Chapter 8

219

CHAPTER 8

REVERSIBLE IMAGE STEGANOGRAPHY BASED ON WAVELETS AND WAVELET-LIKE-TRANSFORM

So far we have focussed on evaluating the performance of algorithms of irreversible image steganography in the ECCs domain and Transform domain for the grayscale and color images. In this Chapter we shall cover the two type of reversible image steganographic algorithms using the Companding technique (also called Reversible Thresholding Method) based on SLT- Perceptual and Robust. We shall also give the comparative study of proposed algorithms with the corresponding modified wavelet based thresholding technique. 8.1. INTRODUCTION The reversible data hiding (RDH) technique enables cover image to be restored to their original form without any distortion after removing the hidden data from the stego-image. This technique is useful in many fields such as law enforcement, medical imagery, astronomical research, content authentication of multimedia data and so on.

A number of RDH techniques have been proposed. Awrangjeb (2003) classifies them into the following six types, viz., Lossless compression and encryption of Bit- planes, Reversible data hiding at Low Pixel-levels, Circular interpretation of Bijective Transformations based on integer Wavelet transform, High capacity based on difference expansion and RDH by histogram shifting. Yang et al (2010) divided the various RDH methods into four categories viz., Data Compression, Difference Expansion, Histogram Shifting and Integer Wavelet Transform. According to X. Zhang (2013), they can be classified into three types, viz., Lossless compression based methods, Difference expansion (DE) and Histogram modification (HM) methods. Yang and Lin (2012) discusses two kinds of RDH schemes which are

• Perceptual quality schemes that provides a perceived high quality in stego-images with a high embedding rate and

• Robustness-oriented schemes which are robust to image processing operations.

Chapter 8

220

In this Chapter, we propose both these schemes based on Slantlet and Complex Wavelet transforms in conjunction with AES. 8.1.1. Review of RDH schemes In this section we briefly summarize the different approaches proposed for RDH. RDH for fragile authentication Honsinger et al (2001) presented the lossless data hiding technique for fragile authentication that does not need much data to be embedded in a cover object. They used modulo-256 addition to embed the hash value of the original image for authentication, but their algorithm couldn’t resist salt-n-pepper noise due to the many wrapped around pixel intensities. Vleeschouwer et al (2003) proposed an improvement over the Honsinger algorithm by circular interpretation of the bijective transformations of the image histograms that reduces salt-n-pepper visual artifacts. This algorithm is a Patchwork histogram rotation, where each bit of message is associated with a group of pixels. Each group of pixels is divided into two-pseudo random sets of pixel – zones i.e. A and B. Since zones A and B are pseudo – randomly generated, they have almost equal average values before embedding. After embedding, depending on the bit to embed, their luminance values are incremented or decremented. The extracted bit is inferred from the comparison between the mean values of zone A and B. Lossless compression technique Fridirch et al. (2002) proposed the joint bi-level image experts group (JBIG) lossless compression technique that compresses a set of selected features from a image to save space for data embedding. Lowest bitplane offering lossless compression can be used unless the image is not noisy. In his scheme, payload is highly dependent on the lossless compression technique. Celik et al (2002) proposed a reversible data hiding technique that uses prediction based conditional entropy coder utilizing static portions of the input signal as side – information to improve the compression efficiency. This spatial domain method is a modification of Least Significant Bit embedding techniques, by using higher order bits. They also proposed a reversible data hiding method based on the idea

Chapter 8

221

of first compressing portion of the signal that are susceptible to embedding distortion and then transmitting it as part of embedded payload. Further in 2005, they improved Fridrich’s technique and proposed the generalized-LSB scheme by compressing the quantization residuals of pixels to yield additional space to embed a message. Integer wavelet transform technique

Xuan et al (2002-2005) proposed a lossless data hiding method based on IWT, which embeds high capacity data into the least significant bit-planes of high frequency wavelet coefficients whose magnitudes are smaller than a certain predefined threshold. Histogram modification is applied as a pre-processing to prevent overflow/underflow. Luo and Yin (2011) have presented a new RDH scheme that utilizes the wavelet transform and better exploits the large wavelet coefficient variance to achieve high capacity and imperceptible embedding. Yang and Lin (2012) have proposed a RDH method that uses the coefficient shifting (CS) algorithm with a mean predictor. Further, they present a robust RDH method using a variant of the CS algorithm that is based on the IWT domain to resist common image processing operations. Yang, Lin and Hu (2012) have further presented a simple RDH scheme based on the IWT. By adjusting the coefficient values, data bits are effectively embedded into the low-high (LH) and high-low (HL) subbands of the IWT domain. Their experiments show that both the host media and secret message can be completely recovered, without distortion, if the stego-images remain intact. Moreover, the resulting perceived quality of the image is highly satisfactory, as is the hiding capacity. Difference expansion technique Tian (2003) proposed a high capacity RDH technique that expands the difference between two neighboring pixels to obtain redundant space for embedding a message. However, his scheme suffers from the location map problem that it is difficult to achieve capacity control. His algorithm was improved by Alattar (2004) who used the DE of vectors of adjacent pixels to obtain additional space for embedding. There have been many techniques developed thereafter to increase the payload and minimizing the distortion which can be referred to Chang and Lu, (2006), Weng et al.’s (2007-2008),

Chapter 8

222

Thodi and Rodriguez (2007), Lin and Hsueh, (2008), Lou, Hu and Liu, (2009). Zhang (2013) has proposed a RDH with optimal value Transfer. In his scheme, the optimal rule of value modification under a payload-distortion criterion is found by using an iterative procedure and the secret data as well as the auxiliary information used for content recovery, are carried by the differences between the original pixel-values and the corresponding values estimated from the neighbors. The estimation errors are modified according to the optimal value transfer rule and the original host content can be perfectly restored after extraction of the hidden data on receiver side. Histogram shifting technique Ni et al. (2006) proposed a RDH scheme that uses the histogram of the pixel values in the cover image to embed secret data into the maximum frequency pixels. However, their payload is quite limited because few images contain a large number of pixels with maximum frequency. Further, their scheme may lead to significant overhead and insufficient visual quality. Chang et al. (2008) suggested the pixel difference instead of simple pixel value for obtaining the higher peak point to embed a large amount of message. Zeng and Li (2009) improved this algorithm using adjacent pixel difference based on scan path and multi-layer embedding to increase the embedding payload. Yu and Wang (2009) proposed an extended subsampling reversible data hiding method, which shifts the histogram of the differences between sub-images obtained through subsampling and embed data by modifying the pixel value according to embedding level. Yang, Hwang and Chou (2010) proposed a RDH based on the interleaving max-min difference histogram. Their experimental results reveal that their algorithm can offer higher embedding capacity. Zeng, L and Ping (2012) have proposed a lossless data hiding scheme based on the pixel difference histogram shifting to spare space for data hiding. Pixel differences are generated between a reference pixel and its neighbors on a pre-assigned block. They claim that the algorithm has very high embedding capacity and low image degradation.

Chapter 8

223

Dynamic reference pixel method Xian-ting Zeng et al. (2012) have proposed a lossless data hiding scheme by using dynamic reference pixel and multi-layer embedding. According to authors, their algorithm offers very high embedding capacity and low image degradation. Companding technique A reversible (lossless) steganographic algorithm based on thresholding technique proposed by Xuan G. et al. (2002, 2011). As discussed in Chapter 1, in the thresholding embedding, a threshold value T is predefined. To embed data into a high frequency coefficient x, the absolute value of the coefficient is compared with T. If |x| < T, the coefficient value is doubled and the new LSB is replaced with an information bit. Equivalently, the binary representation of the coefficient value is shifted towards left by one bit and the to-be-embedded bit is appended as the right-most bit. The resultant coefficient is denoted by x΄. Otherwise, if x ≤ T, the coefficient will be added by T, if x ≥ -T, the coefficient will be subtracted by (T-1) and no bit is embedded into this coefficient. In the data extraction stage, if the coefficient x is less than 2T and larger than (-2T+1), the LSB of this coefficient is the bit embedded into this coefficient. Otherwise, we jump to the next coefficient since the current coefficient has no hidden bit in it. Besides hidden data extraction, the original cover image is also recovered.

The proposed algorithms presented in this Chapter are of two schemes: Perceptual quality and Robust-oriented, in the frequency domain of different wavelet and wavelet-like transforms. To achieve better perceptual quality and embedding capacity, self-synchronizing variable length codes, T-codes are applied to original message, resulting into the secret compressed binary data. For achieving robustness against common statistical attacks and common carrier attacks, AES are used at the pre-processing stage of embedding process.

In the next Section 8.2, we present a reversible steganographic algorithm based on two different Wavelet transforms. These are perceptual quality schemes. The Haar transform and CDF9/7 wavelet transform (adopted by JPEG2000 for image lossless compression), are used to obtain the wavelet coefficients, because the data embedded

Chapter 8

224

into the high frequency sub-bands, HL, LH and HH, have less visible artefacts to human eyes. In order to prevent the overflow and underflow, usulally histogram modification is applied to narrow down the histogram from both sides. This problem is also solved by mapping the grayscale values ≤ 15 to the value of 15 and the grayscale values ≥ 240 to the value 240. Further, different embedding rules apply to high frequency wavelet coefficients according to the absolute value of the coefficient is smaller than T, equal to T, or larger than T. In Section 8.3, we discuss perceptual quality scheme of the reversible steganography based on the Wavelet-like transform, which provides better compression and time localization than DWT. In Section 8.4, we present a robust reversible image steganographic algorithm based on SLT. We extend the Algo 8.3.1 by using AES technique at the pre-processing stage after the T-codes applications to original image.T-codes are used to obtain compressed message and AES applied afterwards provide it security and robustness. It is observed that by this approach the proposed steganographic scheme becomes robust and secure against statistical attacks in addition to fulfilling the basic requirements of image steganography. 8.2. PERCEPTUAL RDH USING WAVELET TRANSFORMS In Chapter 3 it has been shown that Haar transform are a better option than the other wavelets for the data hiding schemes such as modified LSB, Variable mode LSB and Fusion scheme. In this subsection we apply HDWT and CDF9/7 wavelet for the reversible thresholding scheme to find which wavelet is more suitable? 8.2.1. Proposed algorithm The proposed embedding and extraction algorithms based on DWT are as follows: Algo 8.2.1: Embedding ……………………………………….. Input: Cover Image, I, message, M, random-key,k Output: Stego-image, I’, encoding-key, K

Chapter 8

225

Step 1: Obtain the secret message by encoding the message, M with T-encoding. This also generates an encoding-key, K.

Step 2: Read the cover image, I, into a two dimensional decimal array to handle the file data more easily.

Step 3: Do the histogram modification to prevent overflow/underflow that occurs when the changed values.

Step 4: Apply the 2D Haar wavelet transform to the cover image resulting into 4- subbands LL, LH, HL and HH.

Step 5: Calculate hiding capacity (number of bits to be used in hiding message bits) of each coefficient of middle and high sub-bands, using the appropriate threshold, T, to enhance the stego-image quality (usually T= 35).

Step6. The frequency coefficients of middle and high sub-bands, HH, HL and LH obtained through CDF9/7 are converted into integer values using threshold T=0.9.

Step7. Permute the coefficients of sub-bands, HL, LH and HH randomly using a random-key, k and obtain new sub-bands LH’, HL’ and HH’.

Step 8: Embed the secret message into the corresponding randomly chosen coefficients.

Step9. Apply the inverse of the random permutation to obtain stego sub-bands LH, HL and HH, respectively.

Steg10. Form the modified image, E, of size 256 X 256 by merging the stego sub- bands with low sub-band LL

Step11. Finally, obtain stego-image, I’, by taking the inverse Haar/CDF9/7 transform of the modified image, E.

……………………………………….. Random selection of coefficients in Step 8 provides more security where the sequence of the message is only known to both sender and receiver by using a previously agreed upon secret key.

Chapter 8

226

Algo 8.2.1: Extraction ………………………………………..

Input: stego image, stego-key, encoding key Output: original message Step1. Apply 2-level DWT (Haar/CDF9/7) to the stego image Step2. Extract secret data from the selected frequency coefficients of three high sub-

bands HL, LH and HH obtained of Step 1 using the stego-key and the reversible thresholding technique.

Step3. Obtain the original message by T-decoding the secret data, with the help of encoding key

Step4. Recover the original image by reverse operation of the embedding. ……………………………………….. 8.2.2. Experimental results

To evaluate the performance of the proposed data hiding algorithm, 256 x 256 grayscale scale images are used. Simulations were done using MATLAB 7.0. The proposed algorithm based on Haar Wavelet is compared with the algorithm based on CDF9/7 wavelets on grayscale images of .tif and .jpg format. Imperceptiblilty The PSNR values obtained on implementing the proposed algorithm using Haar transform and CDF9/7 transform for some of the image formats are given in the Table 8.1. The Figures 8.2.1 to 8.2.2 show the comparison between Haar and CDF9/7 based thresholding method in terms of PSNR for the embedding capacity = 2000 bytes and 6000 bytes. We observe that Haar based thresholding method performs better than the CDF9/7 in terms of PSNR, irrespective of image formats. From Figures 8.2.1 to 8.2.2, it can be seen that Haar transform performs better than CDF9/7 in terms of PSNR. It can also be observed that the imperceptibility of images for the Algo 8.2.1 is not independent of image formats.The recovered image from Algo 8.2.1 for CDF9/7 based thresholding method is shown in Figure 8.2.5.

Chapter 8

227

Threshold vs Payload

It is noted that as the threshold value T increases, the payload increasesd but the PSNR decreases. The large threshold value means the strong embedding strength. Thus, the payload and PSNR are contending one another and the embedding strength heavily influences these two parameters. For computing threshold we make use of spatial context information of noisy image. Noise parameter estimated from the noise content through median absolute deviation (MAD) estimation, i.e., σn2 = median (|yi|) / 0.6745, yi∈ subband, and the threshold obtained as T= σn2/ σx, x is the subband. From Table 8.2.2, it is observed that the threshold value of sub-bands obtained from CDF9/7 transform is much smaller than the threshold value obtained for the corresponding sub-bands of Haar transform, the payload (%) for CDF9/7 transform based method is more than the Haar transform based method, the PSNR values of stego-images are better of Haar based method than CDF9/7 based method for .bmp, .jpg and .png whereas for ‘New12.tif’ images, CDF9/7 based method has better PSNR values than Haar based method and the PSNR values of recovered-images are better of CDF9/7 based method than Haar based method.

Table 8.2.1: PSNR values for RDH Algo 8.2.1 based on Haar and CDF9/7

Image HAAR (6000 bytes)

CDF9/7 (6000 bytes)

HAAR (2000 bytes)

CDF9/7 (2000 bytes)

C3.jpg 28.747012 26.78702 32.74543 27.74672 Tulips.jpg 28.775221 24.340296 36.32557 24.823396 New7.tif 28.730439 24.565361 38.48209 25.993797 New8.tif 27.852301 20.133592 29.70768 21.746396 New11.tif 28.305625 22.484001 37.10401 24.131382 New12.tif 28.671414 25.151761 34.43308 26.774769 Baboo.bmp 23.996821 19.757215 27.38116 21.856399 C2.bmp 28.808651 28.750585 37.39504 30.791012 Zoneplate.png 13.869799 7.814199 18.93664 8.671013 Tooth1.jpg 29.021136 30.988604 39.24182 33.829992 Peppers.png 28.750906 27.63027 36.13998 28.842123 C1.png 28.737853 30.104708 32.95031 31.545956

Chapter 8

228

Figure 8.2.1: PSNR values of different images based on Haar and CDF9/7 reversible

thresholding method for Algo 8.2.1 with embedding capacity= 2000 bytes Table 8.2.2: Comparison of proposed Algo 8.2.1 with others in terms of PSNR and Payload

Image Original/ Secret

message capacity(bytes)

Threshold Value

PSNR (Haar) Stego/

recovered

PSNR (CDF9/7)

Stego/ recovered

Payload (in%)Haar/

CDF9/7

C3.jpg 3722/1001 63.7509/ 12.1212

52.2967/ 43.9114

50.2678/ 47.1290

97.2595/ 98.1242

C2.bmp 3722/1001 43.3655/ 10.0574

67.8245/ 61.5269

51.2531/ 51.2531

97.7336/ 98.4762

C1.png 3722/1001 117.1238/ 28.9812

51.4987/ 42.0159

49.2711/ 45.9760

99.9919/ 100

New12.tif 3722/1001 63.3803/ 16.1620

45.2160/ 43.5378

49.6356/ 47.8940

97.8373/ 98.7467

C3.jpg 7444/2002 63.7509/ 12.1212

45.5626/ 38.4537

46.8570/ 41.9650

97.2595/ 98.1242

C2.bmp 7444/2002 43.3655/ 10.0574

59.5354/ 54.1294

49.5644/ 49.3003

97.7336/ 98.4762

C1.png 7444/2002 117.1238/ 28.981

48.0345/ 38.5376

47.6385/ 42.7510

99.9919/ 100

New12.tif 7444/2002 63.3803/ 16.1620

43.3213/ 38.8775

47.0732/ 42.4602

97.8373/ 98.7467

Chapter 8

229

Figure 8.2.2: PSNR values of different images based on Haar and CDF9/7 reversible

thresholding Algo 8.2.1 with embedding capacity= 6000 bytes

Structural similarity In the Figure 8.2.3, we have shown the results of SSIM obtained of Algo 8.2.1 for some of the images from the tested database of images using Haar and CDF9/7 transforms. It is observed that Haar transform based P-RDH provides better structural similarity of image than the CDF9/7 based P-RDH method. The doted line in Figure 8.2.3 (seen in middle and bottom) represent the results of SSIM for images for Algo 8.2.1 based on CDF9/7 and the dark lines ( seen at the top) represent the results of SSIM for images for Algo 8.2.1 based on Haar Wavelet. The images shown in this figure are H1 & D1 refer to ‘C1.png’; H2& D2 refer to ‘C2.bmp’; H3 & D3 refer to ‘C3.jpg’ and H4 & D4 refer to ‘New12.tif’. It is noted that in the case of Haar based P-RDH method all the images have their SSIM values close to each other ( lines are seen to be overlapping) whereas it is seen that there is a variation in the values of SSIM for tested images for CDF9/7 based P-RDH Algo 8.2.1. This shows that CDF9/7 based proposed method depends on the intrinsic property of image whereas Haar based proposed method shows tolerance to the intrinsic property of images.

Chapter 8

230

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.93

0.94

0.95

0.96

0.97

0.98

0.99

1

BPP

SS

IM

H1D1H2D2H3D3H4D4

P-RDH

Figure 8.2.3: The comparison between Haar & CDF9/7 in terms of SIMM for Algo 8.2.1

with threshold =35

Provable security The results obtained for the maximum values of KLDiv for some of the tested images for the proposed Algo 8.2.1 are shown in Figure 8.2.4. It is observed that Haar transform shows provable security whereas CDF9/7 lacks provable security. It is obvious to see that both Haar and CDF9/7 based RDH approaches show variation in the values of KLDiv as payload increases for the image ‘C2.bmp’, but remains almost constant ( linear) for other images.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.01

0

0.01

0.02

0.03

0.04

0.05

BPP

max

(KL

Div

)

H1D1H2D2H3D3H4D4

P-RDH

Figure 8.2.4: KLDiv vs BPP for Algo 8.2.1 with threshold=35

Chapter 8

231

original Decomposed stego Modified Recovered

Figure 8.2.5: Recovered image from Algo 8.2.1 based CDF9/7 with secret message=689 bits, threshold=35, T= 6.2413

8.3. PERCEPTUAL RDH BASED ON SLANTLET TRANSFORM In this section, we present a perceptual RDH based on SLT. It is known that SLT, which is a Wavelet-like transform, is a better candidate for signal compression compared to the DWT based scheme and can provide better time localization. The proposed perceptual RDH technique embeds data into the first level high frequency subbands of images, namely, LH, HL and HH. Preprocessing is performed prior to data embedding to ensure no overflow/underflow will take place. The stego-image carrying hidden message is obtained after inverse Slantlet transform. Figure 8.3.1 is the flowchart of the proposed high quality embedding data hiding and for hidden data extraction and original cover image recovery.

Figure 8.3.1: RDH Embedding and Extraction process using SLT

8.3.1. Proposed algorithm The proposed Embedding/Extraction algorithm for P-RDH based on SLT is summarized below:

Chapter 8

232

Algo 8.3.1: Embedding ……………………………………….. Input: 8-bit grayscale image, stego-key Output: stego image, encoding key Step 1. Obain the secret data by applying best T-codes as a source encoder to the

given input text.This generates an encoding key. Step 2. Consider 8-bit greyscale image and decompose it into 4 subbands, viz., HH,

HL, LH and LL, by applying 2-D Slantlet transformation (first taking 1-D Slantlet transform to each column of the image and then to each row of the image)

Step 3. Apply pre-processing to prevent possible “overflow” during embedding ( e.g., replacing the greyscale values 0 to 255 into 15 to 240)

Step 4. Embed data in the randomized coefficients of middle and high frequency bands, LH, HL and HH using the stego key.

Step 5. Obtain stego-image by taking the inverse Slantlet transform of the resulting image from step4.

………………………………………..

Algo 8.3.1: Extraction ……………………………………….. The extraction algorithm is similar to embedding Algo 8.3.1, except that the steps 4 and 5 are replaced by steps 4’and 5’ as given below:

Step 4. Extract embedded secret data and

Step 5. Recover the original image.

Step 6. The original message is then obtained by decoding the secret data.

………………………………………..

Chapter 8

233

8.3.2. Experimental results The Algo 8.3.1 is evaluated and its performance is compared with the Algo 8.2.1 based on DWT. It is implemented using number of different images formats such as .jpg, .tif, .jpg and .png. The results are summarized in the tables below for some of the tested images from the database. Imperceptibility It is observed from the results of Table 8.3.1 and Figure 8.3.2 that the proposed SLT based Companding method is better than the CDF9/7 based Companding method in terms of PSNR (and hence the perceptibility) and SIMM values ( hence the structural similarities).

Table 8.3.1: PSNR values for Algo 8.3.1 with threshold value, T=0.9 and embedding capacity=6000 bytes

Image Haar CDF9/7 SLT C3.jpg 32.512914 26.787020 32.146677 Tulips.jpg 35.064473 24.340296 31.771782 Tooth1.jpg 38.493593 30.988604 41.411807 New7.tif 35.527431 24.565361 32.755009 New8.tif 29.101780 20.133592 27.663867 New11.tif 33.815656 22.484001 29.261890 New12.tif 34.035546 25.151761 34.149406 C2.bmp 36.434773 28.750585 35.441245 Baboo.bmp 27.159670 19.757215 27.005753 C1.png 32.944596 30.104708 35.192180 Zoneplate.png 27.869799 8.449536 22.657796 Peppers.png 35.243893 28.842123 34.107698

Also, on comparing with Haar transform, it is observed that for image formats .jpg, .png and .bmp, the Slantlet based method has better PSNR values than the Haar based transform, however for .tif image Haar transform shows a better option. From Figure 8.3.3, it is observed that image: ‘Tooth1.jpg’ gives best imperceptibility than other images, the lowest imperceptibility is found for the image ‘New11.tif’ and the PSNR values for images: ‘C1.png’, ‘C2.bmp’ and ‘New12.tif’ remains linear as the BPP increases.

Chapter 8

234

Figure 8.3.2: Comparison between Haar, CDF9/7 and Slantlet in terms of PSNR of Algo 8.3.1

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 600028

30

32

34

36

38

40

42

44

46

48

Message-size

PS

NR

c1.pngc2.bmpc3.jpgnew11.tifnew12.tifpeppers.pngtooth1.jpgtulips.jpg

Perceptual RDH with SLT

Figure 8.3.3: PSNR vs Message-size for different image formats for Algo 8.3.1

Structural similarity The Table 8.3.2 shows the SSIM values obtained from the Algo 8.3.1 implementing it on the number of images with threshold value 0.9 for the payload = 6000 bytes. In the Figure 8.3.5 we show the results of SSIM obtained of different images as message-size increase from 1000 bytes to 6000 bytes. It is observed that Tooth1.jpg sustains the structural similarities better than the other images. From Figure 8.3.4, it can be seen that the value of

Chapter 8

235

measure of structural similarity of stego-images for Haar are approximately 1 except for ‘Baboo.bmp’ image. For they are constant (=0.98) for all images except for .png images.

Figure 8.3.4: Comparison between Haar(Blue), CDF9/7(Green) and Slantlet(Red) in terms

of SIMM values of Algo 8.3.1

Table 8.3.2: SSIM values for Algo 8.3.1, T=0.9 & embedding capacity= 6000 bytes

Image Haar CDF9/7 SLT C3.jpg 0.99196 0.97696 0.99332 Tulips.jpg 0.99663 0.97821 0.99846 Tooth1.jpg 0.99835 0.97662 0.97676 New7.tif 0.99689 0.97895 0.99129 New8.tif 0.9858 0.98224 0.91174 New11.tif 0.997 0.98021 0.93004 New12.tif 0.99409 0.97901 0.94235 C2.bmp 0.99839 0.9768 0.98294 Baboo.bmp 0.95781 0.98172 0.9046 C1.png 0.96939 0.97656 0.97782 Zoneplate.png 0.99585 0.92389 0.95801 Peppers.png 0.99653 0.97664 0.9853

Chapter 8

236

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.93

0.94

0.95

0.96

0.97

0.98

0.99

1

BPP

SS

IM

c1.pngc2.bmpc3.jpgnew11.tifnew12.tifpeppers.pngtooth1.jpgtulips.jpg

Perceptual RDH with SLT

Figure 8.3.5: SIMM vs BPP for different image formats obtained on implementing Algo 8.3.1

Security In Figure 8.3.6, we have shown the maximum KLDiv values for different image formats for the proposed Algo 8.3.1. It is seen that .jpg and .png have best results as compared to other image formats. The maximum values of KLDiv are found to be in the range of [0, 0.02]. The images ‘C3.jpg’, ‘New11.tif’, C1.png’ and New11.tif’ shows linear increase, i.e., monotonicity in KLdiv values whereas other image show non-monotonicity as the capacity increases. This shows that the provable security measure KLDiv depends on the intrinsic property of images.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

BPP

KL

Div

c1.pngc2.bmpc3.jpgnew11.tifnew12.tifpeppers.pngtooth1.jpgtulips.jpg

Perceptual RDH WITH SLT

Figure 8.3.6: KLDiv vs BPP for different image formats

Chapter 8

237

Histogram analysis From the histograms of the original images and their corresponding stego-images, as shown in Figure 8.3.7, it is observed through the comparison of histogram of stego images and corresponding original images that the proposed Algo 8.3.1 fails against statistical attacks as the distortion can be viewed through human eyes.

Figure 8.3.7: Histograms of original and stego-images for Slantlet based Algo 8.3.1

Orignal image histogram Stego-image histrogram – T=0.9

Chapter 8

238

Figure 8.3.8: 2-D SLT decomposition, stego-image and recovered image of Tulips.jpg and

Lena.jpg using Algo 8.3.1

Summarizing, a novel perceptual reversible data hiding technique based on Slantlet transform is presented in this section. Comparing with the data hiding techniques based on Haar and CDF9/7 wavelet transform, it is observed that the requirement of imperceptibility is acceptable (no artifact found in the stego-images) and is much better than the corresponding wavelet based Algo 8.2.1. The structural similarity of images is not perfect (SSIM ≠ 1), but can be said to be in the acceptable range, [0.9, 1]. The proposed algo 8.3.1 is not showing very good KLDiv results (≠ 0), but may be accepted as the values lie in the range [0, 0.02]. Further, the original image can be recovered from the stego-image after the hidden data has been extracted. The payload in the propose Algo 8.3.1 is same as in case of wavelet Algo 8.2.1. Through the histogram analysis it is observed that Algo 8.3.1 fails against the statistical attacks. Recovered images for Algo 8.2.1 are shown in Figures II.13 and II. 14 of Appendix II. 8.4. ROBUST REVERSIBLE COMPANDING TECHNIQUE USING SLT AES algorithm is a very secure technique for cryptography and the frequency domain techniques are considered highly secure for steganographic system. The integration of Compression technique (T-codes) and cryptography technique (Modified AES) with Steganography use three keys – encoding key, encrypted key and threshold value, making the present algorithm a highly secured method. Thus, the proposed method

Chapter 8

239

provides not only acceptable image quality but also has almost no distortion in the stego-image after adding Gaussian noise or Salt and Pepper noise. 8.4.1. Proposed algorithm The proposed steganographic algorithm is shown in Figure 8.4.1.

Figure 8.4.1: Embedding and Extraction process for Algo 8.4.1

The steps involved in the proposed algorithm may be stated as follows:

Algo 8.4.1: Embedding ……………………………………….. Input: Cover image, original message, stego key Output: stego image, encoding key Step1. First encode the original message using best T-codes to obtain compressed

binary data. Step2. Apply Modified AES encryption algorithm on the compressed binary data (Step

1) to obtain secret data. Step3. The cover image is transformed into four subbands- LL, LH, HL and HH,

using 2-level of SLT.

Chapter 8

240

Step4. The encrypted codeword (obtained of Step 2) is then embedded in the randomized coefficients of high frequency subbands using reversible thresholding method and stego key.

Step5. The stego image is transmitted through the channel. ……………………………………….. Algo 8.4.1: Extraction ……………………………………….. Input: stego image, stego key, encoding key

Output: original message

Step1. The hidden encrypted codewords are extracted from the high frequency subbands obtained of stego image using stego key.

Step2. Improved AES decryption algorithm is applied on the extracted codes to obtain the encoded message.

Step3. T-decoding is applied to obtain the original message

Step4. The original image is constructed by applying reversible thresholding method.

………………………………………..

Shorter code words may not be the best prefixes because they result in uniform tree generation. Therefore, there is a need to develop an algorithm to choose the best T-codes (see Annexure III) that give a better compression. We proposed a novel algorithm to select best T-codes from the huge data base of T-code sets. The following table gives a numerical explanation for the expressions given for number of Codeword sets and number of Code words within each code set. The table is shown for augmentation levels 0 to 9. 8.4.2. Experimental results The performance of the proposed Algo 8.4.1 based on SLT (using T-codes to encode the original message, improved AES to encrypt the encoded message and reversible thresholding) with the corresponding algorithm based on Wavelet is compared. We have

Chapter 8

241

tested number of standard images and medical images. Two metrics PSNR and SSIM for measuring the stego-image quality have been used. In the consequent sub-sections, the experimental results in respect of different characteristics of steganography are studied.

Imperceptibility The results of the PSNR of the proposed method based on SLT is compared with the Wavelet transform and Slantlet transform and are summarized in the Table 8.4.1 to Table 8.4.4 for the embedding capacity =5000 bytes and for some of the test images as shown in Figure 8.4.2.

I1

I2

I3

I4

Figure 8.4.2: Some of the tested Cover images (I1:Cameraman.tif, I2: Lena.jpg, I3: Nature.jpg and I4: Scenery.jpg)

Table 8.4.1: PSNR values for Algo 8.4.1 based on Wavelet and SLT using Huffman encoding (secret message = 5000 bits)

Image WLT+HUFF WLT+HUFF (addingGaussian) SLT+HUFF SLT+HUFF

(adding Gaussian) I1 19.921678 19.921678 21.452172 21.452389 I2 18.203956 18.203956 32.140011 32.137198 I3 17.292666 17.292666 24.489907 24.489990 I4 17.453638 17.453638 23.198266 23.200940

In Table 8.4.1, PSNR values obtained of some of the test images for WLT and SLT based perceptual RDH using Huffman codes (required to encode the message at preprocessing stage) are presented. In Table 8.4.2, we present the PSNR values

Chapter 8

242

obtained for WLT and SLT based perceptual RDH using T- codes. It is observed that the imperceptibility is better in the SLT based reversible thresholding algorithm than DWT based reversible thresholding method and T-codes further improves the imperceptibility results over the Huffman codes. From Tables 8.4.3 and 8.4.4, we observe that using AES at preprocessing level to encrypt the encoded message, results into better imperceptibility in the case of RDH algorithm based SLT with Huffman codes as encoder whereas WLT based algorithm does not show much change. In case of T-codes based algorithms, results improves slightly.

Figure 8.4.5 illustrate that T-codes alongwith the application of AES provides not only better PSNR values but also robustness against the Gaussian ( as well for Salt-n-Pepper) attack . The similar conclusions of robustness can be drawn for Huffman Codes as shown in Figure 8.4.5. Thus, the proposed method provides not only acceptable image quality but also has almost no distortion in the stego-image after adding Gaussian noise or Salt and Pepper noise. The use of SLT has shown better results than DWT in terms of image metric ‘PSNR’ and robustness.

Figure 8.4.3: (1) WLT+Huff, (2) WLT+Huff+Gaussian (0.01), (3) SLT+Huff , (4)

SLT+Huff+Gaussian

Robustness Table 8.4.1 shows the test results for the proposed method using Huffman codes with and without adding the Gaussian noise. Similarly, Table 8.4.2 shows test results using T-codes with and without adding the Gaussian noise. The embedding capacity (i.e size

Chapter 8

243

of secret message) taken is 5000 bytes. It can be seen through the Figure 8.4.3 and Figure 8.4.4 that the T-code based method performs better than the Huffman code in terms of PSNR and against the Gaussian attack. Table 8.4.3 shows the results using Huffman codes and improved AES encryption with and without the Gaussian noise. Similarly, Table 8.4.4 shows the results using T-codes and modified AES encryption with and without the Gaussian noise.

Table 8.4.2: PSNR values based on Wavelet and SLT using T-code encoding (secret message = 5000 bits)

Image WLT + T-CODE

WLT + T-CODE (adding Gaussian)

SLT+ T-CODE

SLT+ T-CODE (adding Gaussian)

I1 19.276835 18.739734 21.144950 21.146281 I2 16.892371 16.798323 31.866441 31.871396 I3 15.368473 18.578029 24.3046 24.296260 I4 14.086282 9.738723 22.955329 22.951326

Figure 8.4.4: (1) WLT+T-code, (2) WLT+ T-code +Gaussian (0.01), (3) SLT+T-code, (4)

SLT+Tcode +Gaussian

Table 8.4.3: PSNR values based on Wavelet and SLT using Huffman encoding and AES encryption (secret message = 5000 bits)

Image WLT+HUFF +AES

WLT +HUFF +AES (adding

Gaussian) SLT+HUFF

+AES SLT +HUFF +AES (adding Gaussian)

I1 19.922627 19.922627 23.235624 21.450025 I2 18.188314 18.188314 34.095894 32.143663 I3 17.292913 17.292913 26.616492 24.477793 I4 17.454110 17.454110 25.362884 23.197050

Chapter 8

244

Figure 8.4.5: (1) WLT+AES+Huff, (2) WLT+AES+Huff+Gaussian (0.01), (3) SLT+

AES+Huff , (4) SLT+AES+Huff+Gaussian

Table 8.4.4: PSNR values based on Wavelet and SLT using T-codes encoding and AES encryption (secret message = 5000 bits)

Image WLT+T-CODE +AES

WLT +T-CODE +AES (adding

Gaussian) SLT+T-CODE

+AES SLT+T-CODE+AES (adding Gaussian)

I1 18.739734 19.276835 21.143900 21.1446 I2 16.798323 16.892371 31.859676 31.8704 I3 18.578029 15.368473 24.295226 24.2963 I4 9.738723 14.086282 22.952757 22.9471

Figure 8.4.6: (1) WLT+AES+T-code, (2) WLT+AES+T-code+Gaussian (0.01), (3) SLT+

AES+T-code , (4) SLT+AES+ T-code+Gaussian

Chapter 8

245

Security The integration of Compression technique (T-codes) and cryptography technique (Modified AES) with Steganography use three keys – encoding key, encryption key and threshold value, making the present algorithm a highly secured method. The use of encryption in this steganography scheme can lead to ‘security in depth’. To protect the confidential data from unauthorized access, an advanced encryption standard (AES) has been suggested by the researchers (Blois and Iocchi, 2007). AES algorithm is a very secure technique for cryptography and the techniques which use frequency domain are considered highly secured for system for the combination of steganography. Recovery There is no artifact obtained in the stego-image and the original image is recovered with low image degradation from the stego-image (see Figures II.13 to II.15 in Appendix II). Embedding payload The embedded payload in the proposed embedding technique is same as in case of the DWT techniques, as both the transform WLT and SLT result into 1 low subband and 3 high subbands after 1-stage of 2-D decomposition of the cover image. SUMMARY We have presented both, perceptual and robust, form of reversible hiding techniques, known as Companding technique based on Wavelet (Haar and CDF9/7) and Wavelet like transform (SLT). In section 8.1 we have reviewed the different techniques of RDH used by number of scholars. In section 8.2, through the Algo 8.2.1 it is observed that Haar based RDH is performing much better than CDF9/7 in terms of imperceptibility, structural similarity and provable security. Next, we have evaluated and compared the performance of SLT based RDH with the Wavelet (Haar/CDF9/7) based RDH. It is observed through the implementation of Algo 8.3.1 on number of images that SLT based RDH is much better than Wavelets based RDH in terms of PSNR, SSIM and KLDiv, but fails against statistical attacks. Thus, for the robustness, we explore further

Chapter 8

246

the Algo 8.3.1 using T-codes and AES at pre-processing level. The T-codes and AES provide additional layer of security in the system. Further, an improved AES used for the encryption of the encoded message provides more security and robustness to the steganography system. The use of encryption in steganography can lead to ‘security in depth’. To protect the confidential data from unauthorized access, an advanced encryption standard (AES) has been suggested by the researchers. AES algorithm is a very secure technique for cryptography and the techniques which use frequency domain are considered highly secured for system for the combination of steganography.

Through the experimental results presented in the Table 8.4.1 to Table 8.4.2, it is observed that after adding Gaussian noised, the PSNR of stego-images becomes even better than without Gaussian noise. This is due to the fact that in terms of image enhancement, CWTs, such as DD DT DWT performs much better at suppressing noise over the wavelets. The comparative summary of two approaches of RDH – Perceptual and Robust, one based on Wavelets and other based on SLT discussed in this Chapter is given in the Table 8.4.5 with the basic required characteristics of image steganography.

Table 8.4.5: Summary of P-RDH based on WLT and SLT

Attributes CDF9/7 and Haar (P-RDH) SLT (P-RDH) SLT (R-RDH) Imperceptibilty Haar shows Improvement

over CDF9/7 Acceptable, improvement over CDF9/7, but almost same as of Haar

Reasonable, improvement over WLT

Structural Similarity Nearly perfect in case of Haar and satisfactory for CDF9/7

satisfactory Perfect (SSIM ≈ 1)

Provable Secuirty No for CDF9/7, Yes for Haar No NA Security against statistical Attacks

Poor Poor NA

Robusness Poor Poor Good