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Volume 5 Issue 10 October, 2017

Nidhi Jadhav, Khushboo Sawant, vol 5 issue 10, pp 24-30 ,October 2017 Page 24

Image Steganography Based on Pixel Addition and Discrete Cosine Transform (DCT)

Abstract:

With the advent of digital technology, digital images have gained unprecedented importance. Digital images are being used in medicine, telecommunications, defence etc.

Therefore a need of securing the images from unauthorized users and adversaries has emerged as a serious challenge. Image encryption has been one of the most common tools for assuring the security of confidential image data. Although encryption mechanisms secure images from attackers, still there always remains a threat of the encryption mechanism being broken. Therefore Steganography is one of the sought after technique which evades the attacker from recognizing a confidential image under a normal cover image. This paper proposes image steganograpy using discrete cosine transform (DCT) and random pixel injection. Also image compression has been achieved using the Set Partitioning in Hierarchical Trees (SPIHT) algorithm. It has been shown that the proposed technique achieves better performance compared to previously existing techniques.

Keywords: Image Processing, Image Steganography, Image Compression, Discrete Cosine Transform (DCT), Peak Signal to Noise Ratio (PSNR), Set Partitioning in Hierarchical Trees (SPIHT) Mean Square Error (MSE).

I.

INTRODUCTION:

An image may be defined as a two dimensional function, I= f(x, y) where x and y are spatial co- ordinates i.e. co-ordinates corresponding to space or location.[1] The function I essentially contains two basic pieces of information, one being the intensity at a point also called the gray scale value and the R-G-B value which tells about the colour or frequency aspect of the image. If it happens so that the values of (x, y), and the gray level [f(x, y)] are finite and discrete values, then such an image is called a digital image.

If we process the digital images using a digital computer, then this process is called digital image processing. Digital images comprise of finite number of elements each of which has a finite location and value. These elements are called picture elements, image elements, or pixels. Digital images have immense applications ranging from education, defence and military, banking, electronic vision, photography to video filming, medical etc. But during the capturing, storage and retrieval, transmission and receiving of images, they are affected by various types of noise.

This process degrades the quality of the images and the degradation can be nominal to severe depending upon the degradation phenomena.

Introduction to Steganography:

Steganography is an art of conveying secret messages and secret images through cover images in a secret way that only the receiver knows the existence of a message.

Steganography Vs Cryptography:

Cryptography is the practice of „scrambling‟ messages so that even if detected, they are very difficult to decipher. The purpose of Steganography is to conceal the message such that the very existence of the hidden message is concealed. Steganography provides another layer of protection on the secret message, which will be embedded in another media such that the

transmitted data is meaningful and innocuous to everyone.

II.

Fundamental requirements for a Steganography

•Imperceptibility: Means that the embedded messages should not be discernible to the human eye.

•Embedding Capacity: Means the capacity of embedding the secret image.

Nidhi Jadhav

M.Tech Scholar, CSE JDCT,Indore nidhijadhavhi@gmail.com

Khushboo Sawant

Assistant Professor, CSE JDCT,Indore sawantkhushboo@gmail.com

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•Security: Means that the Stegano image should be fool proof and robust.

Any image Steganography model should satisfy the following conditions:

1. It should be able to secure various types of images viz. Photographic Images, Radar Images, Biomedical Images etc.

2. It should render a high amount of randomness to the encrypted data making it infeasible for the adversaries to decrypt by brute force.

3. The key used in the algorithm should change with the state of the images so as to ensure higher levels of security.

4. Finally, it should not be too complex to implement on hardware.

III.

The Discrete Cosine Transform (DCT)

The DCT is defined as:

𝑦 𝑘 = 𝑤(𝑘) 𝑥 𝑛 cos⁡(𝜋 2𝑛 − 1 𝑘 − 1

2𝑁 )

𝑁

𝑖=1

Here

𝑤 𝑘 = 1/ 𝑁 for k=1 and 𝑤 𝑘 = 2/𝑁 for 2< k<N

Some fundamental properties of the DCT are:

The DCT helps separate the image into parts (or spectral sub-bands) of differing importance, with respect to the image's visual quality. The important advantages of DCT are:

DCT is a real transform.

DCT de-correlating performance is very good.

DCT is reversible (with Inverse DCT).

DCT is a separable transform.

DCT has a fast implementation (similar to FFT) The main benefit that we want to derive out of the Discrete Cosine Transform is the capability to reduce the similarity (correlation) among pixels of the steganographic image. It will make tack by brute force extremely difficult or infeasible. Pixel correlation can be reduced using the separation of image pixels into different frequency bands and then re arranging pixels which show high pixel similarity. A graphical illustration ensues.

Fig.1 Graphical Illustration of DCT

IV.

Proposed Methodology

A. Embedding Algorithm:

 Select the original image and cover image.

 Apply DCT to both images.

 Break both the images into different frequency sub bands after breaking the image into 8X8 blocks

 Obtain the DCT coefficient matrix of both images

 Since DCT coefficients < FFT coefficients, therefore DCT is a faster technique

 DCT coefficients are rounded off so that since it requires more time and space complexity to store and operate upon fractional values

 Embed the DCT coefficient values of Original Image into Cover Image

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 Obtain a Stage One Stegno Image B. Pixel Injection method:-

 Generate a random sequence of Pixels.

 Embed the random pixel values into the Stage One Stegno Image.

 The above step generates Stage Two Stegno Image

 The random pixel injection does not allow the attacker to get back the original image even if he is able to crack the pixel imbedding function of Stage One Stegno Image

 Compress image by removing approximate co efficient from the DCT matrix

C. Extracting the Original Image from the Stage Two Stegno Image

 Remove the random pixels injected into Stage Two Stegno Image

 Calculate the Inverse Discrete Cosine Transform (IDCT) of the above image.

 Calculate the Mean Square Error(MSE) and Peak Signal to Noise Ratio(PSNR)

 Since during the Image Processing Stage, DCT is used and it quantizes the pixel values, therefore some differences arise in the extracted image when compared to the Original Image.

 This is an inherent (inbuilt) limitation of any Image Processing mathematical model or tool like DCT or Wavelet Transform or Fast Fourier Transform.

 The lesser the difference between the Original Image and the Extracted Image, the lesser will be the value of error or mean square error (MSE)

 Peak signal to Noise Ratio (PSNR) tells us about the ration of Original Image Values and the unwanted changes in the image (Noise) i.e. S/N. The lower the value of errors or Noise (N) , the higher the value of PSNR.

 Our aim is to obtain lower values of MSE and Higher values of PSNR compared to previous works.

Fig.2 Flowchart of Proposed Work V. The SPIHT Algorithm

The SPIHT method is not a simple extension of traditional methods for image compression, and represents an important advance in the field. The SPIHT (set partitioning in hierarchical trees) is an efficient image coding method using the wavelet transform. Recently, image-coding using the wavelet

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transform has attracted great attention. Among the

many coding algorithms, the embedded zero tree wavelet coding by Shapiro and its improved version, the set partitioning in hierarchical trees (SPIHT) by Said and Pearlman have been very successful.

Compared with JPEG - the current standard for still image compression, the EZW and the SPIHT are more efficient and reduce the blocking artefact.

The method deserves special attention because it provides the following:

1. Good image quality, high PSNR, especially for colour images;

2. It is optimized for progressive image transmission;

3. Produces a fully embedded coded file;

4. Simple quantization algorithm;

5. Can be used for lossless compression;

6. Can code to exact bit rate or distortion;

7. Fast coding/decoding (nearly symmetric);

8. Has wide applications, completely adaptive;

9. Efficient combination with error protection.

Each of these properties is discussed below. Note that different compression methods were developed specifically to achieve at least one of those objectives.

What makes SPIHT really outstanding is that it yields all those qualities simultaneously.

Hierarchical Tree

In general, a wavelet decomposed image typically has non-uniform distribution of energy within and across sub bands. This motivates us to partition each sub band into different regions depending on their significance and then assign these regions with different quantization levels. The proposed coding algorithm is based on the set partitioning in hierarchical trees (SPIHT) algorithm, which is an elegant bit-plane encoding method that generates M embedded bit sequence through M stages of successive quantization.

Let s0, s1, …, sM-1 denote the encoder‟s output bit sequence of each stage. These bit sequences are ordered in such a way that s0 consists of the most significant bit, s1 consists of the next most significant bit, and so on. This process is iterated to achieve compression of the image. The significant steps are mentioned as:

 O(i, j): set of coordinates of all offspring of node (i, j);

 D(i, j): set of coordinates of all descendants of the node (i, j);

 H: set of coordinates of all spatial orientation tree roots (nodes in the highest pyramid level);

 L(i, j)=D(i, j)-O(i, j).

Thus, except at the highest and lowest levels, we have O(i, j)={(2i, 2j), (2i, 2j+1), (2i+1, 2j), (2i+1, 2j+1)}.

Define the following function.

SN(τ)= {1 for max{Ci,j}>2n

= {0, otherwise

Sn(τ) indicate the significance of a set of coordinates ,where T(n) is the preset significant threshold used in the nth stage. A detailed description of the SPIHT coding algorithm is given as follows.

Initially(0) is set to be 2M-1 , where M is selected such that the largest coefficient magnitude, say cmax, satisfies 2M-1≤Cmax<2M . The encoding is progressive in coefficient magnitude for successively using a sequence of thresholds T(n)=2(M-1)-n,n=0.1...,M-1.

Since the thresholds are a power of two, the encoding method can be regarded as "bit-plane" encoding of the wavelet coefficients. At stage n, all coefficients with magnitudes between T(n) and 2T(n) are identified as

"significant," and their positions and sign bits are encoded. This process is called a sorting pass. Then, every coefficient with magnitude at least 2T(n) is

"refined" by encoding the nth most significant bit. This is called a refinement pass. The encoding of significant coefficient position and the scanning of the significant coefficients for refinement are efficiently accomplished through using the following three lists:

the list of significant pixels (LSP), the list of insignificant pixels (LIP), and the list of insignificant set (LIS). Each entry in the LIP and LSP represents an individual pixel which is identified by coordinates (i, j). While in the LIS, each entry represents either the set D(i j) or L(i, j). An LIS entry is regarded as of type A if it represents D(i, j) and of type B if it represents L(i, j).

VI.

PERFORMANCE INDICES

Mean Square Error (MSE)

The MSE represents the cumulative squared error between the encoded and the original image. The effectiveness of the algorithm stands in minimizing the mean square error. If F(X, Y) is the original image, G(X, Y) is the corrupted image and I(X, Y) is the denoised image then MSE is given by

MSE=[Ʃ Ʃ {F(X,Y)-I(X,Y)}2]/MN Here M and N are the image indices

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A low of MSE indicates that the original and the

denoised image are close in characteristics.

Peak Signal Noise Ratio (PSNR)

PSNR represents a measure of the ratio between maximum powers of signal to the power of noise. We are trying to increasing the value of PSNR to the extent possible. PSNR is inversely proportional to the MSE;

its unit is in decibel (dB) and is formally defined by the following equation.

PSNR=10log10 (MN)2/MSE

A high value of PSNR indicates that the effect of noise has been mitigated.

Compression Ratio (CR)

This would mean that the compression of data is high and thus the data sixe reduces significantly. It should be noted though that excessive high values of compression ratio results in lower values of PSNR.

Bits per Pixel (BPP)

Low bits per pixel would imply that each picture element would need lesser bits to be represented on an average value. This depends on the compression- quantization mechanism of the compression algorithm chosen.

VII.

RESULTS

Fig.3 Secret Image

Fig.4 Cover Image

Fig.5 DCT of Image

Fig.6 Random Pixel Injection

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Fig.7 Comparative PSNR Analysis

Fig.8 Comparative RMSE Analysis

Fig.8 Comparative Throughput Analysis

Fig.9 Comparative Compression Ratio Analysis

Conclusion: From the previous discussions and results, it can be concluded that the proposed technique achieves effective image Steganography using a secret image and a Cover image. The proposed technique uses the Discrete Cosine Transform (DCT) for Steganography which is an effective steganographic tool. The algorithm uses random pixel injection which is injecting pixels with random values at random locations of the images.

At the receiving side, the random pixels are stripped off. The SPIHT algorithm has been used for further compression of the image. It has been shown that the proposed technique achieves high values of PSNR, CR, Throughput while achieving low values of RMSE.

References

[1] Nidaa AbdulMohsin Abbas, “Image encryption based on Independent Component Analysis and Arnold‟s Cat Map”,Elesvier ,2015.

[2] Reversibility improved data hiding in encrypted images, by Zang, Kede Ma, Yu Elsevier 2014.

[3] Maniccam S.S., Bourbakis N.G., “Lossless image compression and encryption using SCAN”, Pattern Recognition 34 (2001) 1229-1245 Springer 2014 [4] Acharya B, Patra S. K., Panda G., “A Novel Cryptosystem Using Matrix Transformation”, Proceedings of SPIT-IEEE Colloquium and

International Conference, Mumbai, India, Vol. 4, 92 IEEE 2014.

[5] Gautam A, Panwar M, Gupta P. R., “A New Image Encryption Approach Using Block Based Transformation Algorithm”, International Journal Of Advanced Engineering Sciences And Technologies, Vol No. 8, Issue No. 1, 090 – 096 2013

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Volume 5 Issue 10 October, 2017

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[6]C. H. Kim, “Improved Differential Fault Analysis

on AES Key Schedule”, IEEE Transactions on Information Forensics and Security, Vol. 7, No. 1, pp.

41-50, 2012.

[7] Zhang X, Feng G, Ren Y, and Qian Z. , “Scalable Coding of Encrypted Images”, IEEE Transactions On Image Processing, Vol. 21, No.6, June 2012

[8] Zhang X, “Lossy Compression and Iterative Reconstruction for Encrypted Image”, IEEE Transactions On Information Forensics And Security, Vol. 6, No. 1, March 2011

[9] Guo J M and Le T N, “Secret Communication Using JPEG Double Compression”, IEEE Signal Processing Letters, Vol. 17, No. 10, October 2010 [10]Kushwaha J, Roy B., “Secure Image Data by Double encryption”, International Journal of Computer Applications (0975 – 8887), Volume 5– No.10, August 2010

[11]Liu W, Zeng W, Dong L, and Yao Q, “Efficient Compression Of Encrypted Grayscale Images”, IEEE Transactions on Image Processing, Vol. 19, No. 4, April 2010

[12]Yicong Z., Panetta K, Agaian S, Senior Member,

“Image Encryption Using Binary Key- images”

,Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009

[13]F.Menichelli, R. Menicocci, M. Olivieri and Alessandro Trifiletti, “High Level Side Channel Modeling and Simulation for Security Critical Systems on Chips”, IEEE Transactions on Dependable and Secure Computing, Vol. 5, No. 3, pp. 164-175, 2008 [14]E. Bertino, N. Shang and S. S. Wagstaff, “An Efficient Time-Bound Hierarchical Key Management Scheme for Secure Broadcasting”, IEEE Transactions on Dependable and Secure Computing, Vol. 5, No. 2, pp. 65-70, 2008.

[15] Sudharsanan S, “Shared Key Encryption of JPEG Color Images”, IEEE Transactions On Consumer Electronics, Vol. 51, No. 4, November 2005

[16] Johnson M, Ishwar P, Prabhakaran V, Schonberg D, and Ramchandran K, “On Compressing Encrypted Data”, IEEE Transactions On Signal Processing, Vol.

52, No. 10, October 2004

[17] Bharat B. Madan, K. Goseva-Popstojanova, K.

Vaidyanathan and K.S. Trivedi, “A Method for Modeling and Quantifying the Security Attributes of Intrusion Tolerant Systems”, Journal of Performance Evaluation, Elsevier Science Publishers, Vol. 56, No.

1, pp. 167-186, 2004.

[18] C. P. Su, T. F. Lin, C. T. Huang and C. W. Wu,

“A High-Throughput Low Cost AES Processor”, IEEE Communications Magazine, Vol. 41, No. 12, pp. 86- 91, 2003.

[19] P Huang. K.C. Chang., C.P Chang. and T.M Tu.

“A novel image steganography method using tri-way pixel value differencing”. Journalof Multimedia, 3, 2008.

[20] Potdar V.and Chang E. “Gray level modification steganography for secret communication”. In IEEE International Conference on Industria Informatics., pages 355–368, Berlin, Germany, 2004.

[21] Osman, H.;Mahjoup, W. ; Nabih, A. ; Aly, G.M.

"JPEG encoder for low-cost FPGAs" Published in Computer Engineering & Systems, 2007.ICCES '07.

International Conference on 27-29 Nov. 2007.

References

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