Image Steganography Using Fuzzy Domain Transformation and Pixel Classification Aleem Khalid Alvi
Robin Dawes
School of Computing Queen’s University Kingston, ON, Canada
[email protected]
School of Computing Queen’s University Kingston, ON, Canada
[email protected]
Abstract—Image steganography offers many techniques to hide secret data from an eavesdropper. We use fuzzy logic and image processing techniques to develop a robust and highly imperceptible image steganography scheme. Our proposed scheme uses fuzzy domain transformation of secret data. We exploit image processing techniques for implementation of fuzzy pixel classification for a selection of cover pixels during the embedding of secret data. On the receiving end, unembedding is performed using stego keys. Keywords: image steganography, data hiding, fuzzy logic, fuzzy classification, image processing
I.
INTRODUCTION
Digital information hiding was born with advent of digital technology. Nowadays steganography techniques use different types of digital media such as text, image, audio, video, binary, or html files. Modern steganography techniques rely on data hiding techniques using modern media. Cryptography provides data security by applying encryption/decryption techniques. An encrypted message is susceptible to eavesdroppers' attacks if they know of its presence. The best solution is to hide the message existence by embedding it into cover media. Therefore, role of steganography is clear and strong with use of cryptography. Both techniques provide more secure communication between sending and receiving ends. Furthermore, some MS Windows operating system stores admin password in sam (security access manager) hive file (%SYSTEMROOT%\ system32\config\sam) using a one-way-hash (e.g., NT LAN Manager hash) [1]. The sam hive’s file location is inaccessible to non-administrative users by default. However, it is vulnerable to offline attacks. Tools are available that can recover or simply reset/clear the password [2]. It is best to encrypt the password and hide using steganography. Therefore, combination of both techniques offers safety from attackers [3-4]. In this paper, we propose a unique and robust steganography method using fuzzy techniques. We transform secret data from a spatial domain to fuzzy domain before data hiding. The selection of a pixel from the cover media (an RGB image) depends on fuzzy pixel classification. Image processing techniques are employed for selection process of cover pixels using fuzzy pixel classification. The rest of the paper is organized as follows. In Section II, we provide a survey on steganography that uses fuzzy logic techniques. In Section III, we describe the experimental setup for our proposed steganography technique. In Section
IV, we depict the implementation procedure for the technique. In Section V, we discuss and analyze the results. Finally, we conclude with future research. II.
RELATED WORK
Classification of information hiding methods is based on many attributes such as cover objects, secret objects, hiding techniques, and current technologies. Researchers attempt to develop steganography systems with robustness, security, undetectability, imperceptibility (invisibility or perceptual transparency), and high capacity; however, every method has its own advantages and disadvantages [5]. We measure the capability and quality of steganography methods using these characteristics. Our proposed technique is the combination of domain transformation, data conversion, and substitution based on image properties. It is a kind of private-key steganography. Many steganography techniques can be found in the literature [5-6, 8-10, 11-15, 18]. We discuss steganography techniques that use fuzzy techniques as part of their implementation. Khursheed and Mir [16, 17] were the first to attempt to apply fuzzy logic for hiding data. They endeavor to embed information in a fuzzy logic domain. The advantages are lower computationally expense as compared to other domain transformation methods. Their method provides embedding versatility and safety from common cover attacks, as well as appropriate imperceptibility and payload capacity. However, the secret data is very sensitive and easy to destroy by small changes in the cover without changing any significant visibility. Toony et al. [19] propose an image hiding method. They hide a secret image by employing a fuzzy coding/decoding method. A fuzzy coder compresses each block of the secret image into a smaller block and utilizes model-based steganography to hide the message in a cover image. This causes less distortion in the image and the result is a high quality stego image. The advantages are higher embedding rate and security enhancement. Hussain et al. [20] propose a novel hybrid fuzzy c-means (FCM) and support vector machines (F-SVM) model for image steganography. The F-SVM model provides the capability for embedding the secret-message imperceptible for human visual system (HVS) during payload increment. This hybrid soft computing approach has advantages of complementary features of clustering (using FCM) and classification (using support vector machines). Goodarzi et al. [21] propose a steganography scheme based on the least significant bit (LSB) steganography
mechanism and utilize hybrid edge detector (HED). The HED consists of canny edge detection and fuzzy edge detection algorithms. This scheme resists the HVS, Fridrich's methods, and steganalysis systems, which are based on statistical analysis. In addition, it produces higher quality stego images and high payload capacity. Every steganography method has its limitations. Petitcolas et al. [6] discuss the limitations of some information hiding systems and attacks. Detection and destruction of secret data in a cover medium are considered attacks. They describe many attacks on information hiding techniques. Craver et al. [7] describe three kinds of attacks: robustness attacks, presentation attacks, and interpretation attacks. In Section III, we describe our steganography scheme that utilizes a fuzzy inference system. The system exploits image processing techniques. III.
We use LSB steganography that employs fuzzy logic with image processing techniques. The selection of a pixel for embedding depends on two image properties: silhouette (i.e., edges) and texture (i.e., a pixel contains the entropy value of the 9-by-9 neighborhood pixels around the corresponding pixel in cover image). The process of steganography uses the fuzzy inference system to embed the secret data (i.e., text or image) into the cover image. A. Fuzzy Image Representation and Domain Transformation An image is the combination of pixel values. These values are represented in matrix form. An aggregation of these values shows an image to HVS with image properties such as brightness, homogeneity, noisiness, and edginess, etc. In general, an image representation in spatial and fuzzy domains is shown in (1) and (2), respectively as follows. M
N
(1)
m =1 n =1
A relationship or transformation of a pixel from the spatial to the fuzzy domain using membership function µmn is shown below.
μ mn = μ x ( I mn ) Hence an image in the fuzzy plane is M
N
μ f = ∪∪ μ mn m =1 n =1 M N
μ f = ∪∪ μ x ( I mn )
μ mn = e
2 fh2
(3)
Where fh = fuzzifier, Imax = maximum pixel value of an image, Imn = any gray level pixel value of an image I. In Fig. 1, fh = σ, Imax= b, and Imn = x.
Figure 1. Simple Guassian function graph [23]
EXPERIMENTAL SET UP
I s = ∪∪ I mn
− ( I max − I mn ) 2
(2)
m =1 n =1
We use the general form of Gaussian membership function for image transformation from the spatial domain into the fuzzy domain as shown in Fig. 1. The specific image transformation function with fuzzifier fh is shown below taken from Khurshid and Mir [16]:
Analysis of (3) shows that the difference between Imax and Imn changes the value of µmn significantly. If Imn approaches Imax then µmn approaches 1. Similarly, when Imn approaches 0 then µmn approaches a finite value c. Where c is shown as follows. − ( I max ) 2 0 c = μmn =e
2 fh2
Therefore, values of µmn vary from c to 1. The fuzzifier (fh) is the parameter that has effect on µmn. The inverse transformation function is required to transform the image back to spatial domain. In subsection B, we describe the embedding process using fuzzy inference system (FIS). B. Fuzzy Inference System (FIS) We use Mamdani fuzzy interference system (FIS) for the proposed steganography scheme [24]. Using the fuzzy inference process, a given input (a crisp input) maps to an output (a crisp output) using fuzzy logic methods. The fuzzy inference process requires membership functions, logical operations, and If-Then rules. We implement the FIS in following steps. Step 1: Fuzzify inputs Take input as pixel values and determine the degree to which they belong to each of the appropriate fuzzy sets. We use the membership function shown in (4) to transform the image pixel values from spatial domain to fuzzy domain. Step 2: Apply fuzzy operator. A fuzzy operator AND is used for combining the antecedents. The purpose of the fuzzy operator is to obtain one number that represents the result of the antecedents for specific rule and then apply a number to the output function. Step 3: Apply implication method. We use fuzzy pixel classification using image-processing techniques for LSB embedding in cover image [22]. We use three fuzzy based implication rules as follows: a) IF (cover pixel = silhouette) AND (cover pixel texture value < M) THEN (Do not use cover pixel for embedding)
b) IF (cover pixel ≠ silhouette) AND (cover pixel texture value ≥ M) THEN (Do not use cover pixel for embedding) c) IF (cover pixel ≠ silhouette) AND (cover pixel texture value < M) THEN (Use cover pixel for embedding) In rule (c) the antecedent says that “if cover pixel is a regular pixel” then use this pixel for embedding secret data. Further, M is the mean of all pixels' entropy in the image. The input for the implication process is a single number given by the antecedent, and the output is consequent as part of a fuzzy set. Step 4: Aggregate all outputs We aggregate the output in the final cover image by writing all pixels combined in matrix form and store as an image. Step 5: Defuzzify Using HVS, visualize the cover image. The visualization after embedding should not differ from the visualization of the original cover image. C. Using Image Processing Techniques in Fuzzy Pixel Classification In the step 3 of subsection B, we use fuzzy based If-Then rules to apply fuzzy classification of potential cover pixels. The classification is used to select the appropriate cover pixel for embedding secret data. The purpose of cover pixel selection is to produce less disturbance and distortion in the embedded cover image with respect to HVS. We use texture and silhouette (edge) properties of an image. The texture property is a statistical measure for image pixels. It provides information about the local variability of the intensity values of pixels in an image. For example, smooth texture in specific area of an image shows the range of values will be a smaller in the neighborhood around a pixel. The inverse is rough texture area where the range of pixel values will be larger. The HVS testing first detects the distortion in edges of an image. Therefore doing no embedding in edges will preserve the edges of the image and increase imperceptibility against an eavesdropper’s attack and decrease susceptibility to detection. We use the canny edge detection algorithm for edge detection in images and calculate entropy of each cover pixel by using a block of 9 x 9 neighborhood pixels around a selected pixel for getting texture information. We do not embed in edges and high texture areas to keep image more imperceptible for the HVS testing. The selection can be changed based on the given condition. For example in Fig. 2, we use rule based selection dependent on comparison with the mean texture value (M) of a cover image. Therefore, the capacity in the cover image may be increased if we replace the mean texture value (M) of the cover image with a texture value greater than M. However, this may decrease imperceptibility of the embedded cover image and may increase susceptibility for the eavesdropper.
D. Methodological Steps In subsection B, we describe the FIS for the proposed steganography scheme. Fig. 2 provides step-by-step methodological information using a flowchart representation for embedding process on the sending end of the steganography system. IV.
IMPLEMENTATION
We implement the sending and receiving end algorithms using MATLAB. The stego keys for the receiver are original cover image, extracting software, and size and location of secret payload. It is easily possible to decrease susceptibility and reduce the possibility of cover, statistical, histogram, and profiler attacks if every time the sender communicates using a new image as a cover object. Therefore, the cover image should be unique and can use as a secret key. Similarly starting pixel location for embedding and size of secret data are combined to be used as a secret key. The value of fh works as a tuner of the image for embedding and extracting the secret image or data. The value of fh can be adjusted based on the result of recovering the image. Therefore, the sender must check the recovered secret image before sending the embedded cover image to the destination. In our experiment, we use two different values of fh for embedding and extracting the secret image. The value fh = 65 has better results than fh = 45 in HVS testing. Interestingly, we embed data using fh = 65 and extract using fh = 45 and fh = 95.
Figure 2. Sending end data embeding flowchart
The result is the successful extraction of secret image; however, at fh = 45 the secret image has less perceptibility then at fh = 95. Therefore, fh work like a tuner for achieving good image quality in extraction process. Fig. 3 shows the piece of MATLAB code for the implementation of the image processing techniques for fuzzy pixel classification. The embedding is LSB steganography technique; nevertheless, the selection of a cover pixel is based on fuzzy classification.
objects and use testing techniques. We have found the Baboon is the best selection as cover object. After selection of a cover image, we start testing of imperceptibility of the cover object by embedding the secret images in increasing capacity. The selection process of cover pixels is shown in Fig. 2. We find the number of pixels in the cover object that are appropriate for embedding without producing perceptible disturbance in the texture and silhouette properties of the cover image. Therefore, before we start embedding, we know the available capacity of the cover object. The available capacities based on embedding criteria (shown in Fig. 2) for the selected cover images, i.e., Lena.jpg and Baboon.jpg are 145,313 and 138,518 pixels, respectively. The available cover object capacity may vary by any change in selection of texture value in an algorithm shown in Fig. 2. Permitting embedding in more cover pixels provides more capacity but on the other hand, it decreases imperceptibility. TABLE I. ANALYSIS OF PROPOSED STEGANOGRAPY ALGORITHM USING LENA (COVER) AND TOMAHAWK MISSLE (SECRET) IMAGES
We use ImageJ (ver. 1.46r) software for analysis of results of the proposed steganography scheme. We have selected two standard images of size 512 × 512 as cover object (i.e., Lena and Baboon). The secret images are Tomahawk missile and Spaceship with sizes 160 × 160 and 400 × 400, respectively. We apply HVS, histogram (a statistical tool), and profile testing for analysis the imperceptibility characteristics of the results. These testing techniques select the best cover object among Lena and Baboon with respect to texture and silhouette (edge) properties. For this purpose, embed Tomahawk missile image (160 × 160) into both cover
Original Secret Image (Tomahawk Missile ) fh = 45
ANALYSIS AND RESULTS
fh = 65
V.
Histograms
Stego Image (Embedded Cover Image) (fh = 45)
The use of fuzzy pixel classification creates unique characteristic in steganography scheme. It develops robustness in the steganography system. Fuzzy transformation of an image provides the fractional values of irrational numbers. For storing these values up to significant number of decimal places needs excessive storage. Therefore, we use only two decimal places of fuzzy data (i.e., fuzzy singleton values) of an image for storing into a cover image. We found that the round off of fuzzy singletons to two decimal places is the maximum round off position for the fuzzy data without losing pictorial information. However, on the receiving end, the transformation of secret data (image) into the spatial domain does not show exactly as the original; however, the result is always found to be appropriate and acceptable for visibility.
Extracted Secret Image
Figure 3. Image processing based fuzzy pixel classification algorithm
Images
Original Cover Image (Lena)
Type
Table I shows embedding of the Tomahawk missile image into Lena image. In this case, secret data (160 ×160 =
25600 pixels) is embedded in Lena (available capacity = 145,313) and uses 17.62% of the available cover object capacity. HVS testing shows that original Lena image and Lena stego image has significant difference. The HVS testing uses zooming effect during comparison with the cover image. The difference between cover and stego objects is visible as light shades. This testing cannot be invoked without original cover image. The histograms for the original Lena and stego Lena images look similar in shape. However, statistical testing shows the difference between their statistical values (i.e., mean and standard deviation values). This can draw the attention of an eavesdropper and increase the susceptibility. The original secret image (i.e., Tomahawk missile) is evidently visible after extraction; however, the extracted image at fh = 65 has more visibility as compared to the extracted image at fh = 45. The comparison of histograms of “extracted secret image at fh = 65” with the “original secret image” shows much similarity to each other. Table II shows embedding of Tomahawk missile image into Baboon cover image.
In this case, secret data (160 ×160 = 25,600 pixels) is embedded in Baboon cover image (available capacity = 138,518 pixels) and uses 18.48% available cover object capacity. The histograms for the original Baboon and stego Baboon images are approximately similar in shape. HVS testing shows that the original Baboon image and Baboon stego image has no difference in visibility. However, statistical testing shows the difference between their statistical values (i.e., mean and standard deviation values). However, this is less susceptible to an eavesdropper in comparison to the case shown in Table I, because humans use the HVS at first to judge anything. The original secret image (i.e., Tomahawk missile) is evidently visible after extraction; however, the extracted image at fh = 65 shows more clear view as compare to the extracted image at fh = 45. The comparison of histograms of extracted secret image at fh = 65 with original secret image shows more similarity among each other. Therefore, it shows that Baboon is a more reliable and imperceptible cover image and the value of fh can be used as a tuning parameter for embedding and extracting a good visible secret image.
TABLE II. ANALYSIS OF PROPOSED STEGANOGRAPY ALGORITHM USING BABOON (COVER) AND TOMAHAWK MISSLE (SECRET) IMAGES
TABLE III. ANALYSIS OF PROPOSED STEGANOGRAPY ALGORITHM USING BABOON (COVER) AND A BIRD (SECRET) IMAGES
Original Cover Image (Baboon)
Type
Original Secret Image (Space ship 400 × 400) fh = 45 fh = 65
Histograms
Stego Image (Embedded Cover Image) (fh = 45)
Images
Extracted Secret Image
fh = 45 fh = 65
Extracted Secret Image
Stego Image (Embedded Cover Image) (fh = 45)
Original Secret Image (Tomahawk Missile )
Original Cover Image (Baboon)
Type
Images
Histograms
We use profile testing for Lena and Baboon original and stego images and found it useless. Image profile testing provides the graph of selected area of an image; however, the differences between original and stego images are not visible in the graphs (provided that the size of secret data is small). In Table III, we use 100% cover capacity of Baboon cover image for testing its strength in terms of imperceptibility. We embed the Spaceship secret image of size 400 × 400 pixels. In this case, secret data (400 × 400 = 160,000 pixels) is embedded in Baboon cover image (available capacity = 138,518 pixels). Since secret data is larger than available cover capacity; secret pixels are lost after using all cover capacity in cover image. The lost pixels are visible as a black strip in recovered images at fh = 45 and 65. The HVS testing shows that Baboon cover image is highly imperceptible. However, histogram and statistical results shows significant differences between original and stego images. VI.
ACKNOWLEDGMENT The authors would like to thank Prof. Hamid R. Tizhoosh, Faculty of Engineering, University of Waterloo for his online image processing tutorial and thoughtful comments on fuzzy representation for an image. REFERENCES [2]
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CONCLUSION AND FUTURE WORK
We proposed steganography algorithm based on fuzzy inference system. Our fuzzy inference system uses fuzzy transformation and pixel classification techniques. The fuzzy pixel classification uses the image processing techniques by exploiting texture and silhouette properties. The results show that exploiting the image processing techniques with fuzzy logic increase imperceptibility in stego image significantly. In future work, more image properties can be considered for a cover image to further strengthen imperceptibility.
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