An image steganography using improved hyper-chaotic Henon map and fractal Tromino

ABSTRACT


INTRODUCTION
Technology has blitz scaled over the past years leading to wide usage of multimedia for transferring data, especially the internet of things (IoT) [1].However, today, numerous attackers and hackers can intercept communications using some strategies, therefore protecting transmissions is still required to ensure information security [2].Steganography is an important technology for secret information that can be disseminated across open networks [3].The purpose of image steganography is to incorporate secret data while preventing its existence in personal communication [4].The stego image is created by embedding the secret data in the carrier image, and one of the main goals of image steganography is to reduce the difference between the stego and carrier images [5].Image steganography successfully extracts personal information and achieves error-free recovery of the original image containing secret information [6], [7].Image steganography is primarily utilized to reconstruct the original image without distortion in medical, military, and other domains [8].Image steganography has advantages like maintaining secret information content [9] and hiding transmission with more security [10] and privacy [11].Steganography employs machine learning (ML) [12] and deep learning (DL) [13] approaches to increase hiding capacity, robustness, and security, that performed together in stego image to human vision [14], [15].Ahmad et al. [16] created an enhanced medical image steganography technique to hide patients' information in their medical images.However, the proposed techniques for integrating the system within the medical cover image may not guarantee to give a decent better image.Rahman et al. [17] implemented a least significant bit (LSB) substitution method to accomplish the consistency between the basic measures of steganography images.However, LSB contains an unacceptably large number of embedding messages, resulting in increased processing costs and poor image quality.Durafe et al. [18] designed a hybrid steganography scheme based on the fractal cover, integer wavelet transform (IWT), singular value decomposition (SVD) and discrete wavelet transform (DWT) approaches for hiding the data.However, the information will not be changed since changing the single value elements directly will affect the image's lighting.Lin et al. [19] created a steganography structure for neural style transmission by presenting the Y channel data to avoid steganographic attacks.However, the planned Y-channel still requires a big space for optimization.Liu et al. [20] created a mapping module to increase the quality of the steganography image and its antidetection capabilities.However, the mapping module has different networks for encoding and decoding, which caused resulted in color distortion and artefacts in stego images.After examining every accessible framework, it is clear that traditional approaches are less secure because it is merely a matter of determining whether the secret message is present or not.Since a statistical method was employed to embed the data, the hidden message may be simply recovered.The stego image must be sent to the receiving end across an untrusted channel in order to implement the trained model for carrying out steganography and steganalysis.Images produced by the trained model contains noise, skewing, and blurring.Consequently, it is yet undefined whether to implement the model for image steganography.In order to overcome the abovestated issue, the major contributions are given below.− The hyper-chaotic improved Henon map and fractal Tromino is developed to enhance the embedding capacity, computing efficiency and security.− The grey wolf optimizer (GWO) is used to choose the image pixels that would be utilized to integrate the hidden image in the cover image.− The least significant bit is used to locate the tempered region and to deliver self-recovery features in the digital image.
The overall organization of this study is given as follows: the process of the proposed method is described in section 2. Section explains the steps involved in improved Henon map.Section 4 describes the experimental results of the proposed and existing models.The conclusion of this research is given in section 5.

PROPOSED METHOD
Figure 1 depicts the workflow of the proposed image steganography, and comprehensive explanations of the suggested method are described below.In recent years, technology like video, audio, text, and image were low in complexity and cost-effective.Furthermore, the expediency of image processing implements data transfer, which was a relatively simple way to view and download digital images.An image steganography technique was presented in this study to increase data transmission security.Here, in this block, there are two stages are presented, (i.e.,) transmitter side and receiver side.Initially, the stego image is transferred to receiver side through the channel.Therefore, the stego image is mentioned twice in the block diagram.After passing through it, the same stego image is processed with lifting wavelet transform (LWT) for dividing the images into various sub-bands.Due to that divisions, the security level gets increased in that image.

Collection of images
Steganography involves two types of images in image collections: hidden images and cover images, which are utilized to get better accuracy.The cover image was used to insert the hidden image, to get a noiseless image and a suitable size.MATLAB is used to represent the hidden secret image to cover the image.

Fractal Tromino
The encrypted image is given to fractal Tromino to achieve the most fundamental characteristics of steganography between confusion and diffusion matrix [21].For confusion matrix, it has highly pre-defined and non-linear data to process [22].The dimension ×3 matrix of N was evaluated where ××3 is the dimension of the plain image.The length of 8-bits was utilized by producing two random keys 1 and 2.By using the following rule in (1), the matrix values are generated in step 1.
The range of  is curved in adjacent value, where  in ( 2) is the matrix generated in step 1 for mean value.
The updated matrix in stage 3 was redesigned ××3.This is the preferred fractal Tromino.The evaluated fractal has represented in the Figure 1.

IMPROVED HENON MAP
After fractal Tromino, the improved Henson map was also encrypted with a secret image and showed the most significant chaotic characteristics.However, the two-dimensional chaotic Henon map (2D-CHM) has some drawbacks like discontinuous chaotic intervals and simple chaotic characteristics [23].To overcome the above limitations, 2D-CHM to two-dimensional improved chaotic Henon map (2D-ICHM) was suggested and the mathematical expressions were shown in (3).Where  and  are control parameters.

Lifting wavelet transform
The input secret image is given to the LWT to disguise the image multi-scale analysis for signals and purposes by scaling operations.Hence, it is used for image compression and processing [24].Furthermore, the lifting wavelet transform constants are floating points and it is difficult to evaluate [25].As the basics of lifting wavelet transform, it can be separated into three stages: prediction, update, and splitting which are demonstrated below.a) Splitting: Normally, the unique signal S was decayed by the odd signal 2+1 and even signal 2.b) Prediction: The odd signal  2−1 , remains unchanged while the even signal is  2+1 was projected by interpolation subdivisions.The transformation between the actual and predicted value is   that has shown in (4), where P is represented as a prediction mechanism.c) Update: The update process is the data 2 with  to preserve some characteristics of the original signal S. Then keeping the average value unchanged, and the operations were described in (5).
where U is the prediction operator.

Wavelet sub-bands using grey wolf optimization
The lifting wavelet transform is given to the suggested method to choose the embedding process in the optimal block.The GWO [26] can be classified into three segments hunting, attacking prey and encircling [27].At the initial stage, GWO parameters were modified such as search agents Gs, variable size Gd, and the maximum number of iterations , and vectors were described in ( 6) and (7).
where, 1 and 2 was described as random vectors between the ranges [0,1].The generated arbitrarily of wolves based on the package was determined in (8).The initial range of the  ℎ pack of the  ℎ wolves can be represented by 1.The fitness value utilization of each value was calculated in ( 9) and (10).
The initial range of the  ℎ pack of the  ℎ wolves can be represented by   1 .
Based on the equations,  and ⃗ was act as coefficient vectors. act as the position vector of a grey wolf and  act as a position vector of the prey.Demonstrate the better hunt agents , Second and the third hunt agents  and  by utilizing ( 11)- (16).
,  and  values are updated.The possible outcomes can be taken by utilizing the best values ,  and .The ending values can be checked, whether the  reaches  or not, if else again go to step 5 or if yes, print the current best value.Hence, LSB [28] was utilized to hide the cover image after encryption.Then, LWT was smoothly embedded and used for processing the stego image for the cover image.The position was updated to the existing hunt agent by using (17).The fitness for hunt ranges was utilized in (18).

Decryption phase
The decryption phase was used to process the embedding secret image for cover image transformation, where the embedding process of LSB was utilized as integer unit values.The binary values are then converted to decimal points, LWT is applied to the output image, and the decimals are represented as stego images.Hence, the secret image was extracted without no loss of data, therefore, the retrained secret image has the original secret image.

RESULTS AND DISCUSSION
Here in this section, the experimental results of the proposed method were analyzed using MATLAB.For evaluating the system, the following system specifications was essential such as 8 GB RAM, 3 TB storage, and i9 3.0 GHZ processor.The suggested method performances were authenticated in terms of peak signal-to-noise ratio (PSNR), normalized cross correlation (NCC), structural similarity index (SSIM), entropy, mean average error (MAE), and mean square error (MSE) values.

Quantitative analysis for color image
The quantitative analysis is given to the color image, which was used for the image steganography process.Figures 2 and 3 show the color vision of the sample image 1 and sample image 2. In the Figures 2  and 3, the following images (i.e.,), Figures 2(a The quantitative analysis was used for statistical, mathematical, and measurement to understand the characteristics for performing in numerical values.Table 1 describes the features of suggested steganography for images.Furthermore, the performance evaluation was carried out in five conditions. Table 1 describes the performance analysis of color images for SSIM, PSNR, NCC, Entropy, and MSE.In the color image, butterfly as cover image and baboon as secret PSNR of 69.11 and 40.58,SSIM of 0.999 and 0.999, NCC of 0.985 and 0.972, Entropy of 6.532 and 6.51, and MSE of 0.134 and 0.064 respectively.For the histogram equalization, PSNR, SSIM, NCC, entropy, and MSE of 69.15 dB, 0.956, 0.925, 6.325, and 0.104 respectively in the cover image.Similarly, for the secret image, PSNR as 43.47 dB, SSIM as 0.978, NCC as 0.97, entropy as 6.285 and MSE as 0.134 respectively.The analysis of MAE for color image was illustrated in Tables 2. To prove the embedding capacity of the secret image, Table 3 shows the analysis of secret image (Baboon) with different sizes such as 16 × 16, 32 × 32, 64 × 64, 128 × 128 in terms of PSNR, SSIM, NCC, entropy and MSE.

Encryption quality
The analysis of encryption quality for color image was tabulated in Tables 4. After encryption, the pixels of cover image change have greater image pixels, and overall encryption quality ().As a result, the encryption quality can be expressed as the overall alteration of image pixels in both plain and ciphered images.It can be described as an average amount of changes to each grey level.Let  described the amount of pixels has  gray levels in the  ℎ plain image and  described the amount of ,  ,  pixels has  gray levels in the  ℎ encrypted image.Then, it gives the results as  = (0, 1, 2, 3, … 255) and  = (1, 2, 3) in the encryption efficiency of a color image can be explained in (19).

Quantitative analysis for greyscale image
The quantitative analysis given to the greyscale image was used for image steganography process.Figures 4 and 5 show the representation as greyscale images 1 and 2 respectively.From Figures 4 and 5, the following images such as Figures 4(a

Comparative analysis
Here, in this section, Table 6 illustrated the encryption quality analysis of greyscale images achieved Lena as cover image achieved 902.86 and Cameraman as secret image achieved 918.93 respectively.Further, the proposed method is analyzed with state-of-the-art methods (different encryption techniques) such as Henon map, logistic map and baker's map which is tabulated in Table 7. From the Table 7, it clearly shows that proposed method outperforms the state-of-the-art methods in terms of PSNR (40.98%),SSIM (0.97), NCC (0.97), entropy (5.87) and MSE (0.09).Followed by that, the comparative analysis of the existing and proposed work was described in Table 8.Subramanian et al. [1] designed deep learning techniques which achieved a PSRN value of 64.7% respectively.Rustad et al. [8] implemented a least significant bit which achieved a PSNR value of 57.45% and SSIM of 0.999 respectively.Ahmad et al. [16] suggested medical images to hide the patient's data which achieved 59.50% and SSIM of 0.939 which are shown in Table 8 respectively.From the Table 8, it clearly shows that proposed method outperforms the existing methods in terms of PSNR (70.58) and SSIM (0.999) respectively.When compared to the existing methods, the proposed technique is efficiently avoiding the loss of data and gained the least computational time.Additionally, classifying the optical data of multiple factors was a critical challenge in image steganography which is efficiently solved by the GWO.

CONCLUSION
In this research, a GWO and IWT were utilized for real-time applications that have highly secured data transmission of network structure in digital images.Additionally, a hyper-chaotic map was utilized to guarantee the integrity and privacy of information in the secret image.For inserting the secret information in the cover image, LSB was utilized to hide the secret image.After the process of the embedding system, a hyper-chaotic Henson map was used with the cover image to get the secret image.The suggested scheme evaluated the feature measures such as SSIM, PSNR, MSE, and NCC.As compared to the existing approaches, the proposed method performed better in terms of PSNR 70.58% Db and SSIM 0.999 respectively.In the future, a new optimization technique can be combined with an improved Henon map to improve the image steganography performance.

Table 1 .
Performance analysis for color image for SSIM, PSNR, NCC, MSE, entropy and MAE

Table 2 .
Analysis of MAE for color images

Table 3 .
Analysis of secret image with different sizes

Table 4 .
Analysis of encryption quality for color images

Table 5 .
Performance analysis of greyscale image for SSIM, PSNR, NCC, and MSE

Table 6 .
Encryption quality analysis of greyscale images

Table 7 .
Comparison with state-of-the-art methods

Table 8 .
PSNR and SSIM values for comparative analysis