it is encrypted. Steganography makes people securely transmit sensitive information without attracting any notice. Nowadays, numerous people are used to sharing large amounts of photos from their daily life on social networks through the popular social media and networking services such as facebook, twitter, and instagram. It is not obtrusive to share an ordinary photo, which the resolution is a little bit low. For this kind of application, the highest priority is the embedding capacity, and the cover image is needed not to be recovered. In this paper, we propose a data hiding algorithm in RGB images with super high embedding capacity and acceptable PSNR, which can embed a plenty of secret data in normal photos from daily life and share them unobtrusively. Moreover, the proposed data hiding algorithm is deniable that the sender can claim that the stego image is just a normal image.
The rest of the paper is organized as follows. Section II presents the proposed algorithm. The experiments and analyses of the proposed algorithm are discussed in Section III. Section IV shows the comparisons of the proposed algorithm and relevant schemes. We draw the conclusion in Section V.

II. METHODS AND FLOWS
Suppose that ED is an arbitrary embedding data, and E=e 1 e 2 e 3 … e L is a binary string with length L bits, which is converted from ED. Let C be an 8-bit RGB color cover image with height p pixels and width q pixels. Let C pq be a pq matrix that represents C, where each element c p,q =(rc p,q , gc p,q , bc p,q ) denotes the pixel RGB values. Let N be the length of the embedding binary sub-string in each embedding position. Then we can embed the binary string E to the cover image to produce the stego image S by the following steps.
Step 1. Let S pq be a pq matrix that represents the stego image S, where each element s p,q =(rs p,q , gs p,q , bs p,q ) denotes the pixel RGB values. Let the element s i,j be the embedding position, if i and j are both odd or both even and s i,j is not an edge element; i.e. (i+j) is even, (ij)1, ip, and jq. Let the element s i,j =c i,j if s i,j is not the embedding position.

III. EXPERIMENTS AND ANALYSES
In this section, we simulate the embedding procedure on nine cover images by using Python 3.7, where the embedding binary data is randomly generated. We evaluate the proposed algorithm by embedding rate (ER) and peak signal-to-noise ratio (PSNR), which are defined as follows. It is shown that though the proposed method only performs better than [3], it is no bottleneck to embed more bit while other proposed researches can embed no more than 6 bpp.
The experimental results are shown in Table 4 and Figure  6. Generally, PSNR is said to be barely acceptable when it is greater than 20 dB, and is good when it is greater than 30 dB. In the proposed algorithm for the tested images, the ER achieves 7.4 bpp when the PSNR is nearly 30 dB, the ER achieves 8.8 bpp when the PSNR is nearly 25 dB, and the ER achieves 10.3 bpp when the PSNR is nearly 20 dB. This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation as well as the experimental conclusions that can be drawn. Table 5 lists the comparisons of the proposed and related work. the embedding rate is more than 7.4 bits per pixel (bpp) when the PSNR is nearly 30, and the embedding rate is more than 8.87 bpp when the PSNR is nearly 25. The proposed steganography is efficient because the operation is under the time series domain. The result also demonstrates the proposed steganography is practical under an acceptable distortion after the secrets embedding to generate a stegoimage. Compare to some related work, some of other works lost information [1][2][3][7][8] and some of works are based on transform domain [4,7], which means un-efficiency. From other time domain steganography, though the proposed scheme obtains higher distortion, the capacity is larger than other works.   Table 6 is the structure similarity index measure (SSIM) of the results corresponding to Table 4 and it shows the proposed method is well-performed under this steganalysis (all the return values are near 1). Table 7 and Table 8 are the result of Correlation and Intersection method, obviously, the proposed method obtains the same values under Intersection and still well-performed under Correlation which all values are near 1. Table 9 and Table 10 are the Chi-Square and Bhattacharyya, all the values grow according to the number of embedded secrets. Figure 7 to 10 is the visualization of the Correlation, Intersection, Chi-Square and Bhattacharyya steganalysis. The base is the cover image and result1 to result 7 is the stego-images from N=1 to 7. All the curves point out the statistical measure perform sharply bad since N=6. Table 11 illustrates the LSB enhancement of the stego-images, the results show the steganalysis does not work on the proposed method, duckling and Lena perform well when embedded secrets increase. Table 12 is the image processing attacks for evaluations. Rotation, scaling, cutting pieces and cropping are adopted. Table 13 demonstrates that the proposed method is robust under rotation, scaling and cutting pieces but not resistant under cropping. More cropping percentage makes more data disappear.

V. CONCLUSION AND FUTURE WORKS
In this paper, a time-series steganography is proposed using adjacent mean to embed secrets in a cover image. The operation is efficient because it is under time domain computation and the distortion is acceptable while the bits per pixel is 7.4 and comes with the PSNR 31.26; the bit per pixel is 8.88 and comes with the PSNR 25.77. The proposed method is well-performed under SSIM, Correlation, Intersection and LSB enhancement. More different images will be used to test the performance in the future. for the test images.