Dipanjali R. Khant.

Transcription

1 Design of an Algorithm for Image Steganography using Fractal Mathematics Dr. Hetal N. Patel Electronics and Communication Department A. D. Patel Institute of Technology New V.V. Nagar, Anand, India Dipanjali R. Khant Electronics and Communication Department A. D. Patel Institute of Technology New V.V. Nagar, Anand, India Dr. Darshana Prajapati Mathematics Department M& B Patel Women's Institute of Engineering New V.V. Nagar, Anand, India djprajapati@mbict.ac.in Abstract In order to improve the security of steganography system, we use fractal s as it has tremendous properties, such as ease of generation, sensitive dependence on their initial conditions,self-similarity and details at every scale. Information is embedded during creating fractal s by secret information. The receiver can extract the secret information by comparing the difference between Stego-Images and Cover- Images recovered with the same initial parameters. The attackers can t recover the Cover-Images without the initial parameters.the simulation results shows the imperceptibility and undetectability of the proposed algorithm.the value of PSNReachedup to46, and the value of MSE is vary between the range 0.04 to 3, as well as the value of NCreached up to0.9974and the scale (RGB Histogram) shows very minor difference. Keywords steganography, fractal s,mandelbrot set,steganalysis, NC, MSE, PSNR I. INTRODUCTION The term steganography [7] originated from the Greek word steganos meaning covered or protected and graphein meaning to write. Nowadays, it often refers to the science of invisible communication. Steganography can be defined as the art and science for hiding information in a way to prevent any person from retrieving hiding information without authentication. Steganography means, it is not to alter the structure of the secret message, but hides it inside a coverobject. After embedding process, cover object and stegoobject (carrying hidden information object) looks alike. Due to invisibility or hidden factor it is difficult to recover information without known procedure of steganography. Steganalysis is the process of detecting procedure of steganography [12]. There are two kinds of steganography for data hiding: spatial-domain based and transform-domain based methods. Spatial-domain based methods embed messages in the intensity of pixels of s directly [6] [25]. Among them, the least significant bit (LSB) method is the most wellknown [4] [14] [24]. While transform-domain based methods first transform a cover into a new domain and then messages are embedded in the form of transform coefficients[13] [20]. According to cover file type, steganography is classified into four types which are text, audio,, and video steganography [19]. Each steganography communication system consists of an embedding algorithm and an extracting algorithm [23]. To accommodate a secret message in a digital cover, the original cover is modified by applying the embedding algorithm, the result is modified cover object that contains the secret message and it is called stego object. To extract a secret message from the stego object, the extracting algorithm works in reverse way than the embedding algorithm, the result is the secret information [23]. As in today s era, maximum amount of data are communicated through internet. For secure internet transaction, various kind of data hiding techniques have been developed by researcher. Steganography in fractal s can be considered much more secure [8].Fractal s are generated by iterative functions, which can be encoded and decoded using an initial value. So, using fractal s, the steganography operation becomes efficient and have less distortion. Using an initial value, the original secret data can also be recovered without any visual loss. Mei-Yi Wu et al [17]introduced a novel iterative method of palette-based steganography that minimizes the RMS error between an original and its stego-. The method is based on a palette modification scheme, which can iteratively embed one message bit into each pixel in a palette-based. Shoko Imaizumi et al. [10] discussed an efficient Steganographic scheme for palette-based s that improves the maximum length of the embedded message and does not seriously degrade the quality. Mohamed L. Barakat et al. [22] focused on a novel encryption system based on diffusion and confusion processes in which the information is hidden inside the complex details of fractal s. Huaxiong Zhang et al. [9] gave a method of steganography based on fractal s is presented in which, use of properties of creation of fractal s, information are embedded during creating fractal s by secret information and initial parameters. In this paper, we proposed an algorithm on steganography using fractal s.the rest of the paper is organized as follows. In Section II, we present the Steganography algorithm based on Mandelbrot set fractal s, while Section III describes simulation results and

2 Section IV describes performance analysis. Finally, conclusion has been drawn. II. STEGANOGRAPHY ALGORITHM BASED ON MANDELBROT SET FRACTAL IMAGES In the proposed Image steganography algorithm, the secret is embedded on the fractal cover. Fractal s are more secure because of its characteristics such as forms and colors that characterized its beauty and consistency. Fractal s have high capacity to embed data without any distortion and also its dependence on initial input (which is a secret key) so that no intruder can generate the same fractal without knowing the secret key. In generation process of the fractal s, the secret information are embedded into the fractal in order to obtain the stego-. A. Image generation In the process of generating the cover (Mandelbrot set), true colors are used, which is known as RGB plane and is represented as a matrix of 3D (M N 3). E very pixel is a combination of red, green, and blue colors. The RGB plane is best suited to hide secret information because it contains a large amount of information that provides space to hide such secret information. It also considered as a technique to store a large number of bits in each channel (R, G, B) of the pixel. The Mandelbrot set, named after Benoit Mandelbrot, is a fractal which lie on complex plane. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet, the process of generating it, is based on an extremely simple equation involving complex numbers. The iterated function systems(ifs) are commonly used to generate fractals. It's the set of all complex numbers z for which the sequence is defined by the equation, = +, = 1, 2, (1) Steps to generate Mandelbrot fractal: Step 1: The complex vector is generated by making the real component as x- values and imaginary component as y- value. Step 2: Iterate the function using the equation (1). Step 3: Compute and sum the magnitude of iteratively till the magnitude is lessthan threshold. Step 4: Generate the fractal of the resultant magnitude obtained in step 3, using color determined by the number of iterations. By changing the threshold values and iterating equation (1) for sufficient number of iterations (Table I), we get various fractal s as shown in Fig TABLE I. PARAMETER FOR FRACTAL IMAGE GENERATION Iteration Threshold A B C D E Fig. 2.1 Generation of fractal for the parameter A, B, C, D and E (as per table I). B. Information embedding Fig. 2.2 shows the embedding process to embed the secret into the stego-. The process of embedding is executed in each channel (Red, Green, and Blue) of the cover which is generated by fractal as discussed in section II (A). The fractal and the secret are separatedinto three channels (Red, Green, and Blue) separately. Now extract the bit-plane of secret in red, green and blue channel using bit plane slicing technique. The first bit-plane is the least significant one (LSB) and most of the time is hardly related to the main shapes of the picture. On the other hand, the last bitplane is the most significant one (MSB) and contains the main lines and edges of the picture. Secret Generate fractal Initial parameter Divide into Red, Green and Blue plane Fig. 2.2 embedding process/information embedding model Now, we put the significant message bit-planes of red plane of secret into the cover of red plane, green plane of secret into the cover of green plane and blue plane of secret into the cover of green plane. After embedding the bits into the cover, we reconstruct the cover. This modified is called as Stego- that contains the secret. C. Information extracting Divide into Red, Green and Blue plane Bit-planes extraction Stego - Fig. 2.3 shows the extraction process to extract the secret from the stego-. The initial parameter is used to determine the form of fractal, each value of

3 initial parameter gives its own sets of fractal, so the first step undertaken by the recipient for the purpose of extracting secret information is interested in creating a fractal same as the encoding process and then begin the process of extraction. Secret Generate fractal Divide into Red, Green and Blue plane Divide into Red, Green and Blue plane Extract the secret using bit-plane slicing technique Secret using proposed algorithm. Finally, after embedding process, the stego- will be generated. In the case of color each pixel is composed of RGB values and each of these colors requires 8-bit for its representation. [R (8 bits), G (8 bits), B (8 bi ts)]. In this case, the process of embedding secret is similar to the process of embedding in gray scale but the size of the cover is doubled to accommodate all the bits of the secret s for embedding. Now, we tested the algorithm for various gray scale and color s for embedding process and the results are as shown in the Fig (a) (b) (c) Initial parameter Fig 2.3 extraction process/information extracting model Extract Red, Green and Blue plane from fractal as well as Extract Red, Green and Blue plane from stego-, then subtract the stego- from the created fractal. After obtaining the subtracted, perform bit plane slicing technique to extract the bit of secret. Use the embedding sequence to extract the bit strings from each plane of the. Combine all these bit-planes into one to find the recovered secrete. III. SIMULATION RESULTS In this study, the experimental setup consists of Windows 7 professional operating system, Intel(R) Core(TM) i7-3770m CPU, 3.40 GHz Processor Laptop-PCs having 3.33 gigabytes of memory (RAM) and 32 -bit operating system. The optimization algorithm was implemented by the MATLAB, The Language of Technical Computing using version of (R2012a) licensed by The Math works Inc. The proposed algorithm is tested for both; the gray scale and the color s of size 384x512. The quality of the output stego- is measured through various parameters such as PSNR, MSE, Histogram, and NC etc. A. Encoding The proposed algorithm is implemented in MATLABversion of (R2012a) for computer simulations for various input s. The cover is generated by iterated function and its size is pixels. For experiment purpose the size of the cover and the secret would be same for gray scale s and that of doubled for the color s. The proposed algorithm is simulated for various s of size pixels. The cover which is generated by fractal is of size pixels, which is resized to the size of secret ( pixels) for embedding process for the gray scale. Now, secret is embedded into the cover of cameraman (Img1) Image of bus (Img2) Image of ADIT entrance (Img3) Image of berry (Img4) Image of leaf (Img5)

4 Image of fruits (Img6) Fig. 3.1 Output of embedding process ((a) cover (b) secret (c) stego-) B. Decoding During extraction process, each color plane will be used for bit plane decoding than decoded bits will be used for generate the secret. After extraction algorithm on stego-, the original secret and extracted secret were found similar. IV. PERFORMANCE ANALYSIS Image quality metrics that are used to measure Steganographic s work on a comparison between the original bits with the Steganographic bits, in order to test the difference between both s, The most appropriate metrics for this purpose are: Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE) and RGB Histogram. the proposed scheme is tested over different cover s and secret data and the results demonstrated its effectiveness and robustness, As the value of (PSNR) reached to (45), and the value of (MSE) approximately (0) and NC nearly equal to 1; as well as the scale of RGB Histogram did not show any difference, as shown in Fig A. Histogram analysis Fig. 4.1Histogram analysis Fig. 4.1clearly shows that the proposed steganography algorithm is suitable to use forsteganography purpose, because histogram analysis represents that the distribution of pixels in the secret and stego- is nearlysame. So, visually it is not possible to identify the existence of the embedded message in the cover. B. Peak Signal to Noise Ratio, MSE and NC Analysis The PSNR of a given color component is the ratio of the mean square difference of the component for the two s to the maximum mean square difference that can exist between any two s. It is expressed as a decibel value. = ( ) (2) The mean-squared error (MSE) between cover s and stego-s are defined by = 1 [ (, ) (, )] (3) Where, M=number of rows N=number of columns The NC is one of the best known methods that evaluate the degree of closeness between the cover and the stego. The NC can be calculated using the following equation = [ (, ) (, )] (, ) Where, M=number of rows of N=number of columns (4)

5 The PSNR value approaches to infinity as the MSE approaches to zero; this shows that a higher PSNR value provides a higher quality. Our proposed work also analyze Peak-Signal-to-Noise- Ratio (PSNR), MSE and NC between stego-s and original cover s (using equation (2), (3), and (4))f or various gray scale and color s as shown in Table II. TABLE II. PEAK SIGNAL TO NOISE RATIO AND MSE Sr no. Secret Image Proposed Technique Res: (384x512) PSNR MSE NC 1 Img Img Img Img Img Img Img Img Img Img Img Img Img Img Img From Table II, it can be seen that the PSNR values after steganography are very high, which indicates that the amount of noise introduced in the as a result of steganography is very less. The greater PSNR value (>30dB) shows the better quality recovered. V. CONCLUSION In the proposed algorithm, the fractal s are chosen as the carrier of information hiding due to its characteristics of the ease of generation,sensitive dependence on their initial conditions, self-similarity and details at every scale. The algorithm is tested for different cover s and secret s and it is observed thatthere is enhancement in results of the quality metrics. The simulation results shows imperceptibility and un-detectability in stego-, as the value of PSNR reached upto 45, and the value of MSE is vary between the range of 0.04 to 3, as well as the value of NC reached upto andthe scale (RGB Histogram ) showsvery minor difference. ACKNOWLEDGMENT This work is supported by GUJCOST minor research project grant. Authors thank to Dr. R K Jain (Principal) and Dr.V K Thakar (Head of EC Department) of A. D. Patel Institute of Technology, New V.V. Nagar for their constant motivation, support and encouragement. 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